Massive Multimodality, Deception, and Genetic Algorithms.
Abstract
This paper considers the use of genetic algorithms (GAs) for the solution of problems that are both average-sense misleading (deceptive) and massively multimodal. An archetypical multimodal-deceptive problem, here called a bipolar deceptive problem, is defined and two generalized constructions of such problems are reviewed, one using reflected trap functions and one using low-order Walsh coefficients; sufficient conditions for bipolar deception are also reviewed. The Walsh construction is then used to form a 30-bit, order-six bipolar-deceptive function by concatenating five, six-bit bipolar functions. This test function, with over five million local optima and 32 global optima, poses a difficult challenge to simple and niched GAs alike. Nonetheless, simulations show that a simple GA can reliably find one of the 32 global optima if appropriate signal-to-noise-ratio population sizing is adopted. Simulations also demonstrate that a niched GA can reliably and simultaneously find all 32 global solutions if the population is roughly sized for the expected niche distribution and if the function is appropriately scaled to emphasize global solutions at the expense of suboptimal ones. These results immediately recommend the application of niched GAs using appropriate population sizing and scaling. They also suggest a number of avenues for generalizing the notion of deception.
Authors: David E. Goldberg, Kalyanmoy Deb, Jeffrey Horn