Multiple Criteria Performance Analysis of Non-dominated Sets Obtained by Multi-objective Evolutionary Algorithms for Optimisation

The paper shows the importance of a multi-criteria performance analysis in evaluating the quality of non-dominated sets. The sets are generated by the use of evolutionary algorithms, more specifically through SPEA2 or NSGA-II. Problem examples from different problem domains are analyzed on four criteria of quality. These four criteria namely cardinality of the nondominated set, spread of the solutions, hyper-volume, and set coverage do not favour any algorithm along the problem examples. In the Multiple Shortest Path Problem (MSPP) examples, the spread of solutions is the decisive factor for the 2S|1M configuration, and the cardinality and set coverage for the 3S configuration. The differences in set coverage values between SPEA2 and NSGA-II in the MSPP are small since both algorithms have almost identical non-dominated solutions. In the Decision Tree examples, the decisive factors are set coverage and hyper-volume. The computations show that the decisive criterion or criteria vary in all examples except for the set coverage criterion. This shows the importance of a binary measure in evaluating the quality of nondominated sets, as the measure itself tests for dominance. The various criteria are confronted by means of a multi-criteria decision tool.