Efficient Multi-Objective Evolutionary Algorithm for Constrained Global Optimization of Expensive Functions

Abstract

For real-world engineering design optimizations, it is of great significance to find approximate optimal designs with least number of expensive functional evaluations. This paper proposes to use a surrogate-based multi-objective evolutionary algorithm (SBMO) to address this type of problems. The basic idea is to decompose a multi-objective optimization problem into a number of scalar optimization subproblems and to optimize them simultaneously in a simple-to-implement manner, in which global surrogate models are used to enable full cooperation between subproblems. First, initial samples are selected by design of experiments and expensive simulations are conducted to evaluate them. Second, global surrogate models for objective (and constraint) functions are built through the sampled data and the optimization subproblems are solved simultaneously to suggest new samples. Third, the surrogate models are updated and the optimization proceeds to the next generation. This process is repeated until satisfactory Pareto-front solutions are found. Thanks to decomposition strategy, the infill-sampling criteria and constraint handling dedicated for a single-objective optimization can be directly used in a SBMO. The difference between SBMO and the existing methods such as MOEA/D-EGO is that a combined infill-sampling strategy and dedicated constraint handling are used. Benchmark test cases have demonstrated that SBMO is efficient, robust and has good capability of constraint handling. SBMO has been applied to multi-objective aerodynamic shape optimization of a transonic airfoil. It has been shown that SBMO is well suited for engineering design problems where expensive numerical simulations are employed.