Improving the integration of the IGD+ indicator into the selection mechanism of a Multi-objective Evolutionary Algorithm

In recent years, the design of new selection mechanisms based on quality indicators has become a popular trend in the development of Multi-Objective Evolutionary Algorithms (MOEAs). This trend has been motivated by the well-known limitations of Pareto-based MOEAs when dealing with many-objective optimization problems (i.e., problems having more than 3 objectives). In this paper, we propose a selection mechanism (called IGD+-H) which is based on the combination of the Inverted Generational Distance+ (IGD+) indicator and Kuhn-Munkres' (Hungarian) algorithm to solve Linear Assignment Problems (LAPs). The proposed selection scheme is compared with respect to other selection mechanisms based on the IGD indicator and with respect to the use of the Δp indicator. Our proposed technique is incorporated into a MOEA and is validated using standard test functions. Our comparative study indicates that both Δp and IGD present some limitations when selecting solutions in degenerate multi-objective problems. Our results show that the transformation of the selection mechanism into a linear assignment problem speeds up the convergence of the MOEA and it is able to solve many-objective problems in an effective and efficient manner. We show that our proposed IGD+-H-based selection mechanism is able to achieve a significant speed up (of up to 200×) with respect to the exclusive use of any of the indicators adopted in our study.