# Learning Mixed-Integer Linear Programs from Contextual Examples

Mohit Kumar1 1KU Leuven, Belgium
<EMAIL_ADDRESS>
2University of Trento, Italy
<EMAIL_ADDRESS>Samuel Kolb1 1KU Leuven, Belgium
<EMAIL_ADDRESS>
2University of Trento, Italy
<EMAIL_ADDRESS>Luc De Raedt1 1KU Leuven, Belgium
<EMAIL_ADDRESS>
2University of Trento, Italy
<EMAIL_ADDRESS>Stefano Teso2 1KU Leuven, Belgium
<EMAIL_ADDRESS>
2University of Trento, Italy
<EMAIL_ADDRESS>
###### Abstract

Mixed-integer linear programs (MILPs) are widely used in artificial
intelligence and operations research to model complex decision problems like
scheduling and routing. Designing such programs however requires both domain
and modelling expertise. In this paper, we study the problem of acquiring
MILPs from _contextual_ examples, a novel and realistic setting in which
examples capture solutions and non-solutions within a specific context. The
resulting learning problem involves acquiring continuous parameters – namely,
a cost vector and a feasibility polytope – but has a distinctly combinatorial
flavor. To solve this complex problem, we also contribute missle, an algorithm
for learning MILPs from contextual examples. missle uses a variant of
stochastic local search that is guided by the gradient of a continuous
surrogate loss function. Our empirical evaluation on synthetic data shows that
missle acquires better MILPs faster than alternatives based on stochastic
local search and gradient descent.

##  1 Introduction

Mixed-integer linear programs (MILPs) are widely used in operations research
to model decision problems like personnel rostering [1], timetabling [2], and
routing [3], among many others. A MILP is a constrained optimization program
of the form:

$\displaystyle\textstyle\max_{\bm{\mathrm{x}}}$
$\displaystyle\quad\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}$ (1)
$\displaystyle\mathrm{s.t.}$
$\displaystyle\quad\bm{\mathrm{A}}\bm{\mathrm{x}}\leq\bm{\mathrm{b}}$ (2)

over variables $\bm{\mathrm{x}}=(x_{1},\ldots,x_{n})$. Like in regular linear
programs, the objective function is linear with parameter
$\bm{\mathrm{c}}\in\mathbb{R}^{n}$ (Eq. 1) and the feasible set is a polytope
defined by a coefficient matrix $\bm{\mathrm{A}}\in\mathbb{R}^{m\times n}$ and
a bias vector $\bm{\mathrm{b}}\in\mathbb{R}^{m}$ (Eq. 2). What makes MILPs
special is that some of the variables $\bm{\mathrm{x}}$ are restricted to be
integers. This allows MILPs to capture numerical optimization problems with a
strong combinatorial component. For instance, $0$–$1$ variables can be used to
decide whether an action should be taken or not, like taking a particular
route, buying a machine, or assigning a nurse to a shift. While MILPs are NP-
hard to solve in general, practical solvers like Gurobi [4] and CPLEX [5] can
readily handle large instances, making MILPs the formalism of choice in many
scientific and industrial applications.

Designing MILPs, however, requires substantial modelling expertise, making it
hard for non-experts to take advantage of this powerful framework. One option
is then to use constraint learning [6] to induce MILPs from historical data,
e.g., examples of high-quality solutions (positive examples) and sub-par or
infeasible configurations (negative examples). A major difficulty is that in
practice historical data is collected under the effects of temporary
restrictions and resource limitations. For instance, in a scheduling problem
some workers may be temporarily unavailable due to sickness or parental leave.
We use the term “context” to indicate such temporary constraints. Crucially,
by restricting the feasible space, contexts can substantially alter the set of
optimal solutions, biasing the data, cf. Figure 1. Learning algorithms that
ignore the contextual nature of their supervision are bound to perform poorly
[7]. Existing approaches for learning MILP programs suffer from this issue.

The aim of this work is to amend this situation. In particular, we formalize
contextual learning of MILPs and show that the resulting learning problem
contains both continuous and combinatorial elements that make it challenging
for standard techniques. To solve this issue, we introduce missle, a novel
approach that combines ideas from combinatorial search and gradient-based
optimization. In particular, missle relaxes the original loss to obtain a
natural, smoother surrogate on which gradient information can be readily
computed, and then uses the latter to guide a stochastic local search
procedure. Our empirical evaluation on synthetic data shows that missle
performs better than two natural competitors – namely, pure gradient descent
and pure stochastic local search – in terms of quality of the acquired MILPs
and computational efficiency.

##  2 Learning MILPs from Contextual Data

Our goal is to acquire a MILP – and specifically its parameters
$\bm{\mathrm{A}}$, $\bm{\mathrm{b}}$, and $\bm{\mathrm{c}}$ – from examples of
contextual solutions and non-solutions. Contexts can alter the set of
solutions of a MILP: a configuration $\bm{\mathrm{x}}$ that is optimal in
context $\psi$ might be arbitrarily sub-optimal or even infeasible in a
different context $\psi^{\prime}$, cf. Figure 1. To see this, consider the
following example:

######  Example 1.

A company makes two products ($P_{1}$ and $P_{2}$) using two machines ($M_{1}$
and $M_{2}$). Producing one unit of $P_{1}$ requires $40$ minutes of
processing time on machine $M_{1}$ and $20$ minutes on machine $M_{2}$, while
each unit of $P_{2}$ takes $30$ minutes on $M_{1}$ and $40$ minutes on
$M_{2}$. Both machines can be run for a maximum of 4 hours every day. The
company makes a profit of $\$20$ on each unit of $P_{1}$ and $\$18$ on each
unit of $P_{2}$. The aim is to decide the number of units
$\bm{\mathrm{x}}=(x_{1},x_{2})$ to produce for each product so that the profit
is maximised. This problem can be written as a MILP:

$\displaystyle\max$ $\displaystyle\quad 20x_{1}+18x_{2}$
$\displaystyle\mathrm{s.t.}$ $\displaystyle\quad 40x_{1}+30x_{2}\leq 240$
$\displaystyle\quad 20x_{1}+40x_{2}\leq 240$

The optimal solution for this problem is $\bm{\mathrm{x}}=(3,4)$, giving a
total profit of $\$132$. Now, consider a temporary reduction in demand for
$P_{2}$ and hence the company wants to produce maximum $3$ units every day.
This context can be added as a hard constraint: $x_{2}\leq 3$, leading to a
different optimal solution, namely $\bm{\mathrm{x}}=(6,0)$. Notice that the
solution without context is infeasible in this context.

We define the problem of learning MILPs from contextual examples as follows:

######  Definition 1.

Given a data set of context-specific examples
$S:=\\{(\psi_{k},\bm{\mathrm{x}}_{k},y_{k})\,:\,k=1,\ldots,s\\}$, where
$y_{k}\in\\{0,1\\}$ is $1$ iff $\bm{\mathrm{x}}_{k}$ is a high-quality
solution for context $\psi_{k}$, find a MILP with parameters
$\theta=(\bm{\mathrm{A}},\bm{\mathrm{b}},\bm{\mathrm{c}})$ that can be used to
obtain high-quality configurations in other contexts of interest.

By “high-quality” configurations, we mean configurations that are feasible and
considered (close to) optimal. Going forward we will use $M(\theta)$ to
indicate the MILP defined by $\theta$.

opt. dir.$x_{1}$$x_{2}$$\psi$$x_{1}$$x_{2}$$\psi$$x_{1}$$x_{2}$ Figure 1: Toy
MILP and two contexts. Left: MILP over two integer variables $(x_{1},x_{2})$.
The feasible polytope is in gray, the optimization direction goes top-right.
The optimum is in green. Middle: Once a context $\psi=x_{2}\leq t_{2}$ (blue)
is added, the optimum changes substantially (red). Right: same for
$\psi^{\prime}=x_{1}\leq t_{1}$. A MILP learned using the three optima as
positive examples while ignoring their contextual nature would be forced to
consider all points $(x_{1},x_{2})$ in the plane as having the same cost
(i.e., $c_{1}=c_{2}$), which is clearly undesirable.

###  2.1 Contexts

In the following, we will restrict ourselves to handling contexts that impose
additional _linear_ constraints
$\bm{\mathrm{S}}\bm{\mathrm{x}}\leq\bm{\mathrm{t}}$ to the problem. This
choice is both convenient and flexible. It is convenient because injecting
linear contexts into a MILP gives another MILP, namely:

$\displaystyle\textstyle\max_{\bm{\mathrm{x}}}$
$\displaystyle\quad\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}$ (3)
$\displaystyle\mathrm{s.t.}$
$\displaystyle\quad\bm{\mathrm{A}}\bm{\mathrm{x}}\leq\bm{\mathrm{b}},\quad\bm{\mathrm{S}}\bm{\mathrm{x}}\leq\bm{\mathrm{t}}$
(4)

It is also very flexible: the polytope
$\bm{\mathrm{S}}\bm{\mathrm{x}}\leq\bm{\mathrm{t}}$ can naturally encode
frequently used constraints like partial assignments (which fix the value of a
subset of the variables) and bounding-box constraints (which restrict the
domain of a subset of the variables to a particular range). Furthermore, it is
often possible to encode complex non-linear and logical constraints into this
form using linearization techniques [8].

###  2.2 An initial formulation

Learning a MILP amounts to searching for a program $M(\theta)$ that fits the
data well. Naturally, ignoring the contextual nature of the data – for
instance, by treating all positive examples as if they were global, rather
than contextual, optima – can dramatically reduce the quality of the learned
program [7], cf. Figure 1.

Given a MILP $M(\theta)$ and a context $\psi$, we define
$h_{\theta}(\bm{\mathrm{x}},\psi)$ to be a binary classifier that labels
configuration $\bm{\mathrm{x}}$ as positive if and only if it is solution to
$M(\theta)$ in context $\psi$:

$h_{\theta}(\bm{\mathrm{x}},\psi):=\mathbbm{1}\\!\left\\{\bm{\mathrm{x}}\in\mathcal{X}^{*}(\theta,\psi)\right\\}$
(5)

Here $\mathbbm{1}\\!\left\\{cond\right\\}$ is the indicator function that
evaluates to $1$ if $cond$ holds and to $0$ otherwise, and
$\mathcal{X}^{*}(\theta,\psi)$ is the set of contextual solutions of
$M(\theta)$ in context $\psi$. Given a dataset $S$ of contextual examples, we
propose to learn a MILP by minimizing the following 0-1 loss:

$\textstyle
L_{S}(\theta):=\frac{1}{s}\sum_{k=1}^{s}\mathbbm{1}\\!\left\\{h(\bm{\mathrm{x}}_{k},\psi_{k})\neq
y_{k}\right\\}$ (6)

This amounts to looking for a MILP $M(\theta)$ that minimizes the number of
misclassified training examples.

###  2.3 Advantages and Limitations

The above strategy is motivated by the work of Kumar  _et al._ [7], who have
shown that, under suitable assumptions, classifiers $h_{\theta}$ that make few
mistakes on the training set correspond to programs $M(\theta)$ that output
high-quality configurations in (even unobserved) target contexts.111These
results were obtained for MAX-SAT programs but do carry over to general
constraint optimization programs.

