# A User-Centered Investigation of Personal Music Tours

Giovanni Gabbolini  Insight Centre for Data Analytics, School of Computer
Science & ITUniversity College Cork, Ireland giovanni.gabbolini@insight-
centre.org 0000-0001-7914-9999 and  Derek Bridge  0000-0002-8720-3876 Insight
Centre for Data Analytics, School of Computer Science & ITUniversity College
Cork, Ireland<EMAIL_ADDRESS>
(2022; 2022)

###### Abstract.

Streaming services use recommender systems to surface the right music to
users. Playlists are a popular way to present music in a list-like fashion, as
a plain list of songs. An alternative are tours, where the songs alternate
with segues, which explain the connections between consecutive songs. Tours
address the user need of seeking background information about songs, and are
found to be superior to playlists, given the right user context. In this work,
we provide, for the first time, a user-centered evaluation of two tour-
generation algorithms ( and ) using semi-structured interviews. We assess the
algorithms, we discuss attributes of the tours that the algorithms produce, we
identify which attributes are desirable and which are not, and we enumerate
several possible improvements to the algorithms, along with practical
suggestions on how to implement the improvements. Our main findings are that
generates more likeable tours than , and that three important attributes of
tours are segue diversity, song arrangement and song familiarity. More
generally, we provide insights into how to present music to users, which could
inform the design of user-centered recommender systems.

music recommender systems, playlists, segues, user evaluation.

††copyright: rightsretained††journalyear: 2022††conference: Sixteenth ACM
Conference on Recommender Systems; September 18–23, 2022; Seattle,
USA††booktitle: Sixteenth ACM Conference on Recommender Systems (RecSys ’22),
September 18–23, 2022, Seattle, USA††price: xx.xx††doi:
xx.xxxx/xxxxxxx.xxxxxxx††isbn: xxx-x-xxxx-xxxx-x/xx/xx††journalyear:
2022††copyright: rightsretained††conference: Sixteenth ACM Conference on
Recommender Systems; September 18–23, 2022; Seattle, WA, USA††booktitle:
Sixteenth ACM Conference on Recommender Systems (RecSys ’22), September 18–23,
2022, Seattle, WA, USA††price: xx.xx††doi: xx.xxxx/xxxxxxx.xxxxxxx††isbn: xxx-
x-xxxx-xxxx-x/xx/xx††ccs: Information systems Recommender systems††ccs:
Computing methodologies Artificial intelligence

##  1\. Introduction

ptInterstellar Love by ThundercatPost Requisite by Flying LotusWisdom Eye by
Alice Coltrane (a)

ptInterstellar Love by Thundercat“Interstellar Love was produced by Flying
Lotus”Post Requisite by Flying Lotus“Flying Lotus is the grand-nephew of Alice
Coltrane”Wisdom Eye by Alice Coltrane (b)

ptPost Requisite by Flying Lotus“Flying Lotus is the grand-nephew of Alice
Contrane”Wisdom Eye by Alice Coltrane“Alice Coltrane has done Jazz, &
Thundercat has done Acid Jazz, a genre that derives from Jazz”Interstellar
Love by Thundercat (c)

Figure 1. A playlist of three songs (a), and two tours of three songs,
recommended by (b) and (c). Shaded boxes contain segues; clear boxes contain
songs.

Playlists are a popular feature of music streaming services. Users consume
playlists for 31% of their total listening time (Schedl et al., 2018).
Recommender systems are often used to surface the right playlists to users,
e.g. see (Bonnin and Jannach, 2014) for a review. Playlists present music in a
list-like fashion, as a plain list of songs, such as in Figure 1 (a). Past
research investigates how to present playlists best. For example, (Nakano et
al., 2016; Pohle et al., 2007) propose to arrange songs according to audio
similarity, such as beats per minute, and web-based similarity, such as
Wikipedia categories.

Playlists are limited in that they allow for little interaction with the user:
one song follows the other, from the first to the last. Such a concept is
suited for some occasions, such as passive listening, but is limiting in other
contexts. For example, (Lee et al., 2011) finds that unfamiliar music in
playlists should be explicitly connected to user background knowledge, so as
to keep user interest alive. And, (Lonsdale and North, 2011) finds that users
seek background information while listening to music in order to stay informed
and to build relationships with others.

An alternative to playlists are tours, where the songs alternate with segues,
short textual connections between songs, which explain the connection between
consecutive songs, as in Figures 1 (b) and (c). Tours resemble the popular
format of radio shows, where a presenter speaks and takes the audience from
one song to another. As such, tours augment music with background information,
and help overcome the above limitations of playlists. For example, (Behrooz et
al., 2019) finds that tours offer a better user experience than playlists,
given the right listening context.

Tour recommendation can be framed as a multi-objective problem (Rodriguez et
al., 2012), as algorithms should surface the right songs, the right segues,
and the right combination of the two. Existing algorithms tackle a simpler
problem, in which the right songs are assumed to be known, and the task is to
recommend segues, and an arrangement of the songs. We are aware of only two
works on tours: (Behrooz et al., 2019) and (Gabbolini and Bridge, 2021c). The
authors of (Behrooz et al., 2019) simplify the problem even further, as they
assume they have the right arrangement (ordering) of the songs. They recommend
segues only, by finding the shortest path in a graph where the nodes are
songs, the edges are segues, and the edges’ weights are assigned according to
segue importance (defined manually by the authors) and segue diversity. The
authors of (Gabbolini and Bridge, 2021c) make a step forward, as they
recommend both a song arrangement and the segues, so as to maximise the
interestingness of the segues in the tour.

The two existing works on tours suffer from a number of limitations. In
(Behrooz et al., 2019), the authors set up semi-structured interviews to
evaluate their algorithm, and the concept of tours in general. However, their
study is limited in that they do not investigate three important topics for
implementing a functioning tour recommender: (1) what is a good segue
arrangement; (2) what is a good song arrangement; (3) what are the guidelines
for distinguishing good from bad segues; and (4) what topics should segues
cover. The authors of (Gabbolini and Bridge, 2021c) overcome limitation (3) by
employing an interestingness measure, according to which segues can be scored
for how good they are. The interestingness measure they use is validated in
(Gabbolini and Bridge, 2021a), where it is found to positively correlate with
human perceptions of segue quality. Also, the authors of (Gabbolini and
Bridge, 2021c) partially overcome limitation (2), as they look to arrange
songs so that the average interestingness of the segues in the tour is as high
as possible. However, they do not discuss whether their arrangement strategy
is a good one, especially from the user perspective. Finally, (1) and (4) are
left totally unsolved by (Gabbolini and Bridge, 2021c). In fact, (Gabbolini
and Bridge, 2021c) does not make any consideration about what is a good segue
arrangement, and they have segues covering different topics, but they do not
validate these topics. Finally, both (Behrooz et al., 2019) and (Gabbolini and
Bridge, 2021c) are limited in that the songs themselves are not chosen by a
recommender system, but assumed to be given, which would not be the case for a
functioning tour recommender.

Here, we consider two algorithms proposed in (Gabbolini and Bridge, 2021c),
and , and we set up semi-structured interviews, where interviewees judge tours
recommended by the two algorithms. We omit (Gabbolini and Bridge, 2021c)’s
third algorithm, Hill-Climbing, because (Gabbolini and Bridge, 2021c) found it
to produce tours mostly equivalent to those produced by , especially for small
inputs. We help to overcome the limitations of current work on tours by
investigating: what is a good segue arrangement; what is a good song
arrangement; what topics should segues cover; and how to recommend the right
music in tours. and are also evaluated in (Gabbolini and Bridge, 2021c) via
off-line experiments, and are found to differ in their total segue
interestingness, and in the distribution of interestingness throughout the
tour. With the interviews, we contribute to the first user-centered evaluation
of the two algorithms. We are interested in checking the results of the off-
line experiments, in assessing the overall quality of the tours recommended by
the two algorithms, and the interestingness of their segues, all from the user
perspective. Finally, we are interested in assessing whether users value the
concept of tours in general, a fundamental issue already addressed by (Behrooz
et al., 2019), that we investigate further.

Summing up, we aim to fulfil five goals. Goal (1) is finding attributes of the
tours. Attributes of interest could be: perceived interestingness distribution
within tours; segue diversity; segue narrativity, defined as the quality that
sequences of segues in a tour present a narrative with a coherent text; and
song arrangement. Goal (2) is identifying what attributes of tours are
desirable and not desirable. Goal (3) is assessing the quality of tours, in
terms of segue interestingness and overall tour quality. Goal (4) is assessing
whether users value the concept of tours in general. Goal (5) is identifying
possible improvements to tours. In summary, we formulate the following
research questions:

RQ1::

What are the attributes of the tours?

RQ2::

What attributes of tours are good/bad?

RQ3::

Which algorithm recommends better tours, and why?

RQ4::

How valuable is the concept of tours in general?

RQ5::

What are possible improvements to tours?

Our work adds actionable knowledge, which can inform functional tour
recommender systems. More generally, we provide insights into how to present
music to users, which could inform the design of user-centered music
recommenders.

##  2\. Related work

Music recommendation is a popular research topic with important real-world
applications, such as in streaming services, where recommender systems are
used to surface the right music to users. The music recommendation problem has
unique characteristics compared to other content domains, such as books or
movies (Schedl et al., 2015). For example, it is common to recommend lists of
songs to users, or playlists, while it is less common to recommend lists of
movies or books. As such, the playlist recommendation problem is a well-
studied one. Bonnin and Jannach, for example, provide a review of algorithms
for playlist recommendation (Bonnin and Jannach, 2014). Other research
investigates more user-centered aspects. For example, (Nakano et al., 2016;
Pohle et al., 2007) propose to arrange songs according to audio similarity,
such as beats per minute, and web-based similarity, such as Wikipedia
categories, while (Lee et al., 2011) studies user perception of the similarity
among the songs in playlists, and gives insights on the ideal level of
similarity, so as to inform the design of playlist recommenders.

A related task to playlist recommendation is (automatic) playlist continuation
(APC), which consists of automatically adding one or more tracks to a playlist
in a way that fits the same target characteristics of the original playlist
(Schedl et al., 2018). In the “RecSys Challenge 2018”, participants were asked
to implement an APC system able to continue real user playlists from the
Spotify music streaming service (Chen et al., 2018). The challenge represents
a landmark in APC research, and sets the state of the art to that date. The
most competitive algorithms made use of simple Collaborative Filtering (CF)
recommenders (Zamani et al., 2019), such as Matrix Factorisation (Koren et
al., 2009) and k-Nearest Neighbors (Sarwar et al., 2001) algorithms. More
recently, deep learning APC algorithms were also proposed, e.g. see (Tran et
al., 2019). Our work studies an alternative to playlists: tours. In tours, the
songs alternate with segues, which explain the connection between consecutive
songs.

Segues were first introduced in (Behrooz et al., 2019), and defined in
(Gabbolini and Bridge, 2021a) as “short texts that connect two items”. Both
(Behrooz et al., 2019) and (Gabbolini and Bridge, 2021a) focus on the case
where the items connected by the segues are songs. In (Behrooz et al., 2019),
the authors propose a tour recommendation algorithm where segues are chosen
for their diversity, and importance, defined manually by the authors. In
(Gabbolini and Bridge, 2021a), the authors overcome the manual scoring, as
they propose an interestingness measure, according to which segues can be
scored for how interesting they are. Interestingness is based on statistical
information, e.g. the more rare a segue, the more interesting, and e.g. the
shorter the segue, the more interesting. The authors validate their
interestingness concept in a user trial, and find that it is positively
correlated with human perception of segue quality. In follow-up work
(Gabbolini and Bridge, 2021c), the same authors utilise the interestingness
measure to formulate three tour recommendation algorithms, which they evaluate
via offline experiments. Our work in this paper builds on (Gabbolini and
Bridge, 2021c), as we provide the first user-centered evaluation of the
algorithms that they propose. Also, we investigate the user perspective of
tours, and we provide practical and actionable knowledge which can inform the
development of functional tour recommender systems.

##  3\. Method

We employ two tour recommendation algorithms proposed in (Gabbolini and
Bridge, 2021c), and , without any alteration. The algorithms assume that the
set of songs to be included in the tour are given a priori, and the algorithms
must recommend segues and an arrangement of songs, so as to generate a tour of
the kind shown in Figures 1 (b) and (c).

Given a ‘small’ set of songs, e.g. several order of magnitudes smaller than
the whole catalogue of songs, the goal of the algorithms is to find a
permutation of the songs, and a list of segues between the songs, maximising
the average $interestingness$ of the segues, the $utility$. The algorithms
assume the existence of two functions: $segues$ and $interestingness$. We
represent songs and information about songs in a knowledge graph; the $segues$
function finds paths in the graph between the two songs of interest, and
translates the paths to texts. As $interestingness$, we use the function
proposed originally in (Gabbolini and Bridge, 2021a), which is based on the
infrequency and conciseness of knowledge graph paths before they are
translated to segues. The graph contains a variety of information, such as:
musical genres; locations, e.g. where an artist was born; dates, e.g. when an
artist was born; record labels, e.g. who published a song; and relationships
between artists, between songs, and between artists and songs. The knowledge
graph is built from data harvested from two resources:
Musicbrainz111https://musicbrainz.org and Wikidata222https://www.wikidata.org.
In total, the knowledge graph features 30 distinct nodes types, and 205
distinct edge types. As such, segues cover a variety of different topics.
Examples of segues recommended by the algorithms are in the the shaded boxes
in Figures 1 (b) and (c). We provide a complete description of the nodes and
edges that build up the knowledge graph in the additional
materials333https://doi.org/10.5281/zenodo.6817643 and the implementation of
the algorithms are freely
available444https://github.com/GiovanniGabbolini/play-it-again-sam.

is a heuristic algorithm, while always recommends the tour with highest
$utility$. In particular, builds a solution iteratively, by choosing the next
song to be the one with the segue of highest $interestingness$, while reduces
the recommendation problem to a Traveling Salesman Problem, or TSP, and solves
it optimally.

##  4\. Experiment

We set-up a semi-structured interview experimental protocol, as it suits our
need to answer both open and closed questions in the same sitting (Adams et
al., 2015). For example, one closed question is which of the tours produced by
the two algorithms of Section 3 is preferred (part of RQ3), while one open
question is what can be improved in tours (RQ5).

The interview protocol follows a within-subject design, each participant is
subject to both treatments ( and ), in order to elicit an explicit comparison
of the algorithms. recommend tours which are different from those recommended
by . For example, the first segue in tours by tends to be more interesting
than the last, while in tours by the first and last segues tend to be equally
interesting (Gabbolini and Bridge, 2021c).

The conversation revolves around example tours recommended by the algorithms.
Some days ahead of the interview, we ask participants to send us a list of ten
songs they are familiar with, making sure they are all from different artists.
We set the number of songs to ten so as to reduce fatigue effects. We run the
algorithms on the ten songs, and we prepare a pdf textual file with a visual
representation of the resulting tours, side by side, similar to Figure 1 (b)
and (c). We randomise the order, so that sometimes is on the left hand-side
and is on the right hand-side, and vice versa. We also prepare an mp3 audio
file of the tour, comprising 15-second song previews, and segues that are read
by a Text-to-Speech (TTS) engine, for a total duration of approximately seven
minutes. Songs previews are from the Spotify API
555https://developer.spotify.com/documentation/web-api/libraries/, and the TTS
engine is the Google Text-to-Speech engine666https://pypi.org/project/gTTS/.
We use songs previews rather than entire songs because previews are freely
available. The first tour in the mp3 corresponds to the one that the
participant will see on the left in the pdf, and the second tour will be the
one on the right in the pdf. Both the mp3 and the pdf files are used during
the interview to support the conversation. Algorithm names are excluded from
both the pdf and mp3 files. A sample pdf file and mp3 file used during an
interview are in the additional materials.

This interview study is approved by our organisation’s ethics committee and it
is conducted one-to-one by an author (the interviewer) and a participant (the
interviewee) via Zoom.

###  4.1. Interviewees

We recruit interviewees via a student mailing list within our university in
Ireland. We make sure that the interviewee’s first language is English, so
that they can properly understand the segues. We ended up with 16
interviewees, who we will refer to as $i_{1}$ to $i_{16}$. One interviewee is
a graduate, while the other 15 are currently students. Among them, four are
undergraduates and 11 are postgraduate students. The interviewees have/seek
degrees in a range of disciplines: arts, psychology, medicine, geography,
computer science, history, music, social sciences, food sciences and human-
computer interaction. Also, 15 out of 16 interviewees are users of music
streaming services. We do not collect other demographic information, as we
considered it not essential for the scope of the study.

###  4.2. Interview guide

At the beginning of the interview, the interviewee listens to the mp3 version
of their two tours, and views the pdf. Both the interviewer and the
interviewee can hear the mp3 and both can see the pdf. The pdf remains visible
to both, until the end of the interview. Once the mp3 is over, we ask
questions aimed at answering the RQs of Section 1.

To answer RQ1-2, we ask the interviewee to identify different attributes of
the tours. We start with two open questions about what the interviewee likes
and does not like about the tours, and we continue with other open questions
probing for specific attributes of tours, such as distribution of segue
interestingness throughout the tour (“is the first segue more interesting than
the last?”, and “does the interestingness of segues, from first to last,
increase, decrease, stay equal, or something in the middle?”), segue
diversity, segue narrativity (“are segues linked together to form a narrative,
or are they independent pieces of text?”), segue top-bottom bias (“is the
first segue more interesting than the last?”) and song arrangement. Then, we
ask the interviewer to assess each tour with respect to these attributes, and
eventually express whether that attribute is important for the tours. To
answer RQ3, we ask interviewees to assess the quality of the tours according
to two dimensions: the interestingness of the segues and the overall tour
quality. In particular, we ask interviewees to compare tours recommended by
and tours recommended by , according to the two dimensions. To answer RQ4, it
is necessary to take extra-care, as the interviewee might assume that tours
are the work of the interviewer, and may tend to provide a positive concept
evaluation accordingly. One strategy to relieve the pressure from the
interviewee is showing non-judgemental acceptance, as suggested in (Adams et
al., 2015). Therefore, to answer RQ4, the interviewer asks “People have mixed
opinions on whether they would welcome a tour of their music or not. How do
you see this issue?”. To answer RQ5, the interviewer starts with two open
questions about what the interviewee would like and wouldn’t like to see in
tours, and continues with open questions probing whether tours should feature
non-familiar music or familiar music. We provide the full interview guide text
in the additional materials.

##  5\. Results

Our interviews produce a wealth of material: 11 hours of videos 42 minutes per
interviewee, on average. Interviews are manually transcribed by one of the
authors, and we end up with a corpus of 44-thousand transcribed words.

We conduct a thematic analysis of our data to identify important ideas and
themes from our interviews. Thematic analysis is used for many kinds of
qualitative analysis work in human-computer interaction (HCI), e.g. (Weisz et
al., 2021). We follow the process described by Braun and Clarke (Braun and
Clarke, 2006) in which researchers familiarize themselves with the data, then
generate codes and group them to identify higher-level themes. Each phase of
the analysis is conducted by one author independently, and validated among the
authors. We identify four main themes, “tour attributes”, “tour quality”,
“concept evaluation” and “tour improvements”. The first theme addresses RQ1-2,
the second theme addresses RQ3, the third theme addresses RQ4, and the fourth
theme addresses RQ5. Every theme is covered in one Section below. Each theme
has a number of sub-themes, covered in the subsections.

###  5.1. Tour attributes

We ask interviewees to identify different attributes of the tours, to assess
the tours with respect to each attribute, and eventually express whether that
attribute is important for the tours, as we explained in Section 4.2. Each
subsection below accounts for a different attribute of tours, while Table 1
shows how the tours recommended by the algorithms compare according to the
attributes.

