Two-row and two-column mixed-integer presolve using hash-based pairing methods

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolving techniques successfully is … Read more

MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library

We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of 5,721 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using … Read more

A Comparison of Nonsmooth, Nonconvex, Constrained Optimization Solvers for the Design of Time-Delay Compensators

We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges … Read more

Largest Small n-Polygons: Numerical Results and Conjectured Optima

LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n >= 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for … Read more

Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems

A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with K* cuts} derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all … Read more

A Review and Comparison of Solvers for Convex MINLP

In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers. As a test set, we have used all MINLP instances classified as convex in the problem library MINLPLib, resulting in a test set of 366 convex … Read more

A computational study of global optimization solvers on two trust region subproblems

One of the relevant research topics to which Chris Floudas contributed was quadratically constrained quadratic programming (QCQP). This paper considers one of the simplest hard cases of QCQP, the two trust region subproblem (TTRS). In this case, one needs to minimize a quadratic function constrained by the intersection of two ellipsoids. The Lagrangian dual of … Read more

A note on using performance and data profiles for training algorithms

It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. Citation ACM Transactions on Mathematical Software, 45:2 (2019), Article 20. Article Download View A note on using performance and data profiles for training … Read more

BASBL: Branch-And-Sandwich BiLevel solver. II. Implementation and computational study with the BASBLib test set

We describe BASBL, our implementation of the deterministic global optimization algorithm Branch-and-Sandwich for nonconvex/nonlinear bilevel problems, within the open-source MINOTAUR framework. The solver incorporates the original Branch-and-Sandwich algorithm and modifications proposed in the first part of this work. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature and … Read more

On the effectiveness of primal and dual heuristics for the transportation problem

The transportation problem is one of the most popular problems in linear programming. Over the course of time a multitude of exact solution methods and heuristics have been proposed. Due to substantial progress of exact solvers since the mid of the last century, the interest in heuristics for the transportation problem over the last few … Read more