Do Existing Multiobjective Evolutionary Algorithms Use a Sufficient Number of Operators? An Empirical Investigation for Water Distribution Design Problems

摘要

Multiobjective evolutionary algorithms (MOEAs) have been used extensively to solve water resources problems. Their success is dependent on how well the operators that control an algorithm's search behavior are able to identify near-optimal solutions. As commonly used MOEAs contain a relatively small number of operators (generally between 2 and 7), this study investigates whether the performance of MOEAs could potentially be improved by increasing their operator set size. This is done via a series of controlled computational experiments isolating the influence of the size of the operator set (i.e., how many operators are used, ranging from 2 to 12), the composition of the operator set (i.e., which operators are used, given a set number of operators), the search strategy used (e.g., parent selection and survivor selection), and increasing the operator set size of an existing MOEA. These experiments are performed on six benchmark water distribution optimization problems. Results of the 3,150 optimization runs indicate that operator set size is the dominant factor affecting algorithm performance, having a significantly greater influence than operator set composition and other factors affecting algorithm search behavior. In addition, increasing the operator set size of the state-of-the-art MOEA GALAXY, which has been designed specifically for solving water distribution optimization problems, from its currently used value of 6 to 12 increased its performance significantly. These results suggest there is value in investigating the potential of increasing operator set size for a range of algorithms and problem types.