Chapter 5: Multi-Objective Optimization Using an Evolutionary Algorithm Embedded with Multiple Spatially Distributed Surrogates

For most practical optimization problems involving computationally expensive analysis, a brute force approach relying on actual analysis is not computationally viable. Surrogates and approximations are regularly used in lieu of computationally expensive analysis during the course of optimization. Existing surrogate assisted optimization approaches often use the same approximation model (surrogate) for all objectives and constraints in all regions of the search space. The choice of a type of surrogate model over another is non-trivial and such an a priori choice limits flexibility in representation. In this chapter, we introduce a multi-objective evolutionary algorithm embedded with multiple adaptive spatially distributed surrogates of multiple types. A nondominated sorting genetic algorithm is used as the underlying optimizer. Instead of a single global surrogate, local surrogates of multiple types are constructed around each offspring solution and a multi-objective search is conducted using the best surrogate for the objective and the constraint function. The set of nondominated solutions obtained from each of such local searches are merged to form the potential offspring pool. Top N offspring solutions identified via nondominated sorting and crowding are evaluated using actual analysis resulting in the offspring population. Such an approach offers the flexibility of representation that is often required in practical problems and at the same time capitalizes on the benefits offered by various types of surrogates in different regions of the search space. The performance of the proposed algorithm i.e. surrogate assisted multi-objective optimization algorithm (SAMO) is compared with the baseline Nondominated Sorting Genetic Algorithm II (NSGA-II) to highlight the benefits. The results obtained by SAMO is consistently better (at par with a few) than NSGA-II for the problems presented in this chapter based on an hypervolume metric. One can observe significant benefits in terms of the rate of convergence for SAMO over NSGA-II.