Theory of Modern Heuristic Optimization

Darwinian evolution is intrinsically a robust search and optimization mechanism. Living organisms demonstrate optimized complex behavior at every level: the cell, the organ, the individual, and the population. The problems that biological species have solved are typified by chaos, chance, temporality, and nonlinear inter-activities. These are also characteristics of problems that have proved to be especially intractable to classic methods of optimization and appear routinely in the area of power systems. The evolutionary process can be applied to these problems, where heuristic solutions are not available or generally lead to unsatisfactory results. As a result, evolutionary algorithms have recently received increased interest, particularly with regard to the manner in which they may be applied for practical problem solving. Evolutionary computation, the term now used to describe the field of investigation that concerns all evolutionary algorithms, offers practical advantages to the researcher facing difficult optimization problems. These advantages are multifold, including the simplicity of the approach, its robust response to changing circumstance , its flexibility, and many other facets. This chapter summarizes some of these advantages, offers a brief review of some parts of evolutionary computation theory, and introduces a new optimization technique that models swarming behavior in insects or schooling in fish. The reader who wants to further review the basic concepts of evolutionary algorithms is referred to Fogel [1–3], Bäck [4], and Michalewicz [5]. A primary advantage of evolutionary computation is that it is conceptually simple. The main flowchart that describes every evolutionary algorithm applied for function optimization is depicted in Fig. 1.1. The algorithm consists of initialization, which may be a purely random sampling of possible solutions, followed by iterative variation and selection in light of a performance index. This figure of merit must assign a numeric value to any possible solution such that two competing solutions can be rank ordered. Finer granularity is not required. Thus, the criterion need not be specified with the precision that is required of some other methods. In particular, no gradient information needs to be presented to the algorithm. Over iterations of FIGURE 1.1 The main flowchart of the vast majority of evolutionary algorithms. A population of candidate solutions to a problem at hand is initialized. This often is accomplished by randomly sampling from the space of possible solutions. New solutions are created by randomly varying existing solutions. This random variation may include mutation and/or recom-bination. Competing solutions are evaluated in light …