Table 1. Tours comparison according to several attributes (rows one to four) and overall quality (rows five and six). Columns two to five indicate how many interviewees say that their tour features the attribute more than their tour ( $>$ ), less than ( $<$ ), approximately the same as ( $\simeq$ ), and the number of missing answers (N/A). The total number of interviewees is 16. |  $>$ |  $<$ |  $\simeq$ | N/A
---|---|---|---|---
Segue top-bottom bias | 7 | 0 | 0 | 9
Segue diversity | 9 | 1 | 4 | 2
Segue narrativity | 0 | 6 | 4 | 6
Song arrangement | 5 | 6 | 1 | 4
Segue interestingness | 9 | 5 | 2 | 0
Tour quality | 9 | 5 | 1 | 1

####  5.1.1. Segue top-bottom bias

Many interviewees mention that the first segue in a tour is more interesting
than the last segue, which is a phenomenon we refer to as top-bottom bias.
Among the 16 interviewees, 14 find that exhibits top-bottom bias, as we might
expect. In , the trend is less clear, as we might also expect: seven
interviewees find top-bottom bias, seven do not, and two interviewees cannot
decide. In total, seven interviewees say that the top-bottom bias is stronger
in than in and the rest do not offer an opinion. The results corroborate the
offline results in (Gabbolini and Bridge, 2021c), where is found to have top-
bottom bias, and is not.

(Gabbolini and Bridge, 2021c) also investigates how the interestingness of
segues varies throughout the tour, referring to this as the outline, finding
that in the outline is falling and in it is not falling. In our study here,
the outline of is judged to be falling by six interviewees, bumpy by six,
pyramidical by two, and flat by two. The outline of is judged rising by five
interviewees, falling by four, flat by three, bumpy by two, pyramidical by
one, and in one case we do not have an answer. So, the results corroborate
only partially those in (Gabbolini and Bridge, 2021c), probably because the
$interestingness$ function used in (Gabbolini and Bridge, 2021c) to infer the
outlines, and in the work at hand, only partially corresponds with what humans
judge to be interesting, as we detail in Section 5.2.1.

####  5.1.2. Segue diversity

The majority of the interviewees (14 out of 16) mention that the diversity of
the segues in the tours, or segue diversity for short, is an important
attribute to have. (Notice that this attribute concerns the diversity of the
segues, not of the songs.) Many interviewees mention that tours with low segue
diversity would not be nice to listen to. For example, $i_{8}$ says: “then
(the segues) start repeating, and so it gets less interesting as we go down”;
and $i_{16}$ says: “I think if I was getting the same information […] that
would be becoming boring after a while, I […] want diversity in information”.
Many other interviewees make a similar point, that tours with higher segue
diversity are nice to listen to. For example, $i_{5}$ says: “I just preferred
the diversity, and it was like you didn’t know what was coming next, and what
bit of information you were going to learn was. That was kind of nice, that
you didn’t know!”; and $i_{1}$ says: “I feel like the information is […]
diverse […] I’d say it keeps your attention more that way”. Most of the above
comments refer to the diversity of segues that are relatively close to each
other in a tour. That is, it is important for neighbouring segues to be
diverse, while we have less guidance from our interviewees for segues that are
more remote from each other. For example, $i_{5}$ says: “I felt like (the
segues) grabbed my attention a bit more (in ), because (in ), the last 6 six
were about genres … Maybe those six were also on (), but actually I did not
notice as much”.

Respectively three and four interviewees say that and have low segue
diversity, while respectively six and five of them say that and have high
segue diversity. We do not have an answer in the rest of the cases. The
diversity is sometimes low because neither algorithm implements an explicit
segue diversity mechanism.

Nine interviewees say that their tour is better than their in diversity, one
says the opposite, four say they are not sure, and the rest do not offer an
opinion.

The result may be explained by previous work, as (Gabbolini and Bridge, 2021c)
finds that the standard deviation of the $interestingness$ scores of the
segues in ’s tours is higher than in ’s tours. That is, generates segues with
a broader range of $interestingness$ values, some segues are very interesting
and some are not, and segues with different interestingness values typically
have different topics.

####  5.1.3. Segue narrativity

The narrativity of the segues in tours, or narrativity for short, refers to
the quality that sequences of segues in tours present a narrative with a
coherent text. Very few interviewees (three out of 16) are in favour of
narrativity, as two points against narrativity are made. Point (1) is that
narrativity can correlate with low diversity, and low diversity is something
to avoid, as mentioned in Section 5.1.2. For example, $i_{12}$ says: “I don’t
think (narrativity) really matters per se, like, if you had all (segues)
linked to each other, it could get quite repetitive”. Point (2) is that the
textual flow would not be easy to follow in any case with songs in between.
For example, $i_{6}$ says: “I don’t think […] that any kind of coherent
narrative it’s something I’d look for […] I don’t think it is all that
important really.”; and $i_{8}$ says “I think (the segues) should be
independent! Because if there was a flow there I’d forget what it was saying
before while listening to the song, so I’d lose the flow! So I guess
independent makes much more sense”.

Only two and six interviewees say that respectively and have high segue
narrativity, while respectively nine and six of them say that and have low
segue narrativity. We do not have an answer in the rest of the cases. The
narrativity is oftentimes low because neither algorithm implements an explicit
segue narrativity mechanism.

Six interviewees say that their tour is better than their tour in narrativity,
four say they are not sure, and the rest do not offer an opinion.

####  5.1.4. Song arrangement

Many interviewees (13) give their opinion on what makes a good song
arrangement. The majority of them (11) mention some notion of similarity, with
a variety of different terms, reflecting the fact that music similarity
remains a concept with many definitions (Jones et al., 2007). For example,
they say that subsequent songs should have the same “tempo”, “tone”, ”mood”,
“energy”, “melody” and “artist voice”.

Interviewees do not agree on whether song arrangement is important in tours or
not, as eight of them say it is important, while six say it is not.
Interviewees $i_{6}$ and $i_{7}$ from the former group respectively say: “Oh
definitely! No matter what the context, if you were putting a bunch of songs
together, you are going to want some elements of musical flow between them”
and “you cannot set the tone in one tempo or a mood and change it rapidly […]
there’s nothing worse”. Interviewees from the latter group say that segues
make song arrangement not matter. For example, $i_{2}$ says “with the segues
[…] the order (of songs) doesn’t really matter, cause there’s still a
connection”; and $i_{12}$ says: “you are not listening to this song, and the
next song begins: you listen to this song, and there’s a break where some text
is read out, then you listen to the next one […] so no, I don’t think the
(song) order matters”. Some interviewees even appreciate when subsequent songs
are diverse. (Here, we are referring to song diversity, and not segue
diversity.). For example, $i_{4}$ says: “it was interesting seeing the
connections […] (between) different songs […] (like that two very diverse
bands) both started in 2006, I suppose that was really interesting”; and
$i_{2}$ says: “(the tours) are both pretty interesting […] because […] I tried
to choose music that was diverse, so it’s interesting to see (the segues)”. It
may be that segues between diverse songs are more unexpected, hence more
interesting, as the interestingness guideline (3) of Section 5.2.1 indicates.
However, the interviews do not provide enough material to confirm this
speculation.

Respectively six and seven interviewees say that song arrangement is not good
in and . In fact, of course, neither algorithm optimises for song arrangement,
but for segue interestingness. However, recent work found segue
interestingness to be related to similarity (Gabbolini and Bridge, 2021b),
which could explain why some interviewees say they are happy with the song
arrangements (eight interviewees for and seven for ).

Interviewees do not agree on which algorithm is better in song arrangement, as
five of them say that in the song arrangement is better than , six say the
opposite, one cannot decide, and four interviewees do not offer any opinion.
The result is not surprising as neither algorithm directly considers song
arrangement.

###  5.2. Tour quality

We ask interviewees to compare the quality of the tours recommended by and
according to segue interestingness and the overall tour quality. The results
are in the subsections below, and in Table 1.

####  5.2.1. Segue interestingness

Interviewees mostly agree that has more interesting segues than : nine
interviewees say so, five say the opposite, and two cannot decide. The result
is perhaps surprising, as is supposed to maximise overall segue
interestingness. But ’s model is only partially accurate for two reasons, as
noted in Section 5.4.1: (1) the $interestingness$ function itself is only
partially accurate; (2) the interestingness of a list of segues is not a
simple sum; other factors intervene, for example the segue diversity. In
particular, we suspect that outperforms because it is perceived to be more
diverse, and diversity positively impacts segue interestigness, as noted in
Section 5.1.2.

####  5.2.2. Overall tour quality

Interviewees mostly agree that produces overall better tours than : nine
interviewees say so, five say the opposite, one cannot decide, and in one case
we do not have an answer. Some interviewees mention the reason behind their
choice: nine of them mention more interesting segues; also nine participants
mention better song arrangement. Note that interviewees were free to give
multiple reasons, and some of them mention both segue interestingness and the
song arrangement. We infer that is preferred to because of the segues, which
are more interesting in , as noted in Section 5.2.1, while song arrangement is
equally good in both algorithms, as noted in Section 5.1.4. The result also
highlights the importance of song arrangement, which is mentioned by
interviewees as a key factor when assessing tours.

###  5.3. Concept evaluation

Interviewees evaluate tours positively, as the general opinion is that the
sequences of songs and segues are nice to listen to. For example, $i_{5}$
says: “I’d be happy to listen to that (tour) […] you learn something new about
all tunes you like to listen to”; $i_{7}$ says: “I really like it! […] it is
nice to see how all songs are linked together, it is really cool!”; and
$i_{1}$ says: “I like how the songs […] were linked by pieces of information,
something that they shared”. Some interviewees would like to see tours
available in streaming services. For example, $i_{8}$ says: “I’d certainly use
this prototype if it was implemented in a music streaming platform.”; $i_{6}$
says: “(the segues) would be quite interesting for a listener, if they were
available in a streaming service”; and $i_{5}$ says: “I would like to see
(tours) available, like they aren’t very available. It’d be nice to have the
option (on streaming services) to switch them on and off. It is nice to listen
to text, or to listen to something being spoken, in between listening to
songs”. Finally, the majority of interviewees (nine out of 16) mention that
they would welcome a tour like those they were presented with.

The majority of interviewees find the segues in tours to be interesting, along
a number of different dimensions. For example, $i_{11}$ and $i_{9}$ find
segues to be non-trivial, as $i_{11}$ says: “It was a pretty cool (segue)
actually. Like, I wouldn’t have thought about making a connection”; and
$i_{8}$ finds segues to be surprising “being surprised, by interesting facts,
like what this segues are producing here, that would make the listening
experience more exciting”. More generally, $i_{1-5}$, $i_{7}$, $i_{8}$,
$i_{10-12}$ and $i_{15}$ like the segues. For example, $i_{15}$ says: “I liked
the connections, from top to bottom, like something that ties up everything”.
Some interviewees recognise the value of having segues. For example, $i_{5}$
finds segues to be educational: “I also liked the bits of information […] It
was kind of educational as well as listening to songs”; and $i_{10}$ finds
that segues add to the listening experience: “(segues) add to the music, like
you’d enjoy more your listening experience”. The above results provide some
evidence that the $interestingness$ function, even though only partially
accurate, is nevertheless related to user-centered perceptions of segue
interestingess.

However, four interviewees report that segues are occasionally uninteresting.
For example, $i_{4}$ says: “Some of the connections are a bit weaker […] But I
think it’s mostly very interesting yeah!”; and $i_{12}$ says: “some of the
links are quite tenuous, like two artists are both from the USA, that one felt
a bit grasping”. These opinions agree with previous work, as (Gabbolini and
Bridge, 2021c) finds that the interestingness of segues in tours is not
constant, but subject to considerable deviation. Hence, from (Gabbolini and
Bridge, 2021c) we expect some segues to be considerably less interesting than
others, which is exactly what we report here.

Interviewees mention that tour quality is context-dependent, a similar point
being made in (Behrooz et al., 2019): tours are suited for active listening,
when attending to the music, and not passive listening, e.g. when the music
plays in the background to some other activity. For example, $i_{4}$ says:
“sometimes […] you may just want to listen to your music in the background.
But sometimes, if you want to sit down and think about the music your are
listening to, (the segues) might be like an interesting, like a different,
fun, new way to consume your music.”; and $i_{9}$ says: “a lot of times you
listen to music as a background, whereas I think (for a tour you need)
designated hours in your day, like I’m going to sit down and listen to this”.

###  5.4. Tour improvements

Interviewees identify a number of potential improvements for tours.

####  5.4.1. Interestingness modelling

Many interviewees say what interestingness means for them, and, from this, we
extract four guidelines on how to distinguish interesting from uninteresting
segues.

Guideline (1) is to be specific, as some interviewees say that specific segues
are more interesting than general segues. For example, $i_{1}$ says: “I
wouldn’t like to see information that seems kind of generic maybe […] it just
seems no care and attention has been put in creating that”. $i_{7}$ gives an
example of very general segue: “The bit the says ”one is based in the US and
the other is based in the same country”, because I think this is a way of
linking nearly every one even, I like knowing a little bit more of information
about someone”. The very same kind of segue is criticised also by $i_{12}$.
Interviewees have a different opinion about specific segues. Again $i_{12}$
says, “the segues that are specific, are the most interesting, but the other
like […] these two people are from the same large country, it is a bit …
uninteresting”, and provides an example of a more interesting segue, which
involve a more specific place: “this group founded in (New) Jersey and also
this other”.

Guideline (2) is to limit text length, as some interviewees say that long
segues are typically undesirable. For example, $i_{2}$ says: “I would not want
to see overly long segues”, and $i_{14}$ says “Not too much information, not
too many words, otherwise I’d be like: please!”. We do not investigate how
much text is too much for an interviewee. However, we report that the longest
segue that was shown to $i_{14}$ was of 22 words, while for $i_{2}$ it was of
19 words.

Guideline (3) is to be aware of prior knowledge, as some interviewees say that
segues that contradict their prior knowledge are to be avoided. For example,
$i_{15}$ says “apart from that (same genre segue) on Christmas music, which is
not correct. Apart from that, I enjoyed it”. Also, many interviewees say that
known segues are uninteresting. For example, $i_{14}$ says “One of the segues
was U2 and Fionn Reagan are Irish and […] I know that because I’m Irish! […]
that is just tedious and boring.”; and $i_{12}$ says “the rest (of the segues)
was kind of … I knew them already […] so I’d be kind of ”ehm, okay””. Finally,
many interviewees say that novel/unexpected segues are interesting. For
example, $i_{12}$ says: “I didn’t know some of this stuff, such as (these two
bands) being from the same state, it’s interesting”; and $i_{16}$ says: “(in
good segues) you’d have kind of information that you didn’t know and you were
just learning. Something interesting, like one of those of moments like oh my
god I didn’t know that these two bands were connected”.

Guideline (4) is to avoid controversies, as some interviewees point out that
controversial segues might be typically undesirable, such as those involving
artists personal lives. For example, $i_{11}$ says: “(I don’t want to hear)
scandals related to the artists […] It’d ruin the listening experience”.
Similarly, $i_{8}$ says “(I wouldn’t want to hear something) too particular
like, when this artist was married, or when this artist was in prison”.

Only two of the guidelines above match the $interestingness$ function used by
the algorithms in this work. This function, defined in (Gabbolini and Bridge,
2021a), combines rarity, which arguably entails specificity, and shortness.
Therefore, and strive to maximise an imperfect $interestingness$ function,
that could be improved by considering all four of the guidelines above. Even
so, $interestingness$ does a good job in distinguishing actually interesting
segues from others, as reported in Section 5.2.1. Moreover, in this work we
model the interestingness of a list of segues as the sum of the
$interestingness$ function applied to the individual segues in the list. This
will only approximate human perceptions of interestingness because also other
factors matter. For example, diversity of neighbouring segues makes the tour
more interesting overall. One improvement is to correct the estimate of the
interestingness of a list of segues by taking into account also diversity, and
especially the diversity of nearby segues in tours, as noted in Section 5.1.2.

####  5.4.2. More biographical segues, less genre segues.

Many interviewees highlight examples of interesting and uninteresting segues
seen in the tours. One class of interesting segues are (factual) biographical
segues about the artists. For example, $i_{5}$ likes segues about awards won
by artists; $i_{9}$ likes segues about locations, such as those about where an
artist was born; $i_{3}$ likes segues about live events, such as in which
festival an artist performed; and $i_{9}$ likes segues about dates, such as
when an artist was born. Interviewees would like to see even more biographical
segues, including ones that are not available in tours at the moment. For
example, $i_{12}$ says they would like segues to draw from music news
databases, that gather information such as emerging artists listings,
recording studios, and albums release dates. One class of uninteresting segues
are (musical) genre segues, such as the “jazz” segue in Figure 1 (c). For
example, $i_{1}$, $i_{3}$, $i_{4}$, $i_{6}$, $i_{12}$, $i_{15}$ say that genre
segues are not likeable and uninteresting.

We believe that biographical segues and genre segues are perceived as
respectively interesting and uninteresting at least in part because of
interestingness guideline (3) of Section 5.2.2: to be aware of prior
knowledge. Biographical segues, as facts, match guideline (3): they are not
likely to contradict user prior knowledge, unless the user is wrongly
informed, and specific facts are likely to be novel/unexpected for non-expert
users. For example, the segue “Flying Lotus is the grand-nephew of Alice
Coltrane” of Figure 1 (b) cannot contradict user prior knowledge, unless the
user is wrongly informed about the relation between the two artists, and they
are likely to be novel/unexpected for the user, unless the user is an expert
in artists’ biographies. Genre segues, instead, may often not match guideline
(3): they can contradict user prior knowledge, as people are found to often
disagree on music genres (Sordo et al., 2008), and they can be known to the
user, as genres are one of the most common ways in which people characterise
music (Petridis et al., 2022). Interviewees agree with our interpretation, as
$i_{16}$ is disappointed by a genre segue contradicting their prior knowledge:
“I’d like not to grow a question that would put me off […] you might thinking
about that instead of enjoying the music […] that Leonard Cohen (segue) is a
good example […] I started thinking: is he rock music?”; while $i_{9}$ says
they know genre segues already: “There were someones that were linked by same
genre […] and maybe that’s something you could have come up with yourself […]
I suppose that is something you have an idea of already”; $i_{8}$ also thinks
that genre segues are very trivial: “those (genre) segues have problems, they
are […] very trivial”.

Biographical and genre segues belong to the broader groups of respectively
factual and opinionable segues, which we suspect to be more and less
interesting, again because of interestingness guideline (3): factual segues
are not likely to contradict user prior knowledge, unless the user is wrongly
informed, while opinionable segues, by definition, are more likely to do so.
However, future work is needed to verify our supposition. Some factual segues
that could be included in tours are suggested by the interviewees. For example
$i_{14}$ would like segues drawn from artists’ biographies, both related and
not related to music, e.g. which and how many pets an artist has; $i_{7}$
would like acoustical information segues, such as the tempo or key of a song;
and $i_{9}$ would like lyrics segues, such as which keywords features in the
song lyrics.

Summing up, segues in tours could be improved by including more biographical
information and by avoiding musical genres. Another potential improvement is
to include more factual information, such as those in the last paragraph, and
avoid opinionable statements. The topics of segues can be modified by altering
the knowledge graph available to algorithms, and described in Section 3, to
include the information that should feature in segues, and to exclude the
information that should not feature in the segues.

####  5.4.3. Song selection

The algorithms we are using are given a set of songs as input, and return a
sequence made from this same set of songs, broken up by segues. That is, the
algorithms are not designed to perform any song selection. In this work, we
ask interviewees to send us ten songs they are familiar with, that we input to
the algorithms, as described in Section 4. In this Section, we report what
interviewees say about how to appropriately select the songs in input to the
algorithms. In summary, we find that the right level of familiarity is key.

