Using the NEOS Server for Solving Two Classes of Optimization Problems

Abstract

NEOS server provides free access to the library of necessary software for solving optimization problems. The effective numerical methods developed can be used for a specific application or for solving a wide range of mathematical programming problems. The article is devoted to researching the possibilities of solving optimization problems using NEOS server on the example of two mathematical programming problems: a linear Boolean programming problem for the well-known m-traveler problem and nonlinear programming problem for a special multiextremal problem on the Stiefel’s manifold. The material of the work is presented in 4 sections. Chapter 1 describes general information about using NEOS server for solving optimization problems and focuses on AMPL mathematical programming language as its component. Comparison of the frequency of use of AMPL, GAMS and other input data formats available on the server was conducted. The second section describes the principle of solving optimization problems using NEOS and provides a list of AMPL-supporting solvers available on the server. Statistics of use frequency of the solvers CPLEX, Gurobi and BARON in comparison with other solvers available on the server, as well as general statistics of the number of solved problems on the server in 2021 are given. Chapter 3 describes linear Boolean programming problems for the m-travelers problem, which is equivalent to the well-known traveling salesman problem. Performance indicators for solving these problems using CPLEX and Gurobi solvers are given. In Chapter 4 a study of nonlinear programming problem for a special multiextremal problem on the Stiefel’s manifold is conducted. General formulation of the problem and the formulation of its partial cases depending on the constraints imposed on vector components are given. The efficiency of solving test cases using BARON solver was investigated depending on the number of vectors and their dimensions. Keywords: optimization, NEOS server, AMPL, NEOS solvers, travelling salesman problem, Stiefel’s manifold.