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Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the…

Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…

Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…

Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…

This paper is a short report about our work for the primal task in the Machine Learning for Combinatorial Optimization NeurIPS 2021 Competition. For each dataset of our interest in the competition, we propose customized primal heuristic…

The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…

The EURO/ROADEF 2010 Challenge aimed to schedule the maintenance and refueling operations of French nuclear power plants, ranking the approaches in competition for the quality of primal solutions. This paper justifies the high quality of…

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit…

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…

Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on…

Although the use of metric fluents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is…

This paper explores reoptimization techniques for solving sequences of similar mixed integer programs (MIPs) more effectively. Traditionally, these MIPs are solved independently, without capitalizing on information from previously solved…

We develop a novel primal heuristic for nonconvex Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs). The method is built around a convex approximation that is dynamically adjusted within a feasibility-pump-style…

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…

Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…

We consider the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure. In this NP-hard problem, a single production plant sends the produced items to replenish warehouses from where they are dispatched…

Mixed-integer optimization solvers often find optimal solutions early in the search, yet spend the majority of computation time proving optimality. We exploit this by learning when to terminate solvers early on distributions of similar…

Minimizing the number of reshuffling operations at maritime container terminals incorporates the Pre-Marshalling Problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing…

We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal…