Local Search , Multiobjective Optimization and the Pareto ArchivedEvolution

The Pareto Archived Evolution Strategy 1 (PAES) KC99c, KC99b, KC99a], a local search algorithm for multiobjective optimization tasks, is compared with a modern, proven population-based EA, the Strength Pareto Evolutionary Algorithm (SPEA) of Zitzler and Thiele ZT98, ZDT99, ZT99]. Comparison is carried out with respect to six test functions designed by Deb, each of which is designed to capture and isolate a speciic problem feature that may present diiculties to multiobjective optimizers. Statistical techniques introduced previously, and derived from those of Fonseca and Fleming FF96], are used to process the results to form conndence measures relating to the percentage of the non-dominated front which is covered by each algorithm. These results indicate that, with no attempt at tuning PAES to any of the problems, it outperforms SPEA conclusively on four of the test functions. Some investigation of the mutation rates used by PAES is then carried out. This shows that using a higher mutation rate improves the performance of PAES on two of the test problems so that it outperforms SPEA on a further function in the test suite, T4, a highly multimodal function. The use of Gray encoding of this problem is also found to improve performance signiicantly, while it is found to be detrimental on some of the other problems. We nd that PAES is unable to compete with the performance of SPEA on function T5, a strongly deceptive problem, although with higher mutation rates its performance on this problem is shown to be competitive with a range of other multiobjective EAs including NPGA. The results presented provide evidence that local search may be a powerful technique for optimization in multiobjective spaces. To explain this nding we conjecture that there are fewer local optima in multiobjective problem spaces than in their equivalent objective aggregated spaces, and provide some argument to support this claim.