Chapter 18 - Global Optimization Concepts and Methods

Abstract

This chapter focuses on presentation and discussion of concepts and methods for the global optimum solutions. It also describes multistart, clustering, control random search, acceptance–rejection, stochastic integration, stochastic zooming, and domain elimination and the basic concepts and ideas underlying various methods for global optimization. Global optimization methods can be divided into two major categories: deterministic and stochastic. This classification is mainly based on whether the method incorporates any stochastic elements to solve the global optimization problem. Deterministic methods find the global minimum by an exhaustive search over the set Sb. This chapter also describes four deterministic methods: covering, zooming, generalized descent, and tunneling. Several stochastic methods have been developed as variations of pure random search. All of the stochastic methods involve random elements to determine the global minimum point, each one trying to reduce the computational burden of pure random search. At the outset, a random sample of points in the set Sb is picked. Then each method manipulates the sample points in a different manner. In some cases the two operations are simultaneous; that is, a random point is picked and manipulated or used before the next one is chosen.