Parallel Adaptive Kriging Method with Constraint Aggregation for Expensive Black-Box Optimization Problems

Abstract

Design optimization problems with black-box computation-intensive objective and constraints are extremely challenging in engineering practices. To address this issue, an efficient metamodel-based optimization strategy using parallel adaptive kriging method with constraint aggregation (PAKM-CA) is proposed. In PAKM-CA, the complex expensive constraints are aggregated using the Kreisselmeier and Steinhauser (KS) function. Besides, based on the notion of Pareto nondomination in terms of objective optimality and KS function feasibility, a novel parallel comprehensive feasible expected improvement (PCFEI) function considering the correlations of sample points is developed to effectively determine the sequential infill sample points. The infill sample points with the highest PCFEI function values are selected to dynamically refine the kriging metamodels, which simultaneously improves the optimality and feasibility of optimization. Moreover, the optimization time can be further reduced via the parallel sampling framework of PCFEI. Then the convergence and efficiency merits of PAKM-CA are demonstrated via comparing with competitive state-of-the-art metamodel-based constrained optimization methods on numerical benchmarks. Finally, PAKM-CA is applied to a practical long-range slender guided rocket multidisciplinary design optimization problem to illustrate its effectiveness and practicality for solving real-world engineering problems.