A comparison between MILP and MINLP approaches to optimal solution of Nonlinear Discrete Transportation Problem

Abstract

Finding an exact optimal solution of the Nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the NDTP. When nonlinearities appear within the criterion of optimization, the NDTP can be formulated directly as a Mixed-Integer Nonlinear Programming (MINLP) task or it can be linearized and converted into a Mixed-Integer Linear Programming (MILP) problem. This paper presents a comparison between MILP and MINLP approaches to exact optimal solution of the NDTP. The comparison is based on obtained results of experiments executed on a set of reference test problems. The paper discusses advantages and limitations of both optimization approaches.

First published online: 10 Jul 2014

Keyword : transportation problems, discrete transporting flows, nonlinear costs, optimization methods, mixed-integer linear programming, mixed-integer nonlinear programming