The tours we show during the interviews feature familiar music only. Many
interviewees mention that they would like tours to feature some unfamiliar
songs, along with familiar songs, a concept we refer to as UF-tours
(Unfamiliar/Familiar tours). A UF-tour is similar to popular features of music
steaming services, such as Spotify’s daily
mix777https://newsroom.spotify.com/2018-05-18/how-your-daily-mix-just-gets-
you/, which is a playlist of familiar and unfamiliar music. A UF-tour,
however, is different from a daily mix because the unfamiliar songs are
introduced by a segue. The majority of interviewees (10 out of 16) say they
would welcome a UF-tour. For example, $i_{12}$ says “”Spotify would give your
daily mix (that is) songs you know mixed with similar songs […] I would have
never listened to. (A UF-tour) can be quite interesting actually, because it
creates a connection, it is not just a vague music floating around […] having
that little bit of information to introduce the artist and the actual songs
would be quite interesting I think, I would be you more inclined to go to the
actual artist page and listen to more of their music.””; and $i_{3}$ says:
“I’d be very interested in this, because on Apple Music, if you set auto-play
from your songs, they will bring on just a random song […] while this will
give you why they are similar, what connection do they have.” It is not clear
whether UF-tours are preferred over F-tours (tours of familiar music only),
because not enough interviewees explicitly compared the two concepts.
Interviewee $i_{5}$ suggests a button to switch between an F-tour and a UF-
tour, which can be a sound design choice before future investigation on the
subject.

Many interviewees comment on tours that feature only unfamiliar music, a
concept we refer to as U-tours. The general opinion is mostly negative, as no
interviewee says that they would welcome a U-tour. The main reason is that
segues between two unfamiliar songs lose their meaning. For example, $i_{9}$
says “(segues are valuable) with music that is important to you. If that music
is not important to you in the first place, I think (the segue) it’s just
going to be semantic information […] it wouldn’t bring any value to me”.
Familiar songs are needed to keep interest in the tour alive. For example,
$i_{12}$ says “I think the mix of familiar and novel songs works, because the
familiar songs are kind of an anchor to you, whereas with two unfamiliar songs
[…] (a segue) wouldn’t mean much to me”. The above result also suggests
avoiding segues between two unfamiliar songs in UF-tours.

One difficulty in implementing UF-tours and U-tours is recommending which
unfamiliar music to display in the tour. Interviewees suggest that recommended
music should fit the user’s tastes. For example, $i_{2}$ says “having music
you don’t like […] is kind of inevitable when finding new music but ideally a
tour would have music you will like in advance […] having a tour that doesn’t
read your preference very well […] wouldn’t be good”. Moreover, it may be
important that all songs in a tour are similar to each other, as noted in
Section 5.1.4.

####  5.4.4. Presentation

Tours are presented to interviewees through two mediums, visual and aural, as
explained in Section 4. The visual presentation is similar to Figure 1 (b) and
(c), while the aural presentation is a sequence of songs, alternated by
segues, read by a TTS engine. It is not clear which medium is preferred, as we
do not investigate the matter explicitly.

Interviewees do however identify a number of flaws in the presentation of the
tours. For example, the TTS is perceived as too “robotic”, not human-like, and
it is not liked by some interviewees. For example, $i_{6}$ says: “(would have
been better) if the audio links were not spoken as obviously by a computer,
you know if it was more human-like, more engaging”. Also, some interviewees do
not like the short pauses between the music and the segues, and would like the
song and the segue to overlap a little, similar to radio programs. For
example, $i_{5}$ says: “you could merge the songs a little bit (so that) the
voice over came in towards the end of the first song, while the second song
began while the voice over is running, eliminating that downtime between the
two”. Finally, some interviewees question the rule of having a segue between
every pair of songs, and suggest that, if not interesting enough, a segue
could be skipped. For example, $i_{16}$ says: “If the information isn’t going
to be something that’d grab, I wouldn’t want a segment, you-know? If you can’t
find an interesting enough segment, you will just have to not have a segment”.

##  6\. Conclusion

In this Section, we summarise the interviews reported in Section 5 to answer
all the RQs we pose, we discuss the limitations of the work that we have
presented here, and we outline possible future work on tour recommendation.

###  6.1. Discussion of RQs

RQ1. What are the attributes of tours? (1) According to the interviewees,
tours recommended by feature a segue top-bottom bias, that is the first segue
tends to be more interesting than the last segue, while tours recommended by
do not. (2) Tours do not always feature segue diversity, but tours recommended
by are found to be more diverse than tours recommended by . (3) Tours do not
always feature segue narrativity, that is the quality that the sequence of
segues in tours presents a narrative with a coherent text, but tours
recommended by are found to feature more narrativity than tours recommended by
. (4) Tours do not always feature good song arrangement, and tours recommended
by are found to be equally good in song arrangement to tours recommended by .

RQ2. What attributes of the tours are good/bad? Segue diversity is definitely
a good tour attribute, as 14 out of 16 interviewees say so. Song arrangement
is another good attribute, as interviewees say that good song arrangement is a
reason as important as good segues to prefer a tour over another. Segue
narrativity, instead, is considered a good attribute of tours by only three
interviewees. In conclusion, segue diversity and song arrangement appear to be
the two most important attributes of the tours investigated in this work.

RQ3. Which algorithm recommends better tours, and why? seems to recommend
higher quality tours than . Interviewees motivate their choice mentioning
higher segue interestingness and better song arrangement. We infer that is
preferred to because of segue interestingness, which is higher in , while the
quality of song arrangement is similar in both algorithms. In turn, segues in
could be more interesting because of the higher diversity, which is regarded
as one important characteristics of segues.

RQ4. How valuable is the concept of tours in general? The majority of
interviewees find that the algorithms recommend tours with interesting segues,
and say they would welcome a tour such as those they were presented with.
However, accepting tours is dependent on context: tours require active
listening, and they are not suited for passive listening. In conclusion,
participants mostly evaluate the concept of tours positively in general.

RQ5. What are possible improvements to tours? (1) Take into account user prior
knowledge and controversial content when scoring the segues. In particular,
known segues, segues contradicting user prior knowledge and controversial
segues should have low scores. (2) Include more segues with biographical
information and fewer segues about musical genres. (3) Choose music carefully,
admitting, from time to time, unfamiliar music, always chosen to fit the
user’s tastes. (4) Mind the presentation, employing an appropriate TTS engine
to read the segues, avoiding silences by overlapping songs with segues, and
skipping segues if not interesting enough. (5) Implement a good song
arrangement mechanism based on song similarity, as song arrangement is a
fundamental attribute of tours, but it is not considered by the algorithms we
use. (6) Implement a segue diversity mechanism, as segue diversity is a
fundamental attribute of tours, but it is not considered by the algorithms we
use.

###  6.2. Limitations

Our work has limitations that should be acknowledged. We conduct semi-
structured interviews, as they suit best our need of answering the RQs, as
argued in Section 4. However, this kind of experimental setting could affect
the validity of some results. For example, when evaluating the concept of
tours (RQ4), interviewees could infer that tours are the work of the
interviewers, and may feel pressure to provide a positive evaluation. We
attempt to relieve the pressure, as explained in Section 4.2. However, we
cannot prove the effectiveness of the attempt.

Moreover, semi-structured interviews are a high cost protocol, which
constrains the number of participants (Braun and Clarke, 2006), 16 in our
case. In our case, we resort to a convenience sampling of university students,
which does not imply that our result extends to a broader sample of the
population. Moreover, the small number of participants limits the statistical
power of the experiment, as we cannot afford to have more than two treatments
(Knijnenburg and Willemsen, 2015). In our case, we fix the two treatments to
be the two tour recommendation algorithms, as we explain in Section 1.
Therefore, we do not include any playlist recommendation algorithms among the
treatments, so we cannot assess whether tours are preferable to playlists or
not. By analysing the results of Section 5, we may infer that playlists are
preferable to tours when listening to music passively, and that tours can be
preferable to playlists when listening to music actively, which corroborates
previous work (Behrooz et al., 2019). However, at this stage this is more an
intuition than a definite answer. Similarly, we do not include other
interesting treatments in the experiment, such as a tour recommendation
algorithm which account for segue diversity, such as the one proposed in
(Behrooz et al., 2019). In any case, the work of (Behrooz et al., 2019) is not
fully reproducible, as some fundamental parameters of their algorithm, such as
the author-defined segue importance weights, are not shared in the paper.

Finally, while the interviews hint at several guidelines for the construction
of functional tour recommender systems, we cannot forecast the impact of those
guidelines, and their effectiveness can be only assessed by comparing a tour
recommender that implements those guidelines and a tour recommender that does
not.

###  6.3. Future work

The answers to RQ5 that we present in Section 6.1 are a source of ideas for
future research on tour recommendation. One idea is to develop a mechanism to
mine the user’s prior knowledge, which could be done explicitly by prompting
the user for opinions on segues, which is similar to active learning (Rubens
et al., 2011), or implicitly, by building a personalised classifier. Another
idea is to develop a mechanism to detect controversial content in segues,
which could take inspiration from work on controversial text detection
(Aharoni et al., 2014). The two above ideas are necessary to build a better
model of segue interestingness, as highlighted in Section 5.4.1. Another
research direction is building a tour recommender able to surface the right
music, as current tour recommenders do not have this feature: they assume they
are given the right songs for the tours. Future work could also include an on-
line experiment, such as an A/B test, so as to provide an evaluation of the
concept of tours in a natural environment.

###### Acknowledgements.

This publication has emanated from research conducted with the financial
support of Science Foundation Ireland under Grant number 12/RC/2289-P2 which
is co-funded under the European Regional Development Fund. For the purpose of
Open Access, the author has applied a CC BY public copyright licence to any
Author Accepted Manuscript version arising from this submission.

## References

  * (1)
  * Adams et al. (2015) William C Adams et al. 2015\.  Conducting semi-structured interviews.  _Handbook of practical program evaluation_ 4 (2015), 492–505.
  * Aharoni et al. (2014) Ehud Aharoni, Anatoly Polnarov, Tamar Lavee, Daniel Hershcovich, Ran Levy, Ruty Rinott, Dan Gutfreund, and Noam Slonim. 2014\.  A benchmark dataset for automatic detection of claims and evidence in the context of controversial topics. In _Proceedings of the first workshop on argumentation mining_. 64–68.
  * Behrooz et al. (2019) Morteza Behrooz, Sarah Mennicken, Jennifer Thom, Rohit Kumar, and Henriette Cramer. 2019.  Augmenting Music Listening Experiences on Voice Assistants. In _Proceedings of the 20th International Society for Music Information Retrieval Conference, ISMIR 2019, Delft, The Netherlands, November 4-8, 2019_ , Arthur Flexer, Geoffroy Peeters, Julián Urbano, and Anja Volk (Eds.). 303–310.  http://archives.ismir.net/ismir2019/paper/000035.pdf
  * Bonnin and Jannach (2014) Geoffray Bonnin and Dietmar Jannach. 2014.  Automated generation of music playlists: Survey and experiments.  _ACM Computing Surveys (CSUR)_ 47, 2 (2014), 1–35.
  * Braun and Clarke (2006) Virginia Braun and Victoria Clarke. 2006.  Using thematic analysis in psychology.  _Qualitative research in psychology_ 3, 2 (2006), 77–101.
  * Chen et al. (2018) Ching-Wei Chen, Paul Lamere, Markus Schedl, and Hamed Zamani. 2018.  Recsys challenge 2018: Automatic music playlist continuation. In _Proceedings of the 12th ACM Conference on Recommender Systems_. 527–528.
  * Gabbolini and Bridge (2021a) Giovanni Gabbolini and Derek Bridge. 2021a.  Generating interesting song-to-song segues with Dave. In _Proceedings of the 29th ACM Conference on User Modeling, Adaptation and Personalization_. 98–107.
  * Gabbolini and Bridge (2021b) Giovanni Gabbolini and Derek Bridge. 2021b.  An interpretable music similarity measure based on path interestingness. In _Procs. of the 22nd International Society for Music Information Retrieval Conference_. 213–219.
  * Gabbolini and Bridge (2021c) Giovanni Gabbolini and Derek Bridge. 2021c.  Play It Again, Sam! Recommending Familiar Music in Fresh Ways. In _Fifteenth ACM Conference on Recommender Systems_. Association for Computing Machinery, New York, NY, USA, 697–701.  https://doi.org/10.1145/3460231.3478866
  * Jones et al. (2007) M Cameron Jones, J Stephen Downie, and Andreas F Ehmann. 2007\.  Human Similarity Judgments: Implications for the Design of Formal Evaluations.. In _ISMIR_. 539–542.
  * Knijnenburg and Willemsen (2015) Bart P Knijnenburg and Martijn C Willemsen. 2015.  Evaluating recommender systems with user experiments.  In _Recommender systems handbook_. Springer, 309–352.
  * Koren et al. (2009) Yehuda Koren, Robert Bell, and Chris Volinsky. 2009\.  Matrix factorization techniques for recommender systems.  _Computer_ 42, 8 (2009), 30–37.
  * Lee et al. (2011) Jin Ha Lee, Bobby Bare, and Gary Meek. 2011.  How Similar Is Too Similar?: Exploring Users’ Perceptions of Similarity in Playlist Evaluation.. In _ISMIR_ , Vol. 11. 109–114.
  * Lonsdale and North (2011) Adam J Lonsdale and Adrian C North. 2011.  Why do we listen to music? A uses and gratifications analysis.  _British journal of psychology_ 102, 1 (2011), 108–134.
  * Nakano et al. (2016) Tomoyasu Nakano, Jun Kato, Masahiro Hamasaki, and Masataka Goto. 2016.  PlaylistPlayer: An interface using multiple criteria to change the playback order of a music playlist. In _Proceedings of the 21st International Conference on Intelligent User Interfaces_. 186–190.
  * Petridis et al. (2022) Savvas Petridis, Nediyana Daskalova, Sarah Mennicken, Samuel F Way, Paul Lamere, and Jennifer Thom. 2022\.  TastePaths: Enabling Deeper Exploration and Understanding of Personal Preferences in Recommender Systems. In _27th International Conference on Intelligent User Interfaces_ (Helsinki, Finland) _(IUI ’22)_. Association for Computing Machinery, New York, NY, USA, 120–133.  https://doi.org/10.1145/3490099.3511156
  * Pohle et al. (2007) T. Pohle, P. Knees, M. Schedl, E. Pampalk, and G. Widmer. 2007.  “Reinventing the Wheel”: A Novel Approach to Music Player Interfaces.  _IEEE Transactions on Multimedia_ 9, 3 (2007), 567–575.  https://doi.org/10.1109/TMM.2006.887991
  * Rodriguez et al. (2012) Mario Rodriguez, Christian Posse, and Ethan Zhang. 2012\.  Multiple objective optimization in recommender systems. In _Proceedings of the sixth ACM conference on Recommender systems_. 11–18.
  * Rubens et al. (2011) Neil Rubens, Dain Kaplan, and Masashi Sugiyama. 2011.  Active Learning in Recommender Systems.  In _Recommender Systems Handbook_ , P.B. Kantor, F. Ricci, L. Rokach, and B. Shapira (Eds.). Springer, 735–767.  https://doi.org/10.1007/978-0-387-85820-3_23
  * Sarwar et al. (2001) Badrul Sarwar, George Karypis, Joseph Konstan, and John Riedl. 2001.  Item-based collaborative filtering recommendation algorithms. In _Proceedings of the 10th international conference on World Wide Web_. 285–295.
  * Schedl et al. (2015) Markus Schedl, Peter Knees, Brian McFee, Dmitry Bogdanov, and Marius Kaminskas. 2015.  Music recommender systems.  In _Recommender systems handbook_. Springer, 453–492.
  * Schedl et al. (2018) Markus Schedl, Hamed Zamani, Ching-Wei Chen, Yashar Deldjoo, and Mehdi Elahi. 2018.  Current challenges and visions in music recommender systems research.  _International Journal of Multimedia Information Retrieval_ 7, 2 (2018), 95–116.
  * Sordo et al. (2008) Mohamed Sordo, Oscar Celma, Martin Blech, and Enric Guaus. 2008\.  The quest for musical genres: Do the experts and the wisdom of crowds agree?. In _ISMIR_. 255–260.
  * Tran et al. (2019) Thanh Tran, Renee Sweeney, and Kyumin Lee. 2019\.  Adversarial mahalanobis distance-based attentive song recommender for automatic playlist continuation. In _Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval_. 245–254.
  * Weisz et al. (2021) Justin D Weisz, Michael Muller, Stephanie Houde, John Richards, Steven I Ross, Fernando Martinez, Mayank Agarwal, and Kartik Talamadupula. 2021.  Perfection not required? Human-AI partnerships in code translation. In _26th International Conference on Intelligent User Interfaces_. 402–412.
  * Zamani et al. (2019) Hamed Zamani, Markus Schedl, Paul Lamere, and Ching-Wei Chen. 2019.  An analysis of approaches taken in the acm recsys challenge 2018 for automatic music playlist continuation.  _ACM Transactions on Intelligent Systems and Technology (TIST)_ 10, 5 (2019), 1–21.


# Improving Distribution System Resilience
by Undergrounding Lines and
Deploying Mobile Generators

Babak Taheri  Daniel K. Molzahn  Santiago Grijalva  School of Electrical and
Computer Engineering
Georgia Institute of Technology
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Atlanta, GA,
USA

###### Abstract

To improve the resilience of electric distribution systems, this paper
proposes a stochastic multi-period mixed-integer linear programming model that
determines where to underground distribution lines and how to coordinate
mobile generators in order to serve critical loads during extreme events. The
proposed model represents the service restoration process using the linearized
DistFlow approximation of the AC power flow equations as well as binary
variables for the undergrounding statuses of the lines, the configurations of
switches, and the locations of mobile generators during each time period. The
model also enforces a radial configuration of the distribution network and
considers the transportation times needed to reposition the mobile generators.
Using an extended version of the IEEE 123-bus test system, numerical
simulations show that combining the ability to underground distribution lines
with the deployment of mobile generators can significantly improve the
resilience of the power supply to critical loads.

###### keywords:

Power distribution resilience, mobile generators, undergrounding, service
restoration, natural disasters.

##  1 Introduction

Natural disasters have caused large-scale power outages in recent years, with
the total cost of 308 major natural disasters since 1980 exceeding $2 trillion
in the United States alone [NOAA]. Accordingly, the resilience of distribution
systems has become a topic of substantial interest for researchers and
distribution utilities. The National Infrastructure Advisory Council (NIAC)
states that resilience is “the ability to reduce the magnitude and/or duration
of disruptive events. The effectiveness of a resilient infrastructure or
enterprise depends upon its ability to anticipate, absorb, adapt to, and/or
rapidly recover from a potentially disruptive event” [berkeley2010framework].
In 2011, the UK Energy Research Center provided a similar definition for the
resilience as “the capacity of an energy system to tolerate disturbance and to
continue to deliver affordable energy services to consumers. A resilient
energy system can speedily recover from shocks and can provide alternative
means of satisfying energy service needs in the event of changed external
circumstances” [chaudry2011building]. Survivability and swift restoration
capabilities are the key features of resilient distribution systems.

Resilience can be improved by reducing the initial impact of a disaster and
quickly restoring the supply of power after a disaster occurs. In the
literature, two different approaches have been proposed to enhance
distribution system resilience, namely, infrastructure hardening and smart
operational strategies [gholami2018toward]. Hardening strategies reduce the
impacts of disasters. For example, the approach in [taheri2019hardening]
identifies optimal locations to harden lines and place switches in order to
reduce the effects of high-impact low-probability (HILP) events and enhance
the restoration performance of the system. As another example, the authors of
[ma2019resilience] enhance distribution system resilience by combining line
hardening, installing distributed generators, and adding remote-controlled
switches.

