基于仿真试验和Kriging模型的多目标优化问题全局优化算法

Global optimization of multi-objective optimization problems based on simulation trials and Kriging models

针对复杂工程系统的多目标仿真优化问题,基于Kriging模型,提出一种将优化过程与试验过程相结合的全局多目标优化算法。该算法利用构造的加点准则序贯选取能应对约束和逼近真实Pareto解集的试验点,只需少量仿真试验就能得到优化问题的高精度Pareto解集。考虑试验点的可行性概率、间隔距离和Kriging模型的不确定性,设计亦能有效辨识非连通可行域的加点准则;提出以最大化试验点的期望超体积改进和可行性概率为目标的近似Pareto解集改进准则,使新试验点兼顾改进近似Pareto解集的质量和精确刻画可行域边界。通过三个数值算例将所提算法与已有算法进行比较,计算结果验证了所提算法的有效性和高效性。

Aiming at the multi-objective simulation optimization problem of complex engineering systems, a global multi-objective optimization algorithm based on Kriging model was proposed by combining optimization process with trial process. In this algorithm, the proposed infill sampling criteria was used to sequentially add new trials to han- dle constraints and to approximate true Pareto sets, which could help the algorithm find high-quality Pareto sets in very limited trials. By considering the feasibility probability, the spacing distances and the Kriging model＇s predic- tion uncertainty of trial points, one infill sampling strategy was designed to explore the disconnected feasible regions effectively. An infill sampling criterion was proposed by taking maximum expected hyper-volume improvement and feasibility probability as objectives, so as to balance the improvement of Pareto sets with confirming the boundaries of feasible regions. The proposed algorithm was tested on three typical benchmarks, and the effectiveness and effi- ciency were proved.