Massive Multimodality, Deception, and Genetic Algorithms

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 de ned and two generalized constructions of such problems are reviewed one using re ected trap functions and one using low order Walsh coe cients su cient conditions for bipolar deception are also reviewed The Walsh construction is then used to form a bit order six bipolar deceptive function by concatenating ve six bit bipolar functions This test function with over ve million local optima and global optima poses a di cult challenge to simple and niched GAs alike Nonetheless simulations show that a simple GA can reliably nd one of the global optima if appropriate signal to noise ratio population sizing is adopted Simulations also demonstrate that a niched GA can reliably and simultaneously nd all 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