Impact of Static/Dynamic Tournament Sizing in Evolutionary Multi- and Many-Objective Optimization

Tournament selection is a widely used method for parent selection in multi- and many-objective evolutionary algorithms (MOEAs). The tournament size determines the strength of selection pressure based on each algorithm’s internal criterion; larger sizes increase the likelihood of selecting highly ranked solutions, while smaller sizes promote diversity in parent selection. Despite its importance, many MOEAs adopt a fixed tournament size of two without justification, potentially limiting performance across different phases of the search. This study investigates the effects of both static and dynamic tournament sizing strategies on optimization behavior. In the static setting, several fixed values are tested; in the dynamic setting, two scheduling strategies are employed: one that gradually increases the tournament size (ITS) and one that decreases it (DTS) as the search progresses. Experimental results on DTLZ and WFG benchmark problems with three, five, and nine objectives reveal that static tournament sizes of more than two tend to show higher optimization performance than the typical size of two, although the effect varies by base algorithm. ITS generally outperforms static sizing, especially for AGE-MOEA and AGE-MOEA-II, where its benefits become more pronounced as the number of objectives increases. These findings highlight the importance of tournament sizing as a key design factor in enhancing the performance of MOEAs.