Selective evaluation in multiobjective optimization: A less explored avenue

Population based stochastic algorithms have long been used for the solution of multiobjective optimization problems. In the context of computationally expensive analysis, the existing practice utilizes some form of surrogates or approximations. In this paper, we investigate the effects of selective evaluation of promising solutions and try to derive answers to the following questions: (a) should we discard the solution based on variable values only ? (b) should we evaluate one of its objective functions and then decide to select or discard it ? or (c) should we evaluate both its objective functions before selecting or discarding it ? While evaluation of solutions is crucial for learning, it comes with a computational cost that can be significant for problems involving computationally expensive analysis. Herein, we study the effects of various selective evaluation strategies using support vector machine (SVM) classifier coupled with non-dominated sorting genetic algorithm (NSGA-II). The performance of the strategies have been evaluated using five well studied unconstrained bi-objective optimization problems (DTLZ1-DTLZ5) with limited computational budget. The results clearly indicate the benefits of using certain strategies for certain class of problems and in certain stages of the search process. Furthermore, the results also suggest that some solutions can be discarded without any evaluation, while for others after evaluation of one or both objective(s). Selective evaluation is a rarely investigated field and we hope that this study would prompt design of efficient algorithms that selectively evaluate solutions on the fly i.e. based on the trade-off between need to learn/evaluate and cost to learn.