The simple genetic algorithm-foundations and theory [Book Reviews]

Evolutionary algorithms 1 (EA’s) have been successfully applied to thousands of problems in almost all branches of engineering and science for the last three–four decades. In contrast to their success story, the theoretical understanding of these algorithms is still in its infancy. A theory of EA’s, capable of modeling and predicting their behavior from basic principles, does exist, but it is rudimentary. EA’s are probabilistic algorithms, the analysis of which requires an intimate knowledge of applied probability theory. Considering the last decade in which several attempts have been made to develop theories on EA’s, it becomes clear that there may be different principal roads toward a theoretical understanding. They can be put into the following systematology: 1) using a one-to-one mapping of the EA andthe fitness function to a mathematical theory, 2) using a one-to-one mapping of the EA, but using models of fitness landscapes, 3) using amodelof the EA, but using the real fitness function without simplifications, 4) usingmodelsfor both the EAand the fitness function. For example, the theory based on the schema theorem and the building block hypothesis belongs mainly to 4), and the current development of theory in Beyer [1] belongs mainly to 2). It should be intuitively clear that each of these general roads may have advantages and disadvantages: an analysis based on route 2) should have more predictive power than a more general approach 1). The usefulness of an approach taken can only be assessed in a relative manner. Furthermore, only the future will show which of the approaches are the most prolific ones. This also holds for the book to be reviewed here. Using the systematology given above, Michael D. Vose’s book, The Simple Genetic Algorithm—Foundations and Theory , belongs mainly to category 1). In 19 small chapters, Vose develops his theory of GA’s in finite `-dimensional search spaces for binary as well as general cardinality alphabets. The deductive approach taken starts from a general algorithm, therandom heuristic search (RHS), introduced in Chapter 3. 2