出版社：The Japanese Society for Evolutionary Computation
摘要：Pareto set topology refers to the geometry formed in decision space by Pareto optimal solutions from continuous multi-objective optimization problems. Recent studies have shown that problems with difficult Pareto set topology can present a tough challenge for evolutionary algorithms to find a good approximation of the optimal set of solutions, well-distributed in decision and objective space. One important challenge optimizing these problems is to keep or restore diversity in decision space. In this work, we present a method that learns a model of the topology of solutions from evolutionary algorithm's population by performing parametric cubic interpolations for all variables in decision space. The model uses Catmull-Rom parametric curves as they allow us to deal with any dimension in decision space. According to the Karush-Kuhn-Tucker condition, this method is appropriated for bi-objective problems since their optimal set is a one-dimensional curve. We couple this method with four different evolutionary algorithm approaches by promoting restarts from solutions generated by the model. We argue and discuss the algorithm's behavior and its implications for model building..