A downside of this formulation is that it is computationally challenging.
Solving the above optimization problem is equivalent to minimizing the $0$–$1$
loss on the training set, which is known to be NP-hard [9]. Furthermore, the
objective function is piece-wise constant: there exist infinitely many pairs
of MILP models $\theta^{1}\neq\theta^{2}$ that have the same set of solutions
and that therefore lie on the same plateau of the empirical loss. This makes
it hard to apply optimization procedures based on pure gradient descent, as
the gradient is constant almost everywhere. Standard local search is also not
very effective, as it proceeds by making small uninformed steps and therefore
might spend a long time trapped on a plateau. A second issue is that
evaluating the loss is hard: checking whether an instance
$\bm{\mathrm{x}}_{k}$ is predicted as positive – that is, evaluating
$h(\bm{\mathrm{x}}_{k},\psi_{k})=1$ – involves finding an optimum
$\bm{\mathrm{x}}^{*}\in\mathcal{X}^{*}(\theta;\psi)$ and ensuring that it has
the same value as $\bm{\mathrm{x}}_{k}$. The issue is that computing
$\bm{\mathrm{x}}^{*}$ requires to solve the candidate MILP in context
$\psi_{k}$, which is NP-hard in general. This step needs to be carried out
repeatedly when minimizing Eq. 6, so it is important to keep the number of
optimization steps at a minimum.

##  3 Learning MILPs with MISSLE

Due to the difficulty of optimizing Eq. 6 directly, we employ a smoother
surrogate loss that offers gradient information and use it to guide a
stochastic local search procedure.

###  3.1 A Surrogate Loss

We build a surrogate loss by enumerating the various ways in which $M(\theta)$
can _mislabel_ a contextual example and defining a loss for each case. Below,
we write $\mathrm{dist}_{j}(\bm{\mathrm{x}})$ to indicate the Euclidean
distance between $\bm{\mathrm{x}}$ and the $j$th hyperplane
$(\bm{\mathrm{a}}_{j},b_{j})$ of the feasible polytope [10]:

$\mathrm{dist}_{j}(\bm{\mathrm{x}}):=|\bm{\mathrm{a}}_{j}^{\top}\bm{\mathrm{x}}-b_{j}|\
/\left\lVert\bm{\mathrm{a}}_{j}\right\rVert_{2}$ (7)

Additionally, we write $\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k})$ to
indicate the regret of $\bm{\mathrm{x}}_{k}$ in context $\psi_{k}$, which
measures the difference in quality between $\bm{\mathrm{x}}_{k}$ and a truly
optimal configuration
$\bm{\mathrm{x}}_{k}^{*}\in\mathcal{X}^{*}(\theta,\psi_{k})$ according to the
_learned_ cost vector $\bm{\mathrm{c}}$:

$\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k}):=\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}_{k}^{*}-\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}_{k}=\bm{\mathrm{c}}^{\top}(\bm{\mathrm{x}}_{k}^{*}-\bm{\mathrm{x}}_{k})$
(8)

In the remainder of this section, let $(\psi_{k},\bm{\mathrm{x}}_{k},y_{k})$
be a _misclassified_ example. If it is positive (that is, $y_{k}=1$), then it
is predicted as either infeasible or suboptimal by $M(\theta)$. If it is
feasible, then it is sufficient to make it optimal. This can be achieved by
either increasing the estimated cost of $\bm{\mathrm{x}}_{k}$, by excluding
the actual optimum $\bm{\mathrm{x}}_{k}^{*}$ from the feasible region, or by
bringing $\bm{\mathrm{x}}_{k}$ closer to the boundary. This leads to the
following loss:

$\textstyle\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k})+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k}^{*})+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})$
(9)

where the $\min_{j}$ operations select the closest hyperplane.

On the other hand, if $\bm{\mathrm{x}}_{k}$ is positive but infeasible, then
we have to enlarge the feasible region to make it feasible. This is
accomplished by penalizing the distance between $\bm{\mathrm{x}}_{k}$ and all
the hyperplanes that exclude $\bm{\mathrm{x}}_{k}$ from the feasible region
using the following loss:

$\textstyle\sum_{j}\mathbbm{1}\\!\left\\{\bm{\mathrm{a}}_{j}^{\top}\bm{\mathrm{x}}_{k}>b_{j}\right\\}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})$
(10)

Finally, if $\bm{\mathrm{x}}_{k}$ is negative ($y_{k}=0$) – but classified as
positive – then we want to make it either sub-optimal or infeasible. This can
be achieved by increasing its cost or by adapting the feasible region so that
it excludes this example, giving:

$\textstyle\exp(-|\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k})|)+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})$
(11)

Note that we use exponential just to make sure that the loss is lower bounded
by 0. The full surrogate loss $\tilde{L}_{S}(\theta)$ is obtained by combining
the various cases, as follows:

$\displaystyle\tilde{L}_{S}(\theta):=\frac{1}{s}\sum_{k=1}^{s}$
$\displaystyle\begin{cases}\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k})+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k}^{*})+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})\quad&\text{if}\
\bm{\mathrm{A}}\bm{\mathrm{x}}_{k}\leq\bm{\mathrm{b}}\land y_{k}=1\\\
\sum_{j}\mathbbm{1}\\!\left\\{\bm{\mathrm{a}}_{j}^{\top}\bm{\mathrm{x}}_{k}>b_{j}\right\\}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})\qquad\qquad&\text{if}\
\bm{\mathrm{A}}\bm{\mathrm{x}}_{k}\not\leq\bm{\mathrm{b}}\land y_{k}=1\\\
\exp(-|\mathrm{reg}_{\theta}(\bm{\mathrm{x}}_{k})|)+\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})\quad&\text{if}\
\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}_{k}^{*}=\bm{\mathrm{c}}^{\top}\bm{\mathrm{x}}_{k}\;\land\\\
&\quad\bm{\mathrm{A}}\bm{\mathrm{x}}_{k}\leq\bm{\mathrm{b}}\land
y_{k}=0\end{cases}$

This surrogate loss is inspired by but not identical to the one given by
Paulus  _et al._ [11]. There are three core differences. First, Eq. 9 includes
a term $\min_{j}\mathrm{dist}_{j}(\bm{\mathrm{x}}_{k})$ whose aim is to move
the boundaries closer to $\bm{\mathrm{x}}_{k}$, as an optimal solution for
MILP lies close to the boundary. Second, our surrogate loss includes a term
for mis-classified negative examples, integrated through Eq. 11. Finally, we
integrate the contextual information in the surrogate loss by defining
$\bm{\mathrm{x}}_{k}^{*}$ as an optimal solution in the context $\psi_{k}$.
Apart from these technical differences, another major difference is in the
setting in which we use this loss function. Paulus  _et al._ focus on end-to-
end learning, for instance learning constraints from given textual
descriptions. However, our focus is to use this loss to learn MILPs from
contextual examples.

###  3.2 Searching for a MILP

The goal of missle is to find a program $M(\theta)$ that minimizes the 0-1
loss defined in Eq 6. However, the major barrier here is the continuous search
space. To tackle this we propose a variant of SLS guided by the gradient of
the surrogate loss defined above.

The backbone of all SLS strategies is a heuristic search procedure that
iteratively picks a promising candidate in the neighborhood
$\mathcal{N}(\theta)$ of the current candidate $\theta$, while injecting
randomness in the search to escape local optima. The challenge is how to
define a neighborhood that contains promising candidates and allows the search
algorithm to quickly reach the low-loss regions of the search space. To this
end, we exploit the fact that the surrogate loss $\tilde{L}_{S}$ is
differentiable w.r.t. $\theta$ to design a small set of promising neighbors,
as follows. Each $\theta$ has three neighbours defined by the following moves:

  * •

Perturb the cost vector $\bm{\mathrm{c}}$ by taking a single gradient descent
step of length $\lambda$ while leaving $\bm{\mathrm{A}}$ and $\bm{\mathrm{b}}$
untouched:
$\bm{\mathrm{c}}\leftarrow\bm{\mathrm{c}}-\lambda\nabla_{\bm{\mathrm{c}}}\tilde{L}_{S}(\theta)$.

  * •

Similarly, rotating the hard constraints by performing gradient descent w.r.t.
$\bm{\mathrm{A}}$:
$\bm{\mathrm{A}}\leftarrow\bm{\mathrm{A}}-\lambda\nabla_{\bm{\mathrm{A}}}\tilde{L}_{S}(\theta)$.

  * •

Translate the hard constraints by updating the offsets $\bm{\mathrm{b}}$:
$\bm{\mathrm{b}}\leftarrow\bm{\mathrm{b}}-\lambda\nabla_{\bm{\mathrm{b}}}\tilde{L}_{S}(\theta)$.

In each iteration of the SLS procedure, the next hypothesis is chosen
greedily, picking the candidate
$\theta^{\prime}\in\mathcal{N}(\theta,S,\lambda)$ with minimal _true_ loss
$L_{S}(\theta^{\prime})$. Notice that this is different from the gradient
step, which is based on the surrogate loss $\tilde{L}_{S}$ instead. The
intuition is twofold. On the one hand, the gradient is cheap to compute and
points towards higher-quality candidates, while on the other the SLS procedure
smartly picks among the candidates bypassing any approximations induced by the
surrogate loss. Another advantage of this solution is that it naturally
supports exploring continuous search spaces, whereas most SLS strategies focus
on discrete ones.

We make use of two other minor refinements. First, the learning rate $\lambda$
is adapted during the search, and more specifically it is set close to 1 when
the loss is high and slowly decreased towards 0 as the loss decreases, more
formally: $\textstyle\lambda=\frac{1}{2}\
/\sqrt{\max\\{100\cdot(1-L_{S}(\theta)),1\\}}$. The idea is to take larger
steps so to quickly escape high-loss regions while carefully exploring the
more promising areas. We also normalize both the direction of optimisation
$\bm{\mathrm{c}}$ and the hyperplanes $\bm{\mathrm{A}}$ and $\bm{\mathrm{b}}$
after each step, thus regularizing the learning problem.

###  3.3 MISSLE

The pseudo-code for missle is given in Algorithm 1. It starts with an initial
candidate which is generated by first finding the convex hull of the positive
points in the data, and then randomly picking $m$ sides of this convex hull to
define the initial feasible region, while a random vector is chosen to be the
direction of optimisation. The rest of the code simply iterates through the
neighbourhood picking the best candidate in each iteration, while randomly
restarting with probability $p$, which helps the algorithm in avoiding a local
minima.

Algorithm 1 The missle algorithm. Inputs: data set $S$, max constraints $m$,
learning rate $\lambda$, restart prob. $p$, cutoff $t$, max accuracy $\alpha$.

$\theta\leftarrow initialCandidate(S,m)$,
$\theta_{\text{best}}\leftarrow\theta$

while $\mathrm{runtime}<t$ and $\mathrm{accuracy}(\theta,S)<\alpha$ do

with probability $p$ do

$\theta\leftarrow initialCandidate(S,m)$ $\triangleright$ restart

otherwise

$\theta\leftarrow\operatorname*{argmin}_{\theta^{\prime}\in\mathcal{N}(\theta,S,\lambda)}L_{S}(\theta^{\prime})$
$\triangleright$ best neighbour

if $L_{S}(\theta)<L_{S}(\theta_{\text{best}})$ then

$\theta_{\text{best}}\leftarrow\theta$ $\triangleright$ track best-so-far

return $\theta_{\text{best}}$

##  4 Experiments

We answer empirically the following research questions:

  * •

Q1: How does the performance change over time?

  * •

Q2: Does missle learn high quality models?

  * •

Q3: How does missle compare to pure SGD and SLS approaches?

To answer these questions, we used missle to recover a set of synthetic MILPs
from contextual examples sampled from them and compared its hybrid search
strategy to two natural baselines: stochastic local search (SLS) and
stochastic gradient descent (SGD). The baseline using SGD can be seen as an
extension of the ideas presented by Paulus  _et al._ to learn in our setting.

###  4.1 Experiment Description

To generate the training data, we first randomly generated 5 different ground-
truth models $M^{*}$, each with 5 variables and 5 hard constraints. For each
$M^{*}$, a dataset $S$ was collected by first sampling 250 random contexts and
then taking 1 positive and 2 negative examples from each context. For each
model $M^{*}$, we generated 5 different set of data by changing the seed of
randomization.

The quality of the learned model $M$ was captured by measuring recall,
precision, infeasibility, and regret. Recall tells us what percentage of the
true feasible region is covered by the learned model, while precision tells us
what part of the learned feasible region is actually correct. Infeasibility
gives us the percentage of the optimal solutions in $M$ that are infeasible in
$M^{*}$, while regret measures the quality of the optima in $M^{*}$ as defined
in Equation 8. Naturally, a better model is characterised by higher value of
recall and precision and lower value of infeasibility and regret.

Figure 2: Combining gradient and SLS in missle leads to better performance
(higher recall and precision, lower regret) compared to using them
individually. The only exception is that SLS shows better performance in terms
of infeasibility, however, this is because it learns a very restrictive model,
as is suggested by the low recall value.

###  4.2 Results and Discussion

The results are shown in Figure 2. The x-axis in each plot represents the
cutoff time, which is the maximum time an algorithm is allowed to run before
producing a learnt model. The y-axis for regret is logarithmic to make the
differences more clear. As expected, increasing the cutoff time leads to
better results, specially in terms of infeasibility and regret. With a cutoff
time of 60 minutes, missle achieves $80\%$ recall and $83\%$ precision with
infeasibility $\sim 20\%$ and regret $\sim 2\%$, hence $Q2$ can be answered in
affirmative. To answer $Q3$, we compared missle with the two baselines based
on SGD and SLS, the comparison clearly shows that missle outperforms both
baselines. The only exception is that SLS shows better performance in terms of
infeasibility when the cutoff time is low, however, this is because it learns
a very restrictive model, as is suggested by the low recall value. SLS also
has more than three times the regret attained by missle. Hence, it can be
clearly concluded that combining SLS and SGD in missle leads to better
performance compared to using each individually.

##  5 Related Work

Our work is motivated by advancements in constraint learning [6] and in
particular by Kumar  _et al._ [7], who introduced the problem of learning MAX-
SAT models from contextual examples. Our work extends these ideas to
continuous-discrete optimization. Kumar  _et al._ cast the learning problem
itself as a MILP. This strategy, while principled, can be computationally
challenging. In contrast, missle leverages a hybrid strategy that combines
elements of combinatorial and gradient-based optimization. One advantage is
that missle naturally supports anytime learning.

Typical constraint learning methods [6] – like ConAcq [12] and ModelSeeker
[13] – focus on acquiring constraints in higher-level languages than MILP, but
lack support for cost functions. Those approaches that do support learning
soft constraints require the candidate constraints to be enumerated upfront,
which is not possible in our discrete-continuous setting [14].

Most approaches to learning MILPs from data either learn the cost function or
the hard constraints, but not both. Pawlak and Krawiec [15] acquire the
feasibility polytope from positive and negative examples by encoding the
learning problem itself as a MILP. Schede  _et al._ [16] acquire the
feasibility polytope using a similar strategy, but – building on work on
learning Satisfiability Modulo Theory formulas [17] and decision trees [18]
and on syntax-guided synthesis [19] – implement an incremental learning loop
that achieves much improved efficiency. Approaches for learning polyhedral
classifiers find a convex polytope that separates positive and negative
examples, often by a large margin [20, 21, 22, 23], but do not learn a cost
function. This is not a detail: negative examples in their classification
setting are known to be infeasible, while in ours they can be either
infeasible or suboptimal. This introduces a credit attribution problem that
these approaches are not designed to handle.

There are two notable exceptions. One is the work of Tan  _et al._ [24], which
acquires linear programs using stochastic gradient descent (SGD). Their
technique, however, requires to differentiate through the solver, and this
cannot be done for MILPs. A second one is the work of Paulus  _et al._ [11],
which learns integer programs from examples using SGD and a surrogate loss.
missle uses a similar surrogate loss that however explicitly supports negative
examples, as discussed in Section 3. Another major difference is that – as
shown by our experiments – our hybrid optimization strategy outperforms pure
SGD.

Most importantly, none of the works mentioned above support contextual
examples. Because of this, they are bound to learn sub-par MILPs when applied
to contextual data.

##  6 Conclusion

We introduced the problem of learning MILPs from contextual examples as well
as missle, a practical approach that combines stochastic local search with
gradient-based guidance. Our preliminary evaluation shows that missle
outperforms two natural competitors in terms of scalability and model quality.

This work can be improved and extended in several directions. First and
foremost, a more extensive evaluation is needed. Second, missle should be sped
up by integrating the incremental learning strategy of [16, 17] in which a
model is learned from progressively larger subsets of examples, stopping
whenever the improvement in score saturates. Third, it will be interesting to
see the attribution of positive and negative examples in the learning process,
we believe positive examples carry much more information compared to a
negative example, hence it might be beneficiary to learn from only positive
examples, however this needs more extensive experiments. Finally, if meta-
information about which negatives are infeasible and which ones are sub-
optimal is available, however this information is often not known and thus
missle does not use this information, we will work on a new algorithm that can
utilise this extra information and check the impact on the performance.

### Acknowledgments

This work has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (grant
agreement No. [694980] SYNTH: Synthesising Inductive Data Models). The
research of Stefano Teso was partially supported by TAILOR, a project funded
by EU Horizon 2020 research and innovation programme under GA No 952215.

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##  .12 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan${}^{\textrm{\textdagger}}$, A. Tumasyan Institut für
Hochenergiephysik, Wien, Austria
W. Adam, J.W. Andrejkovic, T. Bergauer, S. Chatterjee, M. Dragicevic, A.
Escalante Del Valle, R. Frühwirth1, M. Jeitler1, N. Krammer, L. Lechner, D.
Liko, I. Mikulec, F.M. Pitters, J. Schieck1, R. Schöfbeck, M. Spanring, S.
Templ, W. Waltenberger, C.-E. Wulz1 Institute for Nuclear Problems, Minsk,
Belarus
V. Chekhovsky, A. Litomin, V. Makarenko Universiteit Antwerpen, Antwerpen,
Belgium
M.R. Darwish2, E.A. De Wolf, X. Janssen, T. Kello3, A. Lelek, H. Rejeb Sfar,
P. Van Mechelen, S. Van Putte, N. Van Remortel Vrije Universiteit Brussel,
Brussel, Belgium
F. Blekman, E.S. Bols, J. D’Hondt, J. De Clercq, M. Delcourt, S. Lowette, S.
Moortgat, A. Morton, D. Müller, A.R. Sahasransu, S. Tavernier, W. Van Doninck,
P. Van Mulders Université Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, B. Clerbaux, G. De Lentdecker, L. Favart, A. Grebenyuk,
A.K. Kalsi, K. Lee, I. Makarenko, L. Moureaux, L. Pétré, A. Popov, N. Postiau,
E. Starling, L. Thomas, C. Vander Velde, P. Vanlaer, D. Vannerom, L. Wezenbeek
Ghent University, Ghent, Belgium
T. Cornelis, D. Dobur, M. Gruchala, G. Mestdach, M. Niedziela, C. Roskas, K.
Skovpen, M. Tytgat, W. Verbeke, B. Vermassen, M. Vit Université Catholique de
Louvain, Louvain-la-Neuve, Belgium
A. Bethani, G. Bruno, F. Bury, C. Caputo, P. David, C. Delaere, I.S. Donertas,
A. Giammanco, V. Lemaitre, K. Mondal, J. Prisciandaro, A. Taliercio, M.
Teklishyn, P. Vischia, S. Wertz, S. Wuyckens Centro Brasileiro de Pesquisas
Fisicas, Rio de Janeiro, Brazil
G.A. Alves, C. Hensel, A. Moraes Universidade do Estado do Rio de Janeiro, Rio
de Janeiro, Brazil
W.L. Aldá Júnior, M. Barroso Ferreira Filho, H. BRANDAO MALBOUISSON, W.
Carvalho, J. Chinellato4, E.M. Da Costa, G.G. Da Silveira5, D. De Jesus
Damiao, S. Fonseca De Souza, J. Martins6, D. Matos Figueiredo, C. Mora
Herrera, K. Mota Amarilo, L. Mundim, H. Nogima, P. Rebello Teles, L.J. Sanchez
Rosas, A. Santoro, S.M. Silva Do Amaral, A. Sznajder, M. Thiel, F. Torres Da
Silva De Araujo, A. Vilela Pereira Universidade Estadual Paulista a,
Universidade Federal do ABC b, São Paulo, Brazil
C.A. Bernardesa,a, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M.
Gregoresa,b, D.S. Lemosa, P.G. Mercadantea,b, S.F. Novaesa, Sandra S. Padulaa
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria
A. Aleksandrov, G. Antchev, I. Atanasov, R. Hadjiiska, P. Iaydjiev, M.
Misheva, M. Rodozov, M. Shopova, G. Sultanov University of Sofia, Sofia,
Bulgaria
A. Dimitrov, T. Ivanov, L. Litov, B. Pavlov, P. Petkov, A. Petrov Beihang
University, Beijing, China
T. Cheng, W. Fang3, Q. Guo, T. Javaid7, M. Mittal, H. Wang, L. Yuan Department
of Physics, Tsinghua University, Beijing, China
M. Ahmad, G. Bauer, C. Dozen8, Z. Hu, Y. Wang, K. Yi9,10 Institute of High
Energy Physics, Beijing, China
E. Chapon, G.M. Chen7, H.S. Chen7, M. Chen, A. Kapoor, D. Leggat, H. Liao,
Z.-A. LIU7, R. Sharma, A. Spiezia, J. Tao, J. Thomas-wilsker, J. Wang, H.
Zhang, S. Zhang7, J. Zhao State Key Laboratory of Nuclear Physics and
Technology, Peking University, Beijing, China
A. Agapitos, Y. Ban, C. Chen, Q. Huang, A. Levin, Q. Li, M. Lu, X. Lyu, Y.
Mao, S.J. Qian, D. Wang, Q. Wang, J. Xiao Sun Yat-Sen University, Guangzhou,
China
Z. You Institute of Modern Physics and Key Laboratory of Nuclear Physics and
Ion-beam Application (MOE) - Fudan University, Shanghai, China
X. Gao3, H. Okawa Zhejiang University, Hangzhou, China
M. Xiao Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C. Florez, J. Fraga, A. Sarkar, M.A. Segura Delgado
Universidad de Antioquia, Medellin, Colombia
J. Jaramillo, J. Mejia Guisao, F. Ramirez, J.D. Ruiz Alvarez, C.A. Salazar
González, N. Vanegas Arbelaez University of Split, Faculty of Electrical
Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
D. Giljanovic, N. Godinovic, D. Lelas, I. Puljak University of Split, Faculty
of Science, Split, Croatia
Z. Antunovic, M. Kovac, T. Sculac Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, D. Majumder, M. Roguljic, A. Starodumov11, T. Susa
University of Cyprus, Nicosia, Cyprus
A. Attikis, E. Erodotou, A. Ioannou, G. Kole, M. Kolosova, S. Konstantinou, J.
Mousa, C. Nicolaou, F. Ptochos, P.A. Razis, H. Rykaczewski, H. Saka Charles
University, Prague, Czech Republic
M. Finger12, M. Finger Jr.12, A. Kveton, J. Tomsa Escuela Politecnica
Nacional, Quito, Ecuador
E. Ayala Universidad San Francisco de Quito, Quito, Ecuador
E. Carrera Jarrin Academy of Scientific Research and Technology of the Arab
Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
S. Abu Zeid13, S. Khalil14, E. Salama15,13 Center for High Energy Physics
(CHEP-FU), Fayoum University, El-Fayoum, Egypt
M.A. Mahmoud, Y. Mohammed National Institute of Chemical Physics and
Biophysics, Tallinn, Estonia
S. Bhowmik, A. Carvalho Antunes De Oliveira, R.K. Dewanjee, K. Ehataht, M.
Kadastik, J. Pata, M. Raidal, C. Veelken Department of Physics, University of
Helsinki, Helsinki, Finland
P. Eerola, L. Forthomme, H. Kirschenmann, K. Osterberg, M. Voutilainen
Helsinki Institute of Physics, Helsinki, Finland
E. Brücken, F. Garcia, J. Havukainen, V. Karimäki, M.S. Kim, R. Kinnunen, T.
Lampén, K. Lassila-Perini, S. Lehti, T. Lindén, H. Siikonen, E. Tuominen, J.
Tuominiemi Lappeenranta University of Technology, Lappeenranta, Finland
P. Luukka, H. Petrow, T. Tuuva IRFU, CEA, Université Paris-Saclay, Gif-sur-
Yvette, France
C. Amendola, M. Besancon, F. Couderc, M. Dejardin, D. Denegri, J.L. Faure, F.
Ferri, S. Ganjour, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry,
B. Lenzi, E. Locci, J. Malcles, J. Rander, A. Rosowsky, M.Ö. Sahin, A. Savoy-
Navarro16, M. Titov, G.B. Yu Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole
Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
S. Ahuja, F. Beaudette, M. Bonanomi, A. Buchot Perraguin, P. Busson, C.
Charlot, O. Davignon, B. Diab, G. Falmagne, R. Granier de Cassagnac, A.
Hakimi, I. Kucher, A. Lobanov, C. Martin Perez, M. Nguyen, C. Ochando, P.
Paganini, J. Rembser, R. Salerno, J.B. Sauvan, Y. Sirois, A. Zabi, A. Zghiche
Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
J.-L. Agram17, J. Andrea, D. Apparu, D. Bloch, G. Bourgatte, J.-M. Brom, E.C.
Chabert, C. Collard, D. Darej, J.-C. Fontaine17, U. Goerlach, C. Grimault,
A.-C. Le Bihan, P. Van Hove Institut de Physique des 2 Infinis de Lyon (IP2I
), Villeurbanne, France
E. Asilar, S. Beauceron, C. Bernet, G. Boudoul, C. Camen, A. Carle, N. Chanon,
D. Contardo, P. Depasse, H. El Mamouni, J. Fay, S. Gascon, M. Gouzevitch, B.
Ille, Sa. Jain, I.B. Laktineh, H. Lattaud, A. Lesauvage, M. Lethuillier, L.
Mirabito, K. Shchablo, L. Torterotot, G. Touquet, M. Vander Donckt, S. Viret
Georgian Technical University, Tbilisi, Georgia
A. Khvedelidze12, Z. Tsamalaidze12 RWTH Aachen University, I. Physikalisches
Institut, Aachen, Germany
L. Feld, K. Klein, M. Lipinski, D. Meuser, A. Pauls, M.P. Rauch, J. Schulz, M.
Teroerde RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
D. Eliseev, M. Erdmann, P. Fackeldey, B. Fischer, S. Ghosh, T. Hebbeker, K.
Hoepfner, H. Keller, L. Mastrolorenzo, M. Merschmeyer, A. Meyer, G. Mocellin,
S. Mondal, S. Mukherjee, D. Noll, A. Novak, T. Pook, A. Pozdnyakov, Y. Rath,
H. Reithler, J. Roemer, A. Schmidt, S.C. Schuler, A. Sharma, S. Wiedenbeck, S.
Zaleski RWTH Aachen University, III. Physikalisches Institut B, Aachen,
Germany
C. Dziwok, G. Flügge, W. Haj Ahmad18, O. Hlushchenko, T. Kress, A. Nowack, C.
Pistone, O. Pooth, D. Roy, H. Sert, A. Stahl19, T. Ziemons Deutsches
Elektronen-Synchrotron, Hamburg, Germany
H. Aarup Petersen, M. Aldaya Martin, P. Asmuss, I. Babounikau, S. Baxter, O.
Behnke, A. Bermúdez Martínez, A.A. Bin Anuar, K. Borras20, V. Botta, D.
Brunner, A. Campbell, A. Cardini, P. Connor, S. Consuegra Rodríguez, V.
Danilov, M.M. Defranchis, L. Didukh, D. Domínguez Damiani, G. Eckerlin, D.
Eckstein, L.I. Estevez Banos, E. Gallo21, A. Geiser, A. Giraldi, A. Grohsjean,
M. Guthoff, A. Harb, A. Jafari22, N.Z. Jomhari, H. Jung, A. Kasem20, M.
Kasemann, H. Kaveh, C. Kleinwort, J. Knolle, D. Krücker, W. Lange, T. Lenz, J.
Lidrych, K. Lipka, W. Lohmann23, T. Madlener, R. Mankel, I.-A. Melzer-
Pellmann, J. Metwally, A.B. Meyer, M. Meyer, J. Mnich, A. Mussgiller, V.
Myronenko, Y. Otarid, D. Pérez Adán, S.K. Pflitsch, D. Pitzl, A. Raspereza, A.
Saggio, A. Saibel, M. Savitskyi, V. Scheurer, C. Schwanenberger, A. Singh,
R.E. Sosa Ricardo, N. Tonon, O. Turkot, A. Vagnerini, M. Van De Klundert, R.
Walsh, D. Walter, Y. Wen, K. Wichmann, C. Wissing, S. Wuchterl, O. Zenaiev, R.
Zlebcik University of Hamburg, Hamburg, Germany
R. Aggleton, S. Bein, L. Benato, A. Benecke, K. De Leo, T. Dreyer, M. Eich, F.
Feindt, A. Fröhlich, C. Garbers, E. Garutti, P. Gunnellini, J. Haller, A.
Hinzmann, A. Karavdina, G. Kasieczka, R. Klanner, R. Kogler, V. Kutzner, J.
Lange, T. Lange, A. Malara, A. Nigamova, K.J. Pena Rodriguez, O. Rieger, P.
Schleper, M. Schröder, J. Schwandt, D. Schwarz, J. Sonneveld, H. Stadie, G.
Steinbrück, A. Tews, B. Vormwald, I. Zoi Karlsruher Institut fuer Technologie,
Karlsruhe, Germany
J. Bechtel, T. Berger, E. Butz, R. Caspart, T. Chwalek, W. De Boer, A.
Dierlamm, A. Droll, K. El Morabit, N. Faltermann, K. Flöh, M. Giffels, J.o.
Gosewisch, A. Gottmann, F. Hartmann19, C. Heidecker, U. Husemann, I. Katkov24,
