Comparison between Single-Objective and Multi-Objective Genetic Algorithms: Performance Comparison and Performance Measures

We compare single-objective genetic algorithms (SOGAs) with multi-objective genetic algorithms (MOGAs) in their applications to multi-objective knapsack problems. First we discuss difficulties in comparing a single solution by SOGAs with a solution set by MOGAs. We also discuss difficulties in comparing several solutions from multiple runs of SOGAs with a large number of solutions from a single run of MOGAs. It is shown that existing performance measures are not necessarily suitable for such comparison. Then we compare SOGAs with MOGAs through computational experiments on multi-objective knapsack problems. Experimental results on two-objective problems show that MOGAs outperform SOGAs even when they are evaluated with respect to a scalar fitness function used in SOGAs. This is because MOGAs are more likely to escape from local optima. On the other hand, experimental results on four-objective problems show that the search ability of MOGAs is degraded by the increase in the number of objectives. Finally we suggest a framework of hybrid algorithms where a scalar fitness function in SOGAs is probabilistically used in MOGAs to improve the convergence of solutions to the Pareto front.