Bayesian network as an adaptive parameter setting approach for genetic algorithms

Parameter setting currently ranks among the most actively researched topics in the evolutionary algorithm (EA) community. This can be explained by the major impact EA parameters have on search performance. However, parameter setting has been shown to be both problem dependent and evolution dependent. Moreover, because parameters interact in complex ways, developing an efficient and beneficial parameter setting approach is not an easy feat, and no broadly recognized solution has emerged to date. In this paper, we borrow the notion of parameter adaptation with the objective of addressing the parameter setting dependencies mentioned above, using a strategy based on a Bayesian network. The adaptive framework is elaborated for a steady-state genetic algorithm (SSGA) to control nine parameters. To judge parameter state productivities, we consider the population's fitness improvement, as well as exploration/exploitation balance management. The performance of this proposal, a Bayesian network for genetic algorithm parameter adaptation (BNGA), is assessed based on the CEC'05 benchmark. BNGA is compared to a static parameter setting, a naive approach, three common adaptive systems (PM, AP, and FAUC-RMAB), and two state-of-the-art EAs (CMA-ES and G-CMA-ES). Our results statistically demonstrate that the performance of BNGA is equivalent to that of FAUC-RMAB, CMA-ES, and G-CMA-ES, and overall is superior to that of all the other SSGA parameter setting approaches. However, these results also reveal that all the approaches considered have great difficulty finding global optima in a multimodal problem set. This suggests a lack of complementarity and/or synergy among parameter states.