A Computational Study for Piecewise Linear Relaxations of Mixed-Integer Nonlinear Programs

Solving mixed-integer nonlinear problems by means of piecewise linear relaxations can be a reasonable alternative to the commonly used spatial branch-and-bound. These relaxations have been modeled by various mixed-integer models in recent decades. The idea is to exploit the availability of mature solvers for mixed-integer problems. In this work, we compare different reformulations in terms … Read more

Solving Hard Bi-objective Knapsack Problems Using Deep Reinforcement Learning

We study a class of bi-objective integer programs known as bi-objective knapsack problems (BOKPs). Our research focuses on the development of innovative exact and approximate solution methods for BOKPs by synergizing algorithmic concepts from two distinct domains: multi-objective integer programming and (deep) reinforcement learning. While novel reinforcement learning techniques have been applied successfully to single-objective … Read more

A novel Pareto-optimal cut selection strategy for Benders Decomposition

Decomposition approaches can be used to generate practically efficient solution algorithms for a wide class of optimization problems. For instance, scenario-expanded two-stage stochastic optimization problems can be solved efficiently in practice using Benders Decomposition. The performance of the approach can be influenced by the choice of the cuts that are added during the course of … Read more

An Integer Programming Approach To Subspace Clustering With Missing Data

In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more

Resilient Relay Logistics Network Design: A k-Shortest Path Approach

Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more

DeLuxing: Deep Lagrangian Underestimate Fixing for Column-Generation-Based Exact Methods

In this paper, we propose an innovative variable fixing strategy called deep Lagrangian underestimate fixing (DeLuxing). It is a highly effective approach for removing unnecessary variables in column-generation (CG)-based exact methods used to solve challenging discrete optimization problems commonly encountered in various industries, including vehicle routing problems (VRPs). DeLuxing employs a novel linear programming (LP) … Read more

Affine FR : an effective facial reduction algorithm for semidefinite relaxations of combinatorial problems

\(\) We develop a new method called \emph{affine FR} for recovering Slater’s condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully automatic and only requires a description of the problem. We provide a rigorous analysis of differences between affine FR and the existing … Read more

A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming

One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more

Optimal Multi-Agent Pickup and Delivery Using Branch-and-Cut-and-Price

Given a set of agents and a set of pickup-delivery requests located on a two-dimensional map, the Multi-Agent Pickup and Delivery problem assigns the requests to the agents such that every agent moves from its start location to the locations of its assigned requests and finally to its end location without colliding into any other … Read more