SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems

We present the algorithm SOCEMO for optimization problems that have multiple conflicting computationally expensive black-box objective functions. The computational expense arising from the objective function evaluations considerably restricts the number of evaluations that can be done to find Pareto-optimal solutions. Frequently used multiobjective optimization methods are based on evolutionary strategies and generally require a prohibitively large number of function evaluations to find a good approximation of the Pareto front. SOCEMO, in contrast, employs surrogate models to approximate the expensive objective functions. These surrogate models are used in the iterative sampling process to decide at which points in the variable domain the next expensive evaluations should be done. Therefore, fewer expensive objective function evaluations are needed, and a good approximation of the Pareto front can be found efficiently. Previous algorithms have generally been tested on problems with few variables (up to 10) and few objective functions (up to 5). In our numerical study, we show that our algorithm performs well for benchmark problems with up to 35 dimensions and up to 10 objective functions, as well as two engineering application problems. We compared the performance of SOCEMO to a variant of NSGA-II and show that SOCEMO's sophisticated search strategy is more efficient than NSGA-II when the number of allowable function evaluations is low.