UNCONSTRAINED DISCRETE NONLINEAR PROGRAMMING

Abstract

In this research several search methods for unconstrained nonlinear discrete variable optimization problems have been developed. Many of these new methods are modifications of effective continuous variable search techniques including gradient–free and gradient–based methods. In order to search only over a set of discrete points, the concepts of integer search direction and the subsequential search procedure are introduced. Other developments include regeneration/ acceleration procedures for gradient–based methods and a second level acceleration procedure applicable to both gradient–free and gradient–based methods. These new methods have been compared with each other and existing techniques using test problems with various characteristics, including penalty functions from constrained problems. In all cases, the best results have been obtained from one of the new methods. Moreover, the success of these new methods in finding good solutions in penalty function problems indicates their usefulness in solving engineering design problems.