On the other hand, smart operational strategies mainly focus on the rapid
recovery of distribution systems by reconfiguring the network and using
available resources to provide energy to disconnected loads after an extreme
event. As an example of smart operational strategies, our previous work in
[taheri2019distribution] proposes a three-stage service restoration model for
improving distribution system resilience using pre-event reconfiguration and
post-event restoration considering both remote-controlled switches and manual
switches. Additionally, the authors of [Amirioun2018Resilience] propose a
proactive management scheme for microgrids to cope with severe windstorms.
This scheme minimizes the number of vulnerable branches in service while the
total loads are supplied. Also, the study in [Lei2019Resilient] presents a
two-stage stochastic programming method for the optimal scheduling of
microgrids in the face of HILP events considering uncertainties associated
with wind generation, electric vehicles, and real-time market prices. For
further examples of both infrastructure hardening and smart operational
strategies, see [bhusal2020, jufri2019, mahzarnia2020].

Recent research has also studied distribution system restoration problems that
consider the deployment of mobile generators [Taheri2021,
Amirioun2018Resilience, Gholami2016Microgrid, Lei2019Resilient,
dugan2021application]. In [Taheri2021], we proposed a two-stage strategy
involving 1) a preparation stage that reconfigures the distribution system and
pre-positions repair crews and mobile generators and 2) a post-HILP stage that
solves a stochastic mixed-integer linear programming (MILP) model to restore
the system using distributed generators, mobile generators, and
reconfiguration of switches. Building on this existing work, this paper
proposes a resilience enhancement strategy that aims to supply power to
critical loads by selectively adding new underground distribution lines prior
to a disaster while considering the capabilities of mobile generators to
restore power during the initial hours of a disaster. We will show that long-
term line undergrounding decisions which are cognizant of short-term mobile
generator deployments yield superior results relative to undergrounding
decisions made without considering mobile generators. We next motivate the use
of underground lines and mobile generators for improving distribution system
resilience.

Connecting Critical Loads by Underground Lines: Critical loads, such as
hospitals, water pumping facilities, and emergency shelters, are prioritized
for energization after extreme events. Improving the connectivity of critical
loads can increase the resilience of their power supply. There are various
advantages and disadvantages to adding new connections via overhead versus
underground distribution lines. For example, compared to overhead distribution
lines, underground lines provide reduced likelihood of damage during natural
disasters and improved aesthetics [liu2020resilient]. However, undergrounding
all of the distribution lines can be prohibitively expensive and also has
drawbacks such as utility employee work hazards during faults and manhole
inspections as well as potential susceptibility to flooding and storm surges.
To take advantage of the reduced susceptibility of underground distribution
lines to extreme events while avoiding their extra costs and potential
downsides, we focus on adding new underground lines that support power supply
to critical loads. Our proposed strategy determines which lines to underground
in order to improve resilience over a range of disaster scenarios while
considering the capabilities of mobile generators during the restoration
process.

Mobile Generators: Mobile generators are increasingly being used by utility
companies [Dominion_energy, SCE, byd]. Careful deployments of mobile
generators can significantly enhance the resilience of distribution systems
[dugan2021application]. In this paper, mobile generators are employed to
improve the restoration process in the aftermath of HILP events. Since they
can be connected to various locations, mobile generators provide significant
flexibility for responding to an extreme event.

To summarize, the need to improve distribution system resilience motivates
stronger connections between critical loads as well as more reliable and
flexible power sources. When utilized appropriately, underground distribution
lines and mobile generators can address these needs. To this end, the main
contribution of this paper is a multiperiod model for distribution system
restoration that considers the ability to underground lines, reconfigure the
network, and reposition mobile generators in order to serve critical loads.

The remainder of this paper is organized as follows: Section 2 describes
mathematical formulations of the stochastic MILP model. To demonstrate this
model, Section LABEL:sec:Results_and_Discussion presents a case study and
simulation results. Finally, Section LABEL:sec:Conclusion concludes the paper
and discusses future work.

##  2 Mathematical Formulation

This section formulates the proposed stochastic MILP model for the system
restoration problem considered in this paper. Fig. 1 shows a sketch of the
proposed strategy along with the line and bus models. Define the sets
$\mathit{\Pi}$, $\mathcal{N}$ and $\mathcal{T}$, respectively, corresponding
to the damage scenarios, the system’s buses, and the time periods for the
restoration problem. Let subscripts $\pi$, $t$, and $m$ denote a particular
scenario, time, and bus, respectively. Each time period has a duration of
$\Delta t$ (e.g., 5 minutes) and we consider a horizon lasting a few hours
after the disaster. The load at each bus $m$ has an assigned weight
$\omega_{m}$ indicating its importance. The variable $P_{\pi,t,m}^{LC}$
denotes the curtailment of active power load at bus $m$ and time $t$ under
scenario $\pi$. The probability of each scenario is denoted by $pr_{\pi}$. The
objective (1) minimizes the total unserved energy during the restoration
process, weighted by the load’s importance:

Figure 1: a) Mobile generator and underground line models, b) bus model, and
c) line model.

$\min\sum_{\pi\in\mathit{\Pi}}\sum_{m\in\mathcal{N}}\sum_{t\in\mathcal{T}}\omega_{m}\cdot
pr_{\pi}\cdot P_{\pi,m,t}^{LC}\cdot\Delta t$ (1)

###  2.1 Power Flow

Let $\mathcal{L}^{E}$, $\mathcal{L}^{A}$, and
$\mathcal{L}=\mathcal{L}^{E}\cup\mathcal{L}^{A}$ denote the set of existing
lines, the set of added underground lines, and the set of all lines,
respectively. In this study, we consider a balanced single-phase equivalent
model of the distribution systems, but the approach could be generalized to
unbalanced three-phase network models as well. Let parameters $P_{t,m}^{D}$
and $Q_{t,m}^{D}$ denote the active and reactive power demand at bus $m$ at
time $t$, respectively. We also define the following variables for each time
period $t$ and scenario $\pi$:

  * 1.

$p_{\pi,t,m,n}^{E}$ and $q_{\pi,t,m,n}^{E}$: active and reactive power flows
on the existing overhead line connecting buses $m$ and $n$,

  * 2.

$p_{\pi,t,m,n}^{A}$ and $q_{\pi,t,m,n}^{A}$: the active and reactive power
flows on the added underground line connecting buses $m$ and $n$,

  * 3.

$P_{\pi,t,m}^{DG}$ and $Q_{\pi,t,m}^{DG}$: active and reactive power of the
distributed generator at bus $m$,

  * 4.

$P^{MG}_{\pi,t,m}$ and $Q^{MG}_{\pi,t,m}$: active and reactive power of the
mobile generator at bus $m$.

The power balance constraints at each bus $m$ are:

$\displaystyle\begin{split}P_{t,m}^{D}+\sum_{\begin{subarray}{c}(i,n)\in\mathcal{L}^{E}\\\
\textrm{~{}s.t.~{}}i=m\end{subarray}}p_{\pi,t,m,n}^{E}+\sum_{n\in\mathcal{N}}p_{\pi,t,m,n}^{A}=P_{\pi,t,m}^{LC}+\\\
P_{\pi,t,m}^{DG}+P^{MG}_{\pi,t,mgm}+\sum_{\begin{subarray}{c}(m,i)\in\mathcal{L}^{E}\\\
\textrm{~{}s.t.~{}}i=n\end{subarray}}p_{\pi,t,n,m}^{E}\end{split}$ (2a)
$\displaystyle\begin{split}Q_{t,m}^{D}+\sum_{\begin{subarray}{c}(i,n)\in\mathcal{L}^{E}\\\
\textrm{~{}s.t.~{}}i=m\end{subarray}}q_{\pi,t,m,n}^{E}+\sum_{n\in\mathcal{N}}q_{\pi,t,m,n}^{A}=Q_{\pi,t,m}^{LC}+\\\
Q_{\pi,t,m}^{DG}+Q^{MG}_{\pi,t,m}+\sum_{\begin{subarray}{c}(m,i)\in\mathcal{L}^{E}\\\
\textrm{~{}s.t.~{}}i=n\end{subarray}}q_{\pi,t,n,m}^{E}\end{split}$ (2b)

Equation (3a) implies that load curtailment at each bus cannot exceed the
total demand of the bus. We also consider a constant power factor load
curtailment model as indicated by (3b).

$\displaystyle 0\leq P_{\pi,t,m}^{LC}\leq P_{t,m}^{D}$ (3a) $\displaystyle
Q_{\pi,t,m}^{LC}\cdot{P_{t,m}^{D}}=P_{\pi,t,m}^{LC}\cdot{Q_{t,m}^{D}}$ (3b)

Let $v_{\pi,t,n}$ denote the voltage magnitude at bus $n$ during time $t$ in
scenario $\pi$. $M$ is a big-M constant. Let $r_{m,n},x_{m,n}$ denote the
resistance and reactance of line $(m,n)$. $\varsigma_{\pi,t,m,n}$ is a binary
variable indicating whether the switch on the line $(m,n)$ at time $t$ in
scenario $\pi$ is closed. $\underline{v}_{m}$ and $\overline{v}_{m}$ are the
upper and lower bounds on the voltage magnitude at bus $m$. To obtain a MILP
formulation, we use the linearized DistFlow approximation of the power flow
equations [baran1989], as in other related work, e.g., [Taheri2019,
Amirioun2018Resilience]. Thus, the voltages of the buses are related as in
(4a), where the big-M method is used to decouple the voltages of two
disconnected buses to account for the behavior of switches. Furthermore, the
voltages of the buses should be within the allowable range as dictated in
(4b).

$(1-\varsigma_{\pi,t,m,n})M-\frac{r_{m,n}\cdot p_{\pi,t,m,n}^{E}+x_{m,n}\cdot
q_{\pi,t,m,n}^{E}}{v_{1}}\leq
v_{\pi,t,n}-v_{\pi,t,m}\leq(\varsigma_{\pi,t,m,n}-1)M-\frac{r_{m,n}\cdot
p_{\pi,t,m,n}^{E}+x_{m,n}\cdot q_{\pi,t,m,n}^{E}}{v_{t}}$ (4a)
$\underline{v}_{m}\leq v_{\pi,t,m}\leq\overline{v}_{m}$ (4b)

We linearize the line flow limits specified in terms of apparent power as
shown in (5), where $\bar{S}_{m,n}$ is the capacity of line $(m,n)$.

$\displaystyle-\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}\leq
p_{\pi,t,m,n}^{E}\leq\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}$ (5a)
$\displaystyle-\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}\leq
q_{\pi,t,m,n}^{E}\leq\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}$ (5b)
$\displaystyle-\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}\leq
p_{\pi,t,m,n}^{E}+q_{\pi,t,m,n}^{E}\leq\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}$
(5c) $\displaystyle-\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\bar{S}_{m,n}\leq
p_{\pi,t,m,n}^{E}-q_{\pi,t,m,n}^{E}\leq\sqrt{2}\varsigma_{tm,n}\cdot\bar{S}_{m,n}$
(5d)

Let $\alpha_{\pi,t,m}$ be a binary variable indicating whether the distributed
generator at bus $m$ is generating power during time $t$ in scenario $\pi$.
$\overline{P}_{m}^{DG}$, $\overline{Q}_{m}^{DG}$, $\underline{P}_{m}^{DG}$,
and $\underline{Q}_{m}^{DG}$ are the maximum/minimum active/reactive power
outputs of the distributed generator at bus $m$. Constraint (6) ensures that
the active and reactive power outputs of distributed generators are within
their allowed ranges.

$\displaystyle\alpha_{\pi,t,m}\cdot\underline{P}_{m}^{DG}\leq
P_{\pi,t,m}^{DG}\leq\alpha_{\pi,t,m}\cdot\overline{P}_{m}^{DG}$ (6a)
$\displaystyle\alpha_{\pi,t,m}\cdot\underline{Q}_{m}^{DG}\leq
Q_{\pi,t,m}^{DG}\leq\alpha_{\pi,t,m}\cdot\overline{Q}_{m}^{DG}$ (6b)

Finally, (7) enforces a radial configuration of distribution system by using
the spanning tree approach wherein each bus except the root bus has either one
or zero parent buses [jabr2012minimum]. In (7), $\lambda_{\pi,t,m,n}$ is a
binary variable indicating whether bus $n$ is the parent of bus $m$ at time
$t$ in scenario $\pi$ and $\Psi_{m}$ denotes the set of buses connected to bus
$m$ by a line.

$\displaystyle\lambda_{\pi,t,m,n}+\lambda_{\pi,t,n,m}=\varsigma_{\pi,t,m,n},$
$\displaystyle\forall n\in\Psi_{m}$ (7a)
$\displaystyle\sum_{m\in\Psi_{m}}\lambda_{\pi,t,m,n}\leq 1,$
$\displaystyle\forall n\in\Psi_{m}$ (7b) $\displaystyle\lambda_{\pi,t,1,n}=0,$
$\displaystyle\forall n\in\Psi_{\text{root }}$ (7c)

###  2.2 Mobile Generators

As shown in Fig. 1, mobile generators can be dispatched from depots to
distribution buses to supply loads after HILP events. This motivates careful
consideration of travel and setup time requirements. In this regard, let
$\chi$ and $\Xi$ denote the sets of depots and mobile generators,
respectively. $\delta_{\pi,dp,mg,m}$ is a binary variable indicating whether
mobile generator $mg$ moves from depot $dp$ to bus $m$ in scenario $\pi$.
$\beta_{m}$ is the maximum number of mobile generators that can be installed
at bus $m$. Constraints (8)–(16) model mobile generator scheduling after the
occurrence of a major disaster. Constraint (8) indicates that at most
$\beta_{m}$ mobile generators can be dispatched to bus $m$.

$\sum_{mg\in\Xi}\sum_{dp\in\chi}\delta_{\pi,dp,mg,m}\leq\beta_{m}$ (8)

Constraint (9) indicates that each mobile generator cannot be dispatched more
than once.

$\sum_{m\in\mathcal{N}}\sum_{dp\in\chi}\delta_{\pi,dp,mg,m}\leq 1$ (9)

Let $\Gamma_{\pi,dp,mg,m}$ denote the arrival time of mobile generator $mg$
from depot $dp$ at bus $m$ in scenario $\pi$. Let $T_{dp,m}$ denote the time
needed for a mobile generator to connect to bus $m$ when departing from depot
$dp$. $\gamma_{\pi,t,mg,m}$ is a binary variable indicating whether a mobile
generator arrives at bus $m$ at time $t$ in scenario $\pi$. Constraint (10)
models the total time required to connect mobile generators to the
distribution buses. Constraints (11) and (12) then ensure consistency among
the decision variables related to the connection times. For example, if the
arrival time of mobile generator 1 to bus 14 is 20 minutes (i.e.,
$\Gamma_{\pi,dp,1,14}=20$), the binary variable $\gamma_{\pi,t,1,14}$ will be
one for $t=20$ and zero for $t\neq 20$.

$\displaystyle\Gamma_{\pi,dp,mg,m}=T_{dp,m}\times\delta_{\pi,dp,mg,m}$ (10)
$\displaystyle\sum_{t\in\mathcal{T}}t\times\gamma_{\pi,t,mg,m}\geq\sum_{dp\in\chi}\Gamma_{\pi,dp,mg,m}$
(11)
$\displaystyle\sum_{t\in\mathcal{T}}t\times\gamma_{\pi,t,mg,m}\leq\sum_{dp\in\chi}\Gamma_{\pi,dp,mg,m}+1-\varepsilon$
(12)

$\kappa_{\pi,t,mg,m}$ is a binary variable indicating whether mobile generator
$mg$ is connected to bus $m$ at time $t$ in scenario $\pi$. Equation (13)
couples $\gamma_{\pi,t,mg,m}$ and $\delta_{\pi,dp,mg,m}$.

$\sum_{t\in\mathcal{T}}\gamma_{\pi,t,mg,m}=\sum_{dp\in\chi}\delta_{\pi,dp,mg,m}$
(13)

In our model, we consider a time frame during which mobile generators can move
from their depot and connect to one bus but cannot subsequently disconnect and
move to another bus. This is enforced by (14).

$\kappa_{\pi,t,mg,m}=\sum_{t=1}^{t}\gamma_{\pi,t,mg,m}$ (14)

$\overline{P}_{mg}$ and $\overline{Q}_{mg}$ are the maximum active and
reactive power outputs of mobile generator $mg$, as modeled by (15) and (16).

$0\leq
P^{MG}_{\pi,t,m}\leq\sum_{mg\in\Xi}\kappa_{\pi,t,mg,m}\times\overline{P}_{mg}$
(15) $0\leq
Q^{MG}_{\pi,t,m}\leq\sum_{mg\in\Xi}\kappa_{\pi,t,mg,m}\times\overline{Q}_{mg}$
(16)

###  2.3 Underground Lines

Construction of underground lines can significantly increase the resilience of
the power supplied to critical loads after HILP events, especially when
installed while considering the capabilities of with mobile generators. In
this regard, let $\tau_{m,n}$ be a binary variable indicating whether an
underground line is constructed between buses $m$ and $n$. The voltages of the
underground lines’ terminal buses are related by (17a). Constraint (17b)
states that underground lines are only in a serviceable state if the lines are
constructed (i.e., $\tau_{m,n}=1$) and the lines’ switches are closed (i.e.,
$\varsigma_{\pi,t,m,n}=1$).

$\displaystyle\left(1-\varsigma_{\pi,t,m,n}\right)M-\frac{r_{m,n}\cdot
p_{\pi,t,m,n}^{A}+x_{m,n}\cdot q_{\pi,t,m,n}^{A}}{v_{1}}$
$\displaystyle\quad\leq v_{\pi,t,n}-v_{\pi,t,m}$
$\displaystyle\quad\leq\left(\varsigma_{\pi,t,m,n}-1\right)M-\frac{r_{m,n}\cdot
p_{\pi,t,m,n}^{A}+x_{m,n}\cdot q_{\pi,t,m,n}^{A}}{v_{1}}$ (17a)
$\displaystyle\tau_{m,n}\geq\varsigma_{\pi,t,m,n}$ (17b)

The linearized form of the underground lines’ flow limits is modeled in (18).

$\displaystyle-\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}\leq
p_{\pi,t,m,n}^{A}\leq\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}$ (18a)
$\displaystyle-\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}\leq
q_{\pi,t,m,n}^{A}\leq\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}$ (18b)
$\displaystyle-\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}\leq
p_{\pi,t,m,n}^{A}+q_{\pi,t,m,n}^{A}\leq\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}$
(18c) $\displaystyle-\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}\leq
p_{\pi,t,m,n}^{A}-q_{\pi,t,m,n}^{A}\leq\sqrt{2}\varsigma_{\pi,t,m,n}\cdot\overline{S}_{m,n}$
(18d)

Let $\ell_{mn}$ denote the length of the line between buses $m$ and $n$.
$C^{A}$, $C^{\text{RCS }}$, and $C^{\text{invest }}$ are the per-length cost
of constructing underground lines, the cost of installing remote-controlled
switches, and the total budget of the distribution utility, respectively.
$\eta^{A}$ is the maximum allowed number of underground lines. Constraint
(19a) ensures that the total investment cost of underground lines and remote-
controlled switches is no greater than the total budget of the distribution
utility. Also, (19b) states that the number of constructed underground lines
must be within the specified limit.

$\displaystyle\sum_{\begin{subarray}{c}(m,n)\in\mathcal{L}^{A}\end{subarray}}\left(\frac{1}{2}\ell_{mn}^{A}\cdot
C^{A}+C^{\text{RCS }}\right)\cdot\tau_{m,n}\leq C^{\text{invest }}$ (19a)
$\displaystyle\sum_{\begin{subarray}{c}(m,n)\in\mathcal{L}^{A}\end{subarray}}\tau_{m,n}/2\leq\eta^{A}$
(19b)

###  2.4 Final Model

The final model is summarized as follows:

$\min~{}(\ref{eq:objective})\textrm{~{}s.t.~{}}(\ref{eq:power
balance})-(\ref{eq:underg})$ (20)

Table 1: Computational Scaling of the Stochastic MILP Model Num. of | Computational scaling | IEEE 123-Bus
---|---|---
Binary variables |  |