P. Keicher, R. Koppenhöfer, S. Maier, M. Metzler, S. Mitra, Th. Müller, M.
Musich, M. Neukum, G. Quast, K. Rabbertz, J. Rauser, D. Savoiu, D. Schäfer, M.
Schnepf, D. Seith, I. Shvetsov, H.J. Simonis, R. Ulrich, J. Van Der Linden,
R.F. Von Cube, M. Wassmer, M. Weber, S. Wieland, R. Wolf, S. Wozniewski, S.
Wunsch Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos,
Aghia Paraskevi, Greece
G. Anagnostou, P. Asenov, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas,
G. Paspalaki, A. Stakia National and Kapodistrian University of Athens,
Athens, Greece
M. Diamantopoulou, D. Karasavvas, G. Karathanasis, P. Kontaxakis, C.K. Koraka,
A. Manousakis-katsikakis, A. Panagiotou, I. Papavergou, N. Saoulidou, K.
Theofilatos, E. Tziaferi, K. Vellidis, E. Vourliotis National Technical
University of Athens, Athens, Greece
G. Bakas, K. Kousouris, I. Papakrivopoulos, G. Tsipolitis, A. Zacharopoulou
University of Ioánnina, Ioánnina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, N. Manthos, I.
Papadopoulos, J. Strologas MTA-ELTE Lendület CMS Particle and Nuclear Physics
Group, Eötvös Loránd University, Budapest, Hungary
M. Csanad, M.M.A. Gadallah25, S. Lökös26, P. Major, K. Mandal, A. Mehta, G.
Pasztor, A.J. Rádl, O. Surányi, G.I. Veres Wigner Research Centre for Physics,
Budapest, Hungary
M. Bartók27, G. Bencze, C. Hajdu, D. Horvath28, F. Sikler, V. Veszpremi, G.
Vesztergombi${}^{\textrm{\textdagger}}$ Institute of Nuclear Research ATOMKI,
Debrecen, Hungary
S. Czellar, J. Karancsi27, J. Molnar, Z. Szillasi, D. Teyssier Institute of
Physics, University of Debrecen, Debrecen, Hungary
P. Raics, Z.L. Trocsanyi29, B. Ujvari Eszterhazy Karoly University, Karoly
Robert Campus, Gyongyos, Hungary
T. Csorgo30, F. Nemes30, T. Novak Indian Institute of Science (IISc),
Bangalore, India
S. Choudhury, J.R. Komaragiri, D. Kumar, L. Panwar, P.C. Tiwari National
Institute of Science Education and Research, HBNI, Bhubaneswar, India
S. Bahinipati31, D. Dash, C. Kar, P. Mal, T. Mishra, V.K. Muraleedharan Nair
Bindhu32, A. Nayak32, P. Saha, N. Sur, S.K. Swain Panjab University,
Chandigarh, India
S. Bansal, S.B. Beri, V. Bhatnagar, G. Chaudhary, S. Chauhan, N. Dhingra33, R.
Gupta, A. Kaur, S. Kaur, P. Kumari, M. Meena, K. Sandeep, J.B. Singh, A.K.
Virdi University of Delhi, Delhi, India
A. Ahmed, A. Bhardwaj, B.C. Choudhary, R.B. Garg, M. Gola, S. Keshri, A.
Kumar, M. Naimuddin, P. Priyanka, K. Ranjan, A. Shah Saha Institute of Nuclear
Physics, HBNI, Kolkata, India
M. Bharti34, R. Bhattacharya, S. Bhattacharya, D. Bhowmik, S. Dutta, S. Ghosh,
B. Gomber35, M. Maity36, S. Nandan, P. Palit, P.K. Rout, G. Saha, B. Sahu, S.
Sarkar, M. Sharan, B. Singh34, S. Thakur34 Indian Institute of Technology
Madras, Madras, India
P.K. Behera, S.C. Behera, P. Kalbhor, A. Muhammad, R. Pradhan, P.R. Pujahari,
A. Sharma, A.K. Sikdar Bhabha Atomic Research Centre, Mumbai, India
D. Dutta, V. Jha, V. Kumar, D.K. Mishra, K. Naskar37, P.K. Netrakanti, L.M.
Pant, P. Shukla Tata Institute of Fundamental Research-A, Mumbai, India
T. Aziz, S. Dugad, G.B. Mohanty, U. Sarkar Tata Institute of Fundamental
Research-B, Mumbai, India
S. Banerjee, S. Bhattacharya, R. Chudasama, M. Guchait, S. Karmakar, S. Kumar,
G. Majumder, K. Mazumdar, S. Mukherjee, D. Roy Indian Institute of Science
Education and Research (IISER), Pune, India
S. Dube, B. Kansal, S. Pandey, A. Rane, A. Rastogi, S. Sharma Department of
Physics, Isfahan University of Technology, Isfahan, Iran
H. Bakhshiansohi38, M. Zeinali39 Institute for Research in Fundamental
Sciences (IPM), Tehran, Iran
S. Chenarani40, S.M. Etesami, M. Khakzad, M. Mohammadi Najafabadi University
College Dublin, Dublin, Ireland
M. Felcini, M. Grunewald INFN Sezione di Bari a, Università di Bari b,
Politecnico di Bari c, Bari, Italy
M. Abbresciaa,b, R. Alya,b,41, C. Arutaa,b, A. Colaleoa, D. Creanzaa,c, N. De
Filippisa,c, M. De Palmaa,b, A. Di Florioa,b, A. Di Pilatoa,b, W.
Elmetenaweea,b, L. Fiorea, A. Gelmia,b, M. Gula, G. Iasellia,c, M. Incea,b, S.
Lezkia,b, G. Maggia,c, M. Maggia, I. Margjekaa,b, V. Mastrapasquaa,b, J.A.
Merlina, S. Mya,b, S. Nuzzoa,b, A. Pompilia,b, G. Pugliesea,c, A. Ranieria, G.
Selvaggia,b, L. Silvestrisa, F.M. Simonea,b, R. Vendittia, P. Verwilligena
INFN Sezione di Bologna a, Università di Bologna b, Bologna, Italy
G. Abbiendia, C. Battilanaa,b, D. Bonacorsia,b, L. Borgonovia, S. Braibant-
Giacomellia,b, L. Brigliadoria, R. Campaninia,b, P. Capiluppia,b, A.
Castroa,b, F.R. Cavalloa, C. Cioccaa, M. Cuffiania,b, G.M. Dallavallea, T.
Diotalevia,b, F. Fabbria, A. Fanfania,b, E. Fontanesia,b, P. Giacomellia, L.
Giommia,b, C. Grandia, L. Guiduccia,b, F. Iemmia,b, S. Lo Meoa,42, S.
Marcellinia, G. Masettia, F.L. Navarriaa,b, A. Perrottaa, F. Primaveraa,b,
A.M. Rossia,b, T. Rovellia,b, G.P. Sirolia,b, N. Tosia INFN Sezione di Catania
a, Università di Catania b, Catania, Italy
S. Albergoa,b,43, S. Costaa,b,43, A. Di Mattiaa, R. Potenzaa,b, A.
Tricomia,b,43, C. Tuvea,b INFN Sezione di Firenze a, Università di Firenze b,
Firenze, Italy
G. Barbaglia, A. Cassesea, R. Ceccarellia,b, V. Ciullia,b, C. Civininia, R.
D’Alessandroa,b, F. Fioria,b, E. Focardia,b, G. Latinoa,b, P. Lenzia,b, M.
Lizzoa,b, M. Meschinia, S. Paolettia, R. Seiditaa,b, G. Sguazzonia, L.
Viliania INFN Laboratori Nazionali di Frascati, Frascati, Italy
L. Benussi, S. Bianco, D. Piccolo INFN Sezione di Genova a, Università di
Genova b, Genova, Italy
M. Bozzoa,b, F. Ferroa, R. Mulargiaa,b, E. Robuttia, S. Tosia,b INFN Sezione
di Milano-Bicocca a, Università di Milano-Bicocca b, Milano, Italy
A. Benagliaa, F. Brivioa,b, F. Cetorellia,b, V. Cirioloa,b,19, F. De Guioa,b,
M.E. Dinardoa,b, P. Dinia, S. Gennaia, A. Ghezzia,b, P. Govonia,b, L.
Guzzia,b, M. Malbertia, S. Malvezzia, A. Massironia, D. Menascea, F. Montia,b,
L. Moronia, M. Paganonia,b, D. Pedrinia, S. Ragazzia,b, N. Redaellia, T.
Tabarelli de Fatisa,b, D. Valsecchia,b,19, D. Zuoloa,b INFN Sezione di Napoli
a, Università di Napoli ’Federico II’ b, Napoli, Italy, Università della
Basilicata c, Potenza, Italy, Università G. Marconi d, Roma, Italy
S. Buontempoa, N. Cavalloa,c, A. De Iorioa,b, F. Fabozzia,c, A.O.M. Iorioa,b,
L. Listaa,b, S. Meolaa,d,19, P. Paoluccia,19, B. Rossia, C. Sciaccaa,b INFN
Sezione di Padova a, Università di Padova b, Padova, Italy, Università di
Trento c, Trento, Italy
P. Azzia, N. Bacchettaa, D. Biselloa,b, P. Bortignona, A. Bragagnoloa,b, R.
Carlina,b, P. Checchiaa, P. De Castro Manzanoa, T. Dorigoa, F. Gasparinia,b,
U. Gasparinia,b, S.Y. Hoha,b, L. Layera,44, M. Margonia,b, A.T. Meneguzzoa,b,
M. Presillaa,b, P. Ronchesea,b, R. Rossina,b, F. Simonettoa,b, G. Stronga, M.
Tosia,b, H. YARARa,b, M. Zanettia,b, P. Zottoa,b, A. Zucchettaa,b, G.
Zumerlea,b INFN Sezione di Pavia a, Università di Pavia b, Pavia, Italy
C. Aime‘a,b, A. Braghieria, S. Calzaferria,b, D. Fiorinaa,b, P. Montagnaa,b,
S.P. Rattia,b, V. Rea, M. Ressegottia,b, C. Riccardia,b, P. Salvinia, I. Vaia,
P. Vituloa,b INFN Sezione di Perugia a, Università di Perugia b, Perugia,
Italy
G.M. Bileia, D. Ciangottinia,b, L. Fanòa,b, P. Laricciaa,b, G. Mantovania,b,
V. Mariania,b, M. Menichellia, F. Moscatellia, A. Piccinellia,b, A. Rossia,b,
A. Santocchiaa,b, D. Spigaa, T. Tedeschia,b INFN Sezione di Pisa a, Università
di Pisa b, Scuola Normale Superiore di Pisa c, Pisa Italy, Università di Siena
d, Siena, Italy
P. Azzurria, G. Bagliesia, V. Bertacchia,c, L. Bianchinia, T. Boccalia, E.
Bossini, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa, M.R. Di Domenicoa,d, S.
Donatoa, A. Giassia, M.T. Grippoa, F. Ligabuea,c, E. Mancaa,c, G. Mandorlia,c,
A. Messineoa,b, F. Pallaa, G. Ramirez-Sancheza,c, A. Rizzia,b, G. Rolandia,c,
S. Roy Chowdhurya,c, A. Scribanoa, N. Shafieia,b, P. Spagnoloa, R. Tenchinia,
G. Tonellia,b, N. Turinia,d, A. Venturia, P.G. Verdinia INFN Sezione di Roma
a, Sapienza Università di Roma b, Rome, Italy
F. Cavallaria, M. Cipriania,b, D. Del Rea,b, E. Di Marcoa, M. Diemoza, E.
Longoa,b, P. Meridiania, G. Organtinia,b, F. Pandolfia, R. Paramattia,b, C.
Quarantaa,b, S. Rahatloua,b, C. Rovellia, F. Santanastasioa,b, L. Soffia,b, R.
Tramontanoa,b INFN Sezione di Torino a, Università di Torino b, Torino, Italy,
Università del Piemonte Orientale c, Novara, Italy
N. Amapanea,b, R. Arcidiaconoa,c, S. Argiroa,b, M. Arneodoa,c, N. Bartosika,
R. Bellana,b, A. Belloraa,b, J. Berenguer Antequeraa,b, C. Biinoa, A.
Cappatia,b, N. Cartigliaa, S. Comettia, M. Costaa,b, R. Covarellia,b, N.
Demariaa, B. Kiania,b, F. Leggera, C. Mariottia, S. Masellia, E. Migliorea,b,
V. Monacoa,b, E. Monteila,b, M. Montenoa, M.M. Obertinoa,b, G. Ortonaa, L.
Pachera,b, N. Pastronea, M. Pelliccionia, G.L. Pinna Angionia,b, M. Ruspaa,c,
R. Salvaticoa,b, K. Shchelinaa,b, F. Sivieroa,b, V. Solaa, A. Solanoa,b, D.
Soldia,b, A. Staianoa, M. Tornagoa,b, D. Trocinoa,b INFN Sezione di Trieste a,
Università di Trieste b, Trieste, Italy
S. Belfortea, V. Candelisea,b, M. Casarsaa, F. Cossuttia, A. Da Rolda,b, G.
Della Riccaa,b, F. Vazzolera,b Kyungpook National University, Daegu, Korea
S. Dogra, C. Huh, B. Kim, D.H. Kim, G.N. Kim, J. Lee, S.W. Lee, C.S. Moon,
Y.D. Oh, S.I. Pak, B.C. Radburn-Smith, S. Sekmen, Y.C. Yang Chonnam National
University, Institute for Universe and Elementary Particles, Kwangju, Korea
H. Kim, D.H. Moon Hanyang University, Seoul, Korea
B. Francois, T.J. Kim, J. Park Korea University, Seoul, Korea
S. Cho, S. Choi, Y. Go, B. Hong, K. Lee, K.S. Lee, J. Lim, J. Park, S.K. Park,
