Multimodal Deceptive Functions

This pap er presents a static analysis of deception in multimodal funct ions. Deception in a bipolar function of unitation (a function with two global optima and a number of decepti ve attractors) is defined, and a set of suffic ient conditions relat ing function values is obtained. A bipolar decept ive function is also constructed from low-order Walsh coeffic ients. Multimodal functions of bounded deception are formed by concatenat ing several bipolar decept ive functions. These functions offer a great challenge to global optimizat ion algorithms (including genetic algorithms) because they are deceptive and have a large number of attractors , of which only a few are global opt ima. These function s also open doors for generalizing the notion of decepti on, and allow us to better understand the importance of deception in the study of genetic algorithms.