We describe Pyomo, an open source tool for modeling optimization applications in Python. Pyomo can be used to de fine symbolic problems, create concrete problem instances, and solve these instances with standard solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS, but Pyomo’s modeling objects are … Read more
In recent years, there has been an increased literature on so-called Generalized Network Design Problems, such as the Generalized Minimum Spanning Tree Problem and the Generalized Traveling Salesman Problem. In such problems, the node set of a graph is partitioned into clusters, and the feasible solutions must contain one node from each cluster. Up to … Read more
We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature — the cut, boolean quadric, multicut and clique partitioning polytopes — are faces of binary … Read more
We study the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. In \cite{Amico}, the authors … Read more
Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of Scip … Read more
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative … Read more
The n-step mixed integer rounding (MIR) inequalities of Kianfar and Fathi are valid inequalities for the mixed-integer knapsack set that are derived by using periodic n-step MIR functions and define facets for group problems. The mingling and 2-step mingling inequalities of Atamturk and Gunluk are also derived based on MIR and they incorporate upper bounds … Read more
In optimization-based classification model selection, for example when using linear programming formulations, a standard approach is to penalize the L1 norm of some linear functional in order to select sparse models. Instead, we propose a novel integer linear program for sparse classifier selection, generalizing the minimum disagreement hyperplane problem whose complexity has been investigated in … Read more
The NP-hard Maximum Monomial Agreement (MMA) problem consists of finding a single logical conjunction that best fits a weighted dataset of “positive” and “negative” binary vectors. Computing classifiers using boosting methods involves a maximum agreement subproblem at each iteration, although such subproblems are typically solved by heuristic methods. Here, we describe an exact branch and … Read more
The Traveling Salesman Problem with Time Windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within a given time window. We present an extended formulation for the problem based on partitioning the time windows into sub-windows, which we call “buckets”. We … Read more