On the utility of the multimodal problem generator for assessing the performance of Evolutionary Algorithms

TL;DR

This paper critically evaluates the multimodal problem generator, revealing that evolutionary algorithms require large populations to find global optima and are not well-suited for peak-in-a-haystack problems, questioning its utility for performance assessment.

Contribution

The paper demonstrates the limitations of the multimodal problem generator in evaluating evolutionary algorithms and highlights the need for alternative benchmarking approaches.

Findings

Population size must grow linearly with the number of peaks.

Evolutionary algorithms struggle with peak-in-a-haystack problems.

The multimodal problem generator is not ideal for performance assessment.

Abstract

This paper looks in detail at how an evolutionary algorithm attempts to solve instances from the multimodal problem generator. The paper shows that in order to consistently reach the global optimum, an evolutionary algorithm requires a population size that should grow at least linearly with the number of peaks. It is also shown a close relationship between the supply and decision making issues that have been identified previously in the context of population sizing models for additively decomposable problems. The most important result of the paper, however, is that solving an instance of the multimodal problem generator is like solving a peak-in-a-haystack, and it is argued that evolutionary algorithms are not the best algorithms for such a task. Finally, and as opposed to what several researchers have been doing, it is our strong belief that the multimodal problem generator is not adequate for assessing the performance of evolutionary algorithms.