A New Multi-Objective Evolutionary Algorithm Based on a Performance Assessment Indicator

An emerging trend in the design of multi-objective evolutionary algorithms (MOEAs) is to select individuals through the optimization of a quality assessment indicator. However, the most commonly adopted indicator in current use is the hypervolume which becomes very expensive (computationally speaking) as we increase the number of objectives. In this paper, we propose, instead, the use of another indicator called Delta (p). Although the Delta(p) indicator is not Pareto compliant, we show here how it can be incorporated into the selection mechanism of an evolutionary algorithm (for that sake, we adopt differential evolution as our search engine) in order to produce a MOEA. The resulting MOEA (called Delta (p)-Differential Evolution, or DDE) is validated using standard test problems and performance indicators reported in the specialized literature. Our results are compared with respect to those obtained by both a Pareto-based MOEA (NSGA-II) and a hypervolume-based MOEA (SMS-EMOA). Our preliminary results indicate that our proposed approach is competitive with respect to these two MOEAs for continuous problems having two and three objective functions. Additionally, our proposed approach is better than NSGA-II and provides competitive results with respect to SMS-EMOA for continuous many-objective problems. However, in this case, the main advantage of our proposal is that its computational cost is significantly lower than that of SMS-EMOA.