J. Yoo Kyung Hee University, Department of Physics, Seoul, Republic of Korea
J. Goh, A. Gurtu Sejong University, Seoul, Korea
H.S. Kim, Y. Kim Seoul National University, Seoul, Korea
J. Almond, J.H. Bhyun, J. Choi, S. Jeon, J. Kim, J.S. Kim, S. Ko, H. Kwon, H.
Lee, S. Lee, B.H. Oh, M. Oh, S.B. Oh, H. Seo, U.K. Yang, I. Yoon University of
Seoul, Seoul, Korea
D. Jeon, J.H. Kim, B. Ko, J.S.H. Lee, I.C. Park, Y. Roh, D. Song, I.J. Watson
Yonsei University, Department of Physics, Seoul, Korea
S. Ha, H.D. Yoo Sungkyunkwan University, Suwon, Korea
Y. Choi, Y. Jeong, H. Lee, Y. Lee, I. Yu College of Engineering and
Technology, American University of the Middle East (AUM), Egaila, Kuwait
T. Beyrouthy, Y. Maghrbi Riga Technical University, Riga, Latvia
V. Veckalns45 Vilnius University, Vilnius, Lithuania
M. Ambrozas, A. Juodagalvis, A. Rinkevicius, G. Tamulaitis, A. Vaitkevicius
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur,
Malaysia
W.A.T. Wan Abdullah, M.N. Yusli, Z. Zolkapli Universidad de Sonora (UNISON),
Hermosillo, Mexico
J.F. Benitez, A. Castaneda Hernandez, J.A. Murillo Quijada, L. Valencia Palomo
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
G. Ayala, H. Castilla-Valdez, E. De La Cruz-Burelo, I. Heredia-De La Cruz46,
R. Lopez-Fernandez, C.A. Mondragon Herrera, D.A. Perez Navarro, A. Sanchez-
Hernandez Universidad Iberoamericana, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera, M. Ramirez-Garcia, F. Vazquez Valencia
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada University of Montenegro,
Podgorica, Montenegro
J. Mijuskovic47, N. Raicevic University of Auckland, Auckland, New Zealand
D. Krofcheck University of Canterbury, Christchurch, New Zealand
S. Bheesette, P.H. Butler National Centre for Physics, Quaid-I-Azam
University, Islamabad, Pakistan
A. Ahmad, M.I. Asghar, A. Awais, M.I.M. Awan, H.R. Hoorani, W.A. Khan, S.
Qazi, M.A. Shah, M. Shoaib AGH University of Science and Technology Faculty of
Computer Science, Electronics and Telecommunications, Krakow, Poland
V. Avati, L. Grzanka, M. Malawski National Centre for Nuclear Research,
Swierk, Poland
H. Bialkowska, M. Bluj, B. Boimska, T. Frueboes, M. Górski, M. Kazana, M.
Szleper, P. Traczyk, P. Zalewski Institute of Experimental Physics, Faculty of
Physics, University of Warsaw, Warsaw, Poland
K. Bunkowski, K. Doroba, A. Kalinowski, M. Konecki, J. Krolikowski, M. Walczak
Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa,
Portugal
M. Araujo, P. Bargassa, D. Bastos, A. Boletti, P. Faccioli, M. Gallinaro, J.
Hollar, N. Leonardo, T. Niknejad, J. Seixas, O. Toldaiev, J. Varela Joint
Institute for Nuclear Research, Dubna, Russia
S. Afanasiev, D. Budkouski, P. Bunin, M. Gavrilenko, I. Golutvin, I. Gorbunov,
A. Kamenev, V. Karjavine, A. Lanev, A. Malakhov, V. Matveev48,49, V. Palichik,
V. Perelygin, M. Savina, D. Seitova, V. Shalaev, S. Shmatov, S. Shulha, V.
Smirnov, O. Teryaev, N. Voytishin, A. Zarubin, I. Zhizhin Petersburg Nuclear
Physics Institute, Gatchina (St. Petersburg), Russia
G. Gavrilov, V. Golovtcov, Y. Ivanov, V. Kim50, E. Kuznetsova51, V. Murzin, V.
Oreshkin, I. Smirnov, D. Sosnov, V. Sulimov, L. Uvarov, S. Volkov, A. Vorobyev
Institute for Nuclear Research, Moscow, Russia
Yu. Andreev, A. Dermenev, S. Gninenko, N. Golubev, A. Karneyeu, M. Kirsanov,
N. Krasnikov, A. Pashenkov, G. Pivovarov, D.
Tlisov${}^{\textrm{\textdagger}}$, A. Toropin Institute for Theoretical and
Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’,
Moscow, Russia
V. Epshteyn, V. Gavrilov, N. Lychkovskaya, A. Nikitenko52, V. Popov, G.
Safronov, A. Spiridonov, A. Stepennov, M. Toms, E. Vlasov, A. Zhokin Moscow
Institute of Physics and Technology, Moscow, Russia
T. Aushev National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
R. Chistov53, M. Danilov54, A. Oskin, P. Parygin, S. Polikarpov54 P.N. Lebedev
Physical Institute, Moscow, Russia
V. Andreev, M. Azarkin, I. Dremin, M. Kirakosyan, A. Terkulov Skobeltsyn
Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow,
Russia
A. Belyaev, E. Boos, V. Bunichev, M. Dubinin55, L. Dudko, A. Gribushin, V.
Klyukhin, O. Kodolova, I. Lokhtin, S. Obraztsov, M. Perfilov, S. Petrushanko,
V. Savrin Novosibirsk State University (NSU), Novosibirsk, Russia
V. Blinov56, T. Dimova56, L. Kardapoltsev56, I. Ovtin56, Y. Skovpen56
Institute for High Energy Physics of National Research Centre ‘Kurchatov
Institute’, Protvino, Russia
I. Azhgirey, I. Bayshev, V. Kachanov, A. Kalinin, D. Konstantinov, V. Petrov,
R. Ryutin, A. Sobol, S. Troshin, N. Tyurin, A. Uzunian, A. Volkov National
Research Tomsk Polytechnic University, Tomsk, Russia
A. Babaev, V. Okhotnikov, L. Sukhikh Tomsk State University, Tomsk, Russia
V. Borchsh, V. Ivanchenko, E. Tcherniaev University of Belgrade: Faculty of
Physics and VINCA Institute of Nuclear Sciences, Belgrade, Serbia
P. Adzic57, M. Dordevic, P. Milenovic, J. Milosevic, V. Milosevic Centro de
Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid,
Spain
M. Aguilar-Benitez, J. Alcaraz Maestre, A. Álvarez Fernández, I. Bachiller, M.
Barrio Luna, Cristina F. Bedoya, C.A. Carrillo Montoya, M. Cepeda, M. Cerrada,
N. Colino, B. De La Cruz, A. Delgado Peris, J.P. Fernández Ramos, J. Flix,
M.C. Fouz, O. Gonzalez Lopez, S. Goy Lopez, J.M. Hernandez, M.I. Josa, J. León
Holgado, D. Moran, Á. Navarro Tobar, A. Pérez-Calero Yzquierdo, J. Puerta
Pelayo, I. Redondo, L. Romero, S. Sánchez Navas, M.S. Soares, L. Urda Gómez,
C. Willmott Universidad Autónoma de Madrid, Madrid, Spain
J.F. de Trocóniz, R. Reyes-Almanza Universidad de Oviedo, Instituto
Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA),
Oviedo, Spain
B. Alvarez Gonzalez, J. Cuevas, C. Erice, J. Fernandez Menendez, S. Folgueras,
I. Gonzalez Caballero, E. Palencia Cortezon, C. Ramón Álvarez, J. Ripoll Sau,
V. Rodríguez Bouza, A. Trapote Instituto de Física de Cantabria (IFCA), CSIC-
Universidad de Cantabria, Santander, Spain
J.A. Brochero Cifuentes, I.J. Cabrillo, A. Calderon, B. Chazin Quero, J.
Duarte Campderros, M. Fernandez, C. Fernandez Madrazo, P.J. Fernández Manteca,
A. García Alonso, G. Gomez, C. Martinez Rivero, P. Martinez Ruiz del Arbol, F.
Matorras, J. Piedra Gomez, C. Prieels, F. Ricci-Tam, T. Rodrigo, A. Ruiz-
Jimeno, L. Scodellaro, N. Trevisani, I. Vila, J.M. Vizan Garcia University of
Colombo, Colombo, Sri Lanka
MK Jayananda, B. Kailasapathy58, D.U.J. Sonnadara, DDC Wickramarathna
University of Ruhuna, Department of Physics, Matara, Sri Lanka
W.G.D. Dharmaratna, K. Liyanage, N. Perera, N. Wickramage CERN, European
Organization for Nuclear Research, Geneva, Switzerland
T.K. Aarrestad, D. Abbaneo, J. Alimena, E. Auffray, G. Auzinger, J. Baechler,
P. Baillon, A.H. Ball, D. Barney, J. Bendavid, N. Beni, M. Bianco, A. Bocci,
E. Brondolin, T. Camporesi, M. Capeans Garrido, G. Cerminara, S.S. Chhibra, L.
Cristella, D. d’Enterria, A. Dabrowski, N. Daci, A. David, A. De Roeck, M.
Deile, R. Di Maria, M. Dobson, M. Dünser, N. Dupont, A. Elliott-Peisert, N.
Emriskova, F. Fallavollita59, D. Fasanella, S. Fiorendi, A. Florent, G.
Franzoni, J. Fulcher, W. Funk, S. Giani, D. Gigi, K. Gill, F. Glege, L.
Gouskos, M. Haranko, J. Hegeman, Y. Iiyama, V. Innocente, T. James, P. Janot,
J. Kaspar, J. Kieseler, M. Komm, N. Kratochwil, C. Lange, S. Laurila, P.
Lecoq, K. Long, C. Lourenço, L. Malgeri, S. Mallios, M. Mannelli, F. Meijers,
S. Mersi, E. Meschi, F. Moortgat, M. Mulders, S. Orfanelli, L. Orsini, F.
Pantaleo19, L. Pape, E. Perez, M. Peruzzi, A. Petrilli, G. Petrucciani, A.
Pfeiffer, M. Pierini, M. Pitt, H. Qu, T. Quast, D. Rabady, A. Racz, M. Rieger,
M. Rovere, H. Sakulin, J. Salfeld-Nebgen, S. Scarfi, C. Schäfer, C. Schwick,
M. Selvaggi, A. Sharma, P. Silva, W. Snoeys, P. Sphicas60, S. Summers, V.R.
Tavolaro, D. Treille, A. Tsirou, G.P. Van Onsem, M. Verzetti, K.A. Wozniak,
W.D. Zeuner Paul Scherrer Institut, Villigen, Switzerland
L. Caminada61, A. Ebrahimi, W. Erdmann, R. Horisberger, Q. Ingram, H.C.
Kaestli, D. Kotlinski, U. Langenegger, M. Missiroli, T. Rohe ETH Zurich -
Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
K. Androsov62, M. Backhaus, P. Berger, A. Calandri, N. Chernyavskaya, A. De
Cosa, G. Dissertori, M. Dittmar, M. Donegà, C. Dorfer, T. Gadek, T.A. Gómez
Espinosa, C. Grab, D. Hits, W. Lustermann, A.-M. Lyon, R.A. Manzoni, M.T.
Meinhard, F. Micheli, F. Nessi-Tedaldi, J. Niedziela, F. Pauss, V. Perovic, G.
Perrin, S. Pigazzini, M.G. Ratti, M. Reichmann, C. Reissel, T. Reitenspiess,
B. Ristic, D. Ruini, D.A. Sanz Becerra, M. Schönenberger, V. Stampf, J.
Steggemann62, R. Wallny, D.H. Zhu Universität Zürich, Zurich, Switzerland
C. Amsler63, C. Botta, D. Brzhechko, M.F. Canelli, A. De Wit, R. Del Burgo,
J.K. Heikkilä, M. Huwiler, A. Jofrehei, B. Kilminster, S. Leontsinis, A.
Macchiolo, P. Meiring, V.M. Mikuni, U. Molinatti, I. Neutelings, G. Rauco, A.
Reimers, P. Robmann, S. Sanchez Cruz, K. Schweiger, Y. Takahashi National
Central University, Chung-Li, Taiwan
C. Adloff64, C.M. Kuo, W. Lin, A. Roy, T. Sarkar36, S.S. Yu National Taiwan
University (NTU), Taipei, Taiwan
L. Ceard, P. Chang, Y. Chao, K.F. Chen, P.H. Chen, W.-S. Hou, Y.y. Li, R.-S.
Lu, E. Paganis, A. Psallidas, A. Steen, E. Yazgan, P.r. Yu Chulalongkorn
University, Faculty of Science, Department of Physics, Bangkok, Thailand
B. Asavapibhop, C. Asawatangtrakuldee, N. Srimanobhas Çukurova University,
Physics Department, Science and Art Faculty, Adana, Turkey
F. Boran, S. Damarseckin65, Z.S. Demiroglu, F. Dolek, I. Dumanoglu66, E.
