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The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the…

This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…

Determining what to eat to satisfy nutritional requirements is one of the oldest optimization problems in operations research, yet existing formulations have two persistent limitations: continuous variables produce impractical fractional…

Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…

Heating, Ventilation, and Air Conditioning (HVAC) is a major electricity end-use with a substantial potential for providing grid services, such as demand response. Harnessing this flexibility requires accurate modeling of the thermal…

The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid…

We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…

Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…

Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition…

In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…

We consider the problem of finding an n-agent joint-policy for the optimal finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new…

It is a well known fact that finite time optimal controllers, such as MPC does not necessarily result in closed loop stable systems. Within the MPC community it is common practice to add a final state constraint and/or a final state penalty…

The cyclic hoist scheduling problem originates in electroplating lines, where a single or multiple hoists transport parts between processing tanks subject to technological constraints. The objective is typically to determine a cyclic…

This paper addresses the Oral Examination Timetabling Problem (OETP) for France's prestigious engineering schools, an organization managed by the Service des Concours Communs Polytechniques (SCCP). The scheduling is highly complex,…

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it…

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs…