We introduce a new facility layout problem, the so-called T-Row Facility Layout Problem (TRFLP). The TRFLP consists of a set of one-dimensional departments with pairwise transport weights between them and two orthogonal rows which form a T such that departments in different rows cannot overlap. The aim is to find a non-overlapping assignment of the … Read more
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size. ArticleDownload View PDF
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and material science among others, and are known to be NP-Hard for … Read more
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP … Read more
We translate the algorithmic question of whether to linearize convex Mixed-Integer Quadratic Programming problems (MIQPs) into a classification task, and use machine learning (ML) techniques to tackle it. We represent MIQPs and the linearization decision by careful target and feature engineering. Computational experiments and evaluation metrics are designed to further incorporate the optimization knowledge in … Read more
In this study, we consider the two-echelon location-routing problem with time windows (2E-LRPTW) to address the strategic and tactical decisions of the urban freight transportation. In the rst echelon, freights are delivered from city distribution centers (CDCs) to intermediate facilities, called satellites, in large batches. In the second echelon, goods are consolidated into smaller vehicles … Read more
We describe a simple method to test if a given matrix is copositive by solving a single mixed-integer linear programming (MILP) problem. This methodology requires no special coding to implement and takes advantage of the computational power of modern MILP solvers. Numerical experiments demonstrate that the method is robust and efficient. CitationDept. of Business Analytics, … Read more
This paper presents new structural properties for the Carrier-Vehicle Traveling Salesman Problem. The authors provide a new mixed integer second order conic optimization formulation, with associated optimality cuts based on the structural properties, and an Iterated Local Search (ILS) algorithm. Computational experiments on instances from the literature demonstrate the superiority of the new formulation to … Read more
We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical … Read more
We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more