Eskut, G. Gokbulut, Y. Guler, E. Gurpinar Guler67, I. Hos68, C. Isik, E.E.
Kangal69, O. Kara, A. Kayis Topaksu, U. Kiminsu, G. Onengut, K. Ozdemir70, A.
Polatoz, A.E. Simsek, B. Tali71, U.G. Tok, S. Turkcapar, I.S. Zorbakir, C.
Zorbilmez Middle East Technical University, Physics Department, Ankara, Turkey
B. Isildak72, G. Karapinar73, K. Ocalan74, M. Yalvac75 Bogazici University,
Istanbul, Turkey
B. Akgun, I.O. Atakisi, E. Gülmez, M. Kaya76, O. Kaya77, Ö. Özçelik, S.
Tekten78, E.A. Yetkin79 Istanbul Technical University, Istanbul, Turkey
A. Cakir, K. Cankocak66, Y. Komurcu, S. Sen80 Istanbul University, Istanbul,
Turkey
F. Aydogmus Sen, S. Cerci71, B. Kaynak, S. Ozkorucuklu, D. Sunar Cerci71
Institute for Scintillation Materials of National Academy of Science of
Ukraine, Kharkov, Ukraine
B. Grynyov National Scientific Center, Kharkov Institute of Physics and
Technology, Kharkov, Ukraine
L. Levchuk University of Bristol, Bristol, United Kingdom
E. Bhal, S. Bologna, J.J. Brooke, A. Bundock, E. Clement, D. Cussans, H.
Flacher, J. Goldstein, G.P. Heath, H.F. Heath, L. Kreczko, B. Krikler, S.
Paramesvaran, T. Sakuma, S. Seif El Nasr-Storey, V.J. Smith, N. Stylianou81,
J. Taylor, A. Titterton Rutherford Appleton Laboratory, Didcot, United Kingdom
K.W. Bell, A. Belyaev82, C. Brew, R.M. Brown, D.J.A. Cockerill, K.V. Ellis, K.
Harder, S. Harper, J. Linacre, K. Manolopoulos, D.M. Newbold, E. Olaiya, D.
Petyt, T. Reis, T. Schuh, C.H. Shepherd-Themistocleous, A. Thea, I.R. Tomalin,
T. Williams Imperial College, London, United Kingdom
R. Bainbridge, P. Bloch, S. Bonomally, J. Borg, S. Breeze, O. Buchmuller, V.
Cepaitis, G.S. Chahal83, D. Colling, P. Dauncey, G. Davies, M. Della Negra, S.
Fayer, G. Fedi, G. Hall, M.H. Hassanshahi, G. Iles, J. Langford, L. Lyons,
A.-M. Magnan, S. Malik, A. Martelli, J. Nash84, V. Palladino, M. Pesaresi,
D.M. Raymond, A. Richards, A. Rose, E. Scott, C. Seez, A. Shtipliyski, A.
Tapper, K. Uchida, T. Virdee19, N. Wardle, S.N. Webb, D. Winterbottom, A.G.
Zecchinelli Brunel University, Uxbridge, United Kingdom
J.E. Cole, A. Khan, P. Kyberd, C.K. Mackay, I.D. Reid, L. Teodorescu, S. Zahid
Baylor University, Waco, USA
S. Abdullin, A. Brinkerhoff, B. Caraway, J. Dittmann, K. Hatakeyama, A.R.
Kanuganti, B. McMaster, N. Pastika, S. Sawant, C. Smith, C. Sutantawibul, J.
Wilson Catholic University of America, Washington, DC, USA
R. Bartek, A. Dominguez, R. Uniyal, A.M. Vargas Hernandez The University of
Alabama, Tuscaloosa, USA
A. Buccilli, O. Charaf, S.I. Cooper, D. Di Croce, S.V. Gleyzer, C. Henderson,
C.U. Perez, P. Rumerio, C. West Boston University, Boston, USA
A. Akpinar, A. Albert, D. Arcaro, C. Cosby, Z. Demiragli, D. Gastler, J.
Rohlf, K. Salyer, D. Sperka, D. Spitzbart, I. Suarez, S. Yuan, D. Zou Brown
University, Providence, USA
G. Benelli, B. Burkle, X. Coubez20, D. Cutts, Y.t. Duh, M. Hadley, U. Heintz,
J.M. Hogan85, K.H.M. Kwok, E. Laird, G. Landsberg, K.T. Lau, J. Lee, J. Luo,
M. Narain, S. Sagir86, E. Usai, W.Y. Wong, X. Yan, D. Yu, W. Zhang University
of California, Davis, Davis, USA
C. Brainerd, R. Breedon, M. Calderon De La Barca Sanchez, M. Chertok, J.
Conway, P.T. Cox, R. Erbacher, F. Jensen, O. Kukral, R. Lander, M. Mulhearn,
D. Pellett, D. Taylor, M. Tripathi, Y. Yao, F. Zhang University of California,
Los Angeles, USA
M. Bachtis, R. Cousins, A. Dasgupta, A. Datta, D. Hamilton, J. Hauser, M.
Ignatenko, M.A. Iqbal, T. Lam, N. Mccoll, W.A. Nash, S. Regnard, D. Saltzberg,
C. Schnaible, B. Stone, V. Valuev University of California, Riverside,
Riverside, USA
K. Burt, Y. Chen, R. Clare, J.W. Gary, G. Hanson, G. Karapostoli, O.R. Long,
N. Manganelli, M. Olmedo Negrete, W. Si, S. Wimpenny, Y. Zhang University of
California, San Diego, La Jolla, USA
J.G. Branson, P. Chang, S. Cittolin, S. Cooperstein, N. Deelen, J. Duarte, R.
Gerosa, L. Giannini, D. Gilbert, J. Guiang, V. Krutelyov, R. Lee, J. Letts, M.
Masciovecchio, S. May, S. Padhi, M. Pieri, B.V. Sathia Narayanan, V. Sharma,
M. Tadel, A. Vartak, F. Würthwein, Y. Xiang, A. Yagil University of
California, Santa Barbara - Department of Physics, Santa Barbara, USA
N. Amin, C. Campagnari, M. Citron, A. Dorsett, V. Dutta, J. Incandela, M.
Kilpatrick, B. Marsh, H. Mei, A. Ovcharova, M. Quinnan, J. Richman, U. Sarica,
D. Stuart, S. Wang California Institute of Technology, Pasadena, USA
A. Bornheim, O. Cerri, I. Dutta, J.M. Lawhorn, N. Lu, J. Mao, H.B. Newman, J.
Ngadiuba, T.Q. Nguyen, M. Spiropulu, J.R. Vlimant, C. Wang, S. Xie, Z. Zhang,
R.Y. Zhu Carnegie Mellon University, Pittsburgh, USA
J. Alison, M.B. Andrews, T. Ferguson, T. Mudholkar, M. Paulini, I. Vorobiev
University of Colorado Boulder, Boulder, USA
J.P. Cumalat, W.T. Ford, E. MacDonald, R. Patel, A. Perloff, K. Stenson, K.A.
Ulmer, S.R. Wagner Cornell University, Ithaca, USA
J. Alexander, Y. Cheng, J. Chu, D.J. Cranshaw, K. Mcdermott, J. Monroy, J.R.
Patterson, D. Quach, A. Ryd, W. Sun, S.M. Tan, Z. Tao, J. Thom, P. Wittich, M.
Zientek Fermi National Accelerator Laboratory, Batavia, USA
M. Albrow, M. Alyari, G. Apollinari, A. Apresyan, A. Apyan, S. Banerjee,
L.A.T. Bauerdick, A. Beretvas, D. Berry, J. Berryhill, P.C. Bhat, K. Burkett,
J.N. Butler, A. Canepa, G.B. Cerati, H.W.K. Cheung, F. Chlebana, M. Cremonesi,
K.F. Di Petrillo, V.D. Elvira, J. Freeman, Z. Gecse, L. Gray, D. Green, S.
Grünendahl, O. Gutsche, R.M. Harris, R. Heller, T.C. Herwig, J. Hirschauer, B.
Jayatilaka, S. Jindariani, M. Johnson, U. Joshi, P. Klabbers, T. Klijnsma, B.
Klima, M.J. Kortelainen, S. Lammel, D. Lincoln, R. Lipton, T. Liu, J. Lykken,
C. Madrid, K. Maeshima, C. Mantilla, D. Mason, P. McBride, P. Merkel, S.
Mrenna, S. Nahn, V. O’Dell, V. Papadimitriou, K. Pedro, C. Pena55, O.
Prokofyev, F. Ravera, A. Reinsvold Hall, L. Ristori, B. Schneider, E. Sexton-
Kennedy, N. Smith, A. Soha, L. Spiegel, S. Stoynev, J. Strait, L. Taylor, S.
Tkaczyk, N.V. Tran, L. Uplegger, E.W. Vaandering, H.A. Weber, A. Woodard
University of Florida, Gainesville, USA
D. Acosta, P. Avery, D. Bourilkov, L. Cadamuro, V. Cherepanov, F. Errico, R.D.
Field, D. Guerrero, B.M. Joshi, M. Kim, J. Konigsberg, A. Korytov, K.H. Lo, K.
Matchev, N. Menendez, G. Mitselmakher, D. Rosenzweig, K. Shi, J. Sturdy, J.
Wang, E. Yigitbasi, X. Zuo Florida State University, Tallahassee, USA
T. Adams, A. Askew, D. Diaz, R. Habibullah, S. Hagopian, V. Hagopian, K.F.
Johnson, R. Khurana, T. Kolberg, G. Martinez, H. Prosper, C. Schiber, R.
Yohay, J. Zhang Florida Institute of Technology, Melbourne, USA
M.M. Baarmand, S. Butalla, T. Elkafrawy13, M. Hohlmann, R. Kumar Verma, D.
Noonan, M. Rahmani, M. Saunders, F. Yumiceva University of Illinois at Chicago
(UIC), Chicago, USA
M.R. Adams, L. Apanasevich, H. Becerril Gonzalez, R. Cavanaugh, X. Chen, S.
Dittmer, O. Evdokimov, C.E. Gerber, D.A. Hangal, D.J. Hofman, C. Mills, G. Oh,
T. Roy, M.B. Tonjes, N. Varelas, J. Viinikainen, X. Wang, Z. Wu, Z. Ye The
University of Iowa, Iowa City, USA
M. Alhusseini, K. Dilsiz87, S. Durgut, R.P. Gandrajula, M. Haytmyradov, V.
Khristenko, O.K. Köseyan, J.-P. Merlo, A. Mestvirishvili88, A. Moeller, J.
Nachtman, H. Ogul89, Y. Onel, F. Ozok90, A. Penzo, C. Snyder, E. Tiras91, J.
Wetzel Johns Hopkins University, Baltimore, USA
O. Amram, B. Blumenfeld, L. Corcodilos, J. Davis, M. Eminizer, A.V. Gritsan,
S. Kyriacou, P. Maksimovic, J. Roskes, M. Swartz, T.Á. Vámi The University of
Kansas, Lawrence, USA
C. Baldenegro Barrera, P. Baringer, A. Bean, A. Bylinkin, T. Isidori, S.
Khalil, J. King, G. Krintiras, A. Kropivnitskaya, C. Lindsey, N. Minafra, M.
Murray, C. Rogan, C. Royon, S. Sanders, E. Schmitz, J.D. Tapia Takaki, Q.
Wang, J. Williams, G. Wilson Kansas State University, Manhattan, USA
S. Duric, A. Ivanov, K. Kaadze, D. Kim, Y. Maravin, T. Mitchell, A. Modak, K.
Nam Lawrence Livermore National Laboratory, Livermore, USA
F. Rebassoo, D. Wright University of Maryland, College Park, USA
E. Adams, A. Baden, O. Baron, A. Belloni, S.C. Eno, Y. Feng, N.J. Hadley, S.
Jabeen, R.G. Kellogg, T. Koeth, A.C. Mignerey, S. Nabili, M. Seidel, A. Skuja,
S.C. Tonwar, L. Wang, K. Wong Massachusetts Institute of Technology,
Cambridge, USA
D. Abercrombie, R. Bi, S. Brandt, W. Busza, I.A. Cali, Y. Chen, M. D’Alfonso,
G. Gomez Ceballos, M. Goncharov, P. Harris, M. Hu, M. Klute, D. Kovalskyi, J.
Krupa, Y.-J. Lee, B. Maier, A.C. Marini, C. Mironov, C. Paus, D. Rankin, C.
Roland, G. Roland, Z. Shi, G.S.F. Stephans, K. Tatar, J. Wang, Z. Wang, B.
Wyslouch University of Minnesota, Minneapolis, USA
R.M. Chatterjee, A. Evans, P. Hansen, J. Hiltbrand, Sh. Jain, M. Krohn, Y.
Kubota, Z. Lesko, J. Mans, M. Revering, R. Rusack, R. Saradhy, N. Schroeder,
N. Strobbe, M.A. Wadud University of Mississippi, Oxford, USA
J.G. Acosta, S. Oliveros University of Nebraska-Lincoln, Lincoln, USA
K. Bloom, M. Bryson, S. Chauhan, D.R. Claes, C. Fangmeier, L. Finco, F. Golf,
J.R. González Fernández, C. Joo, I. Kravchenko, J.E. Siado, G.R.
Snow${}^{\textrm{\textdagger}}$, W. Tabb, F. Yan State University of New York
at Buffalo, Buffalo, USA
G. Agarwal, H. Bandyopadhyay, L. Hay, I. Iashvili, A. Kharchilava, C. McLean,
D. Nguyen, J. Pekkanen, S. Rappoccio, A. Williams Northeastern University,
Boston, USA
G. Alverson, E. Barberis, C. Freer, Y. Haddad, A. Hortiangtham, J. Li, G.
Madigan, B. Marzocchi, D.M. Morse, V. Nguyen, T. Orimoto, A. Parker, L.
Skinnari, A. Tishelman-Charny, T. Wamorkar, B. Wang, A. Wisecarver, D. Wood
Northwestern University, Evanston, USA
S. Bhattacharya, J. Bueghly, Z. Chen, A. Gilbert, T. Gunter, K.A. Hahn, N.
Odell, M.H. Schmitt, K. Sung, M. Velasco University of Notre Dame, Notre Dame,
USA
R. Band, R. Bucci, N. Dev, R. Goldouzian, M. Hildreth, K. Hurtado Anampa, C.
Jessop, K. Lannon, N. Loukas, N. Marinelli, I. Mcalister, F. Meng, K. Mohrman,
Y. Musienko48, R. Ruchti, P. Siddireddy, M. Wayne, A. Wightman, M. Wolf, M.
Zarucki, L. Zygala The Ohio State University, Columbus, USA
B. Bylsma, B. Cardwell, L.S. Durkin, B. Francis, C. Hill, A. Lefeld, B.L.
Winer, B.R. Yates Princeton University, Princeton, USA
F.M. Addesa, B. Bonham, P. Das, G. Dezoort, P. Elmer, A. Frankenthal, B.
Greenberg, N. Haubrich, S. Higginbotham, A. Kalogeropoulos, G. Kopp, S. Kwan,
D. Lange, M.T. Lucchini, D. Marlow, K. Mei, I. Ojalvo, J. Olsen, C. Palmer, D.
Stickland, C. Tully University of Puerto Rico, Mayaguez, USA
S. Malik, S. Norberg Purdue University, West Lafayette, USA
A.S. Bakshi, V.E. Barnes, R. Chawla, S. Das, L. Gutay, M. Jones, A.W. Jung, S.
Karmarkar, M. Liu, G. Negro, N. Neumeister, C.C. Peng, S. Piperov, A. Purohit,
J.F. Schulte, M. Stojanovic16, J. Thieman, F. Wang, R. Xiao, W. Xie Purdue
University Northwest, Hammond, USA
J. Dolen, N. Parashar Rice University, Houston, USA
A. Baty, S. Dildick, K.M. Ecklund, S. Freed, F.J.M. Geurts, A. Kumar, W. Li,
B.P. Padley, R. Redjimi, J. Roberts${}^{\textrm{\textdagger}}$, W. Shi, A.G.
Stahl Leiton University of Rochester, Rochester, USA
A. Bodek, P. de Barbaro, R. Demina, J.L. Dulemba, C. Fallon, T. Ferbel, M.
Galanti, A. Garcia-Bellido, O. Hindrichs, A. Khukhunaishvili, E. Ranken, R.
Taus Rutgers, The State University of New Jersey, Piscataway, USA
B. Chiarito, J.P. Chou, A. Gandrakota, Y. Gershtein, E. Halkiadakis, A. Hart,
M. Heindl, E. Hughes, S. Kaplan, O. Karacheban23, I. Laflotte, A. Lath, R.
Montalvo, K. Nash, M. Osherson, S. Salur, S. Schnetzer, S. Somalwar, R. Stone,
S.A. Thayil, S. Thomas, H. Wang University of Tennessee, Knoxville, USA
H. Acharya, A.G. Delannoy, S. Spanier Texas A&M University, College Station,
USA
O. Bouhali92, M. Dalchenko, A. Delgado, R. Eusebi, J. Gilmore, T. Huang, T.
Kamon93, H. Kim, S. Luo, S. Malhotra, R. Mueller, D. Overton, D. Rathjens, A.
Safonov Texas Tech University, Lubbock, USA
N. Akchurin, J. Damgov, V. Hegde, S. Kunori, K. Lamichhane, S.W. Lee, T.
Mengke, S. Muthumuni, T. Peltola, S. Undleeb, I. Volobouev, Z. Wang, A.
Whitbeck Vanderbilt University, Nashville, USA
E. Appelt, S. Greene, A. Gurrola, W. Johns, C. Maguire, A. Melo, H. Ni, K.
Padeken, F. Romeo, P. Sheldon, S. Tuo, J. Velkovska University of Virginia,
Charlottesville, USA
M.W. Arenton, B. Cox, G. Cummings, J. Hakala, R. Hirosky, M. Joyce, A.
Ledovskoy, A. Li, C. Neu, B. Tannenwald, E. Wolfe Wayne State University,
Detroit, USA
P.E. Karchin, N. Poudyal, P. Thapa University of Wisconsin - Madison, Madison,
WI, USA
K. Black, T. Bose, J. Buchanan, C. Caillol, S. Dasu, I. De Bruyn, P.
Everaerts, F. Fienga, C. Galloni, H. He, M. Herndon, A. Hervé, U. Hussain, A.
Lanaro, A. Loeliger, R. Loveless, J. Madhusudanan Sreekala, A. Mallampalli, A.
Mohammadi, D. Pinna, A. Savin, V. Shang, V. Sharma, W.H. Smith, D. Teague, S.
Trembath-reichert, W. Vetens †: Deceased
1: Also at Vienna University of Technology, Vienna, Austria
2: Also at Institute of Basic and Applied Sciences, Faculty of Engineering,
Arab Academy for Science, Technology and Maritime Transport, Alexandria,
Egypt, Alexandria, Egypt
3: Also at Université Libre de Bruxelles, Bruxelles, Belgium
4: Also at Universidade Estadual de Campinas, Campinas, Brazil
5: Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil
6: Also at UFMS, Nova Andradina, Brazil
7: Also at University of Chinese Academy of Sciences, Beijing, China
8: Also at Department of Physics, Tsinghua University, Beijing, China,
Beijing, China
9: Also at Nanjing Normal University Department of Physics, Nanjing, China
10: Now at The University of Iowa, Iowa City, USA
11: Also at Institute for Theoretical and Experimental Physics named by A.I.
Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
12: Also at Joint Institute for Nuclear Research, Dubna, Russia
13: Also at Ain Shams University, Cairo, Egypt
14: Also at Zewail City of Science and Technology, Zewail, Egypt
15: Also at British University in Egypt, Cairo, Egypt
16: Also at Purdue University, West Lafayette, USA
17: Also at Université de Haute Alsace, Mulhouse, France
18: Also at Erzincan Binali Yildirim University, Erzincan, Turkey
19: Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
20: Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
21: Also at University of Hamburg, Hamburg, Germany
22: Also at Department of Physics, Isfahan University of Technology, Isfahan,
Iran, Isfahan, Iran
23: Also at Brandenburg University of Technology, Cottbus, Germany
24: Also at Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State
University, Moscow, Russia
25: Also at Physics Department, Faculty of Science, Assiut University, Assiut,
Egypt
26: Also at Eszterhazy Karoly University, Karoly Robert Campus, Gyongyos,
Hungary
27: Also at Institute of Physics, University of Debrecen, Debrecen, Hungary,
Debrecen, Hungary
28: Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary
29: Also at MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary, Budapest, Hungary
30: Also at Wigner Research Centre for Physics, Budapest, Hungary
31: Also at IIT Bhubaneswar, Bhubaneswar, India, Bhubaneswar, India
32: Also at Institute of Physics, Bhubaneswar, India
33: Also at G.H.G. Khalsa College, Punjab, India
34: Also at Shoolini University, Solan, India
35: Also at University of Hyderabad, Hyderabad, India
36: Also at University of Visva-Bharati, Santiniketan, India
37: Also at Indian Institute of Technology (IIT), Mumbai, India
38: Also at Deutsches Elektronen-Synchrotron, Hamburg, Germany
39: Also at Sharif University of Technology, Tehran, Iran
40: Also at Department of Physics, University of Science and Technology of
Mazandaran, Behshahr, Iran
41: Now at INFN Sezione di Bari a, Università di Bari b, Politecnico di Bari
c, Bari, Italy
42: Also at Italian National Agency for New Technologies, Energy and
Sustainable Economic Development, Bologna, Italy
43: Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia,
Catania, Italy
44: Also at Università di Napoli ’Federico II’, NAPOLI, Italy
45: Also at Riga Technical University, Riga, Latvia, Riga, Latvia
46: Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
47: Also at IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
48: Also at Institute for Nuclear Research, Moscow, Russia
49: Now at National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
50: Also at St. Petersburg State Polytechnical University, St. Petersburg,
Russia
51: Also at University of Florida, Gainesville, USA
52: Also at Imperial College, London, United Kingdom
53: Also at Moscow Institute of Physics and Technology, Moscow, Russia,
Moscow, Russia
54: Also at P.N. Lebedev Physical Institute, Moscow, Russia
55: Also at California Institute of Technology, Pasadena, USA
56: Also at Budker Institute of Nuclear Physics, Novosibirsk, Russia
57: Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia
58: Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri
Lanka
59: Also at INFN Sezione di Pavia a, Università di Pavia b, Pavia, Italy,
Pavia, Italy
60: Also at National and Kapodistrian University of Athens, Athens, Greece
61: Also at Universität Zürich, Zurich, Switzerland
62: Also at Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
63: Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria,
Vienna, Austria
64: Also at Laboratoire d’Annecy-le-Vieux de Physique des Particules,
IN2P3-CNRS, Annecy-le-Vieux, France
65: Also at Şırnak University, Sirnak, Turkey
66: Also at Near East University, Research Center of Experimental Health
Science, Nicosia, Turkey
67: Also at Konya Technical University, Konya, Turkey
68: Also at Istanbul University - Cerraphasa, Faculty of Engineering,
Istanbul, Turkey
69: Also at Mersin University, Mersin, Turkey
70: Also at Piri Reis University, Istanbul, Turkey
71: Also at Adiyaman University, Adiyaman, Turkey
72: Also at Ozyegin University, Istanbul, Turkey
73: Also at Izmir Institute of Technology, Izmir, Turkey
74: Also at Necmettin Erbakan University, Konya, Turkey
75: Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey, Yozgat, Turkey
76: Also at Marmara University, Istanbul, Turkey
77: Also at Milli Savunma University, Istanbul, Turkey
78: Also at Kafkas University, Kars, Turkey
79: Also at Istanbul Bilgi University, Istanbul, Turkey
80: Also at Hacettepe University, Ankara, Turkey
81: Also at Vrije Universiteit Brussel, Brussel, Belgium
82: Also at School of Physics and Astronomy, University of Southampton,
Southampton, United Kingdom
83: Also at IPPP Durham University, Durham, United Kingdom
84: Also at Monash University, Faculty of Science, Clayton, Australia
85: Also at Bethel University, St. Paul, Minneapolis, USA, St. Paul, USA
86: Also at Karamanoğlu Mehmetbey University, Karaman, Turkey
87: Also at Bingol University, Bingol, Turkey
88: Also at Georgian Technical University, Tbilisi, Georgia
89: Also at Sinop University, Sinop, Turkey
90: Also at Mimar Sinan University, Istanbul, Istanbul, Turkey
91: Also at Erciyes University, KAYSERI, Turkey
92: Also at Texas A&M University at Qatar, Doha, Qatar
93: Also at Kyungpook National University, Daegu, Korea, Daegu, Korea