Strong mixed-integer programming formulations for trained neural networks

We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more

Pattern-based models and a cooperative parallel metaheuristic for high school timetabling problems

High school timetabling problems consist in building periodic timetables for class-teacher meetings considering compulsory and non-compulsory requisites. This family of problems has been widely studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the efficient obtention of optimal or near-optimal solutions is still a challenge for many problems of practical size. In … Read more

n-step cutset inequalities: facets for multi-module capacitated network design problem

Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on links. In network design problems, decisions are made on installation of flow transfer capacities on the links and routing of flow from a set of source nodes to a set of sink nodes through the links. Many … Read more

Enhancing large neighbourhood search heuristics for Benders’ decomposition

A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search … Read more

Interval-based Dynamic Discretization Discovery for Solving the Continuous-Time Service Network Design Problem

We introduce an effective and efficient iterative algorithm for solving the Continuous-Time Service Network Design Problem. The algorithm achieves its efficiency by carefully and dynamically refining partially time-expanded network models so that only a small number of small integer programs, defined over these networks, need to be solved. An extensive computational study shows that the … Read more

New Valid Inequalities for the Fixed-Charge and Single-Node Flow Polytopes

The most effective software packages for solving mixed 0-1 linear programs use strong valid linear inequalities derived from polyhedral theory. We introduce a new procedure which enables one to take known valid inequalities for the knapsack polytope, and convert them into valid inequalities for the fixed-charge and single-node flow polytopes. The resulting inequalities are very … Read more

Dynamic Courier Routing for a Food Delivery Service

Services like Grubhub and UberEats have revolutionized the way that diners can find and order from restaurants. The standard business model for such services, however, allows diners to order from only one restaurant at a time. Inspired by a food delivery service in the southeastern United States, this paper proposes the framework for a more … Read more

Scalable Branching on Dual Decomposition of Stochastic Mixed-Integer Programming Problems

We present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caro e and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including 1) branching on the optimal solutions … Read more

Empirical Bounds on Linear Regions of Deep Rectifier Networks

One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for … Read more

Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative mixed integer linear programming formulations. Our first formulation is based on casting a standard quadratic program … Read more