A Distribution Information-Based Kriging-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization Problems
提出DISK算法，利用Kriging模型和决策空间分布信息指导搜索，解决昂贵高维多目标优化问题，并扩展至约束问题。
This article proposes a distribution information-based Kriging-assisted evolutionary algorithm (named DISK) to tackle expensive many-objective optimization problems (EMaOPs). In DISK, we design a new Pareto dominance relationship (called DIPD) to guide the evolutionary search and candidate selection. DIPD works based on the Kriging models and incorporates the decision-space distribution information of the nondominated solutions in the database. Such distribution information can be used to assess the possibility of an unknown solution being located in/close to the decision-space promising region. Thanks to this property, DIPD is capable of preserving the predicted elitist solutions located in/close to the decision-space promising region. These solutions are very likely to possess good original Pareto optimality and are beneficial for improving the convergence of the nondominated-solution set in the database. In addition, to further ensure the diversity of the nondominated-solution set in the database, we also design an adaptive exploration strategy, which explores the objective-space unknown region farthest away from the nondominated solutions in the database once the optimization process stagnates. Furthermore, through a feasibility-first mechanism, we extend DISK to deal with constrained EMaOPs, obtaining <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {DISK}^{+}$ </tex-math></inline-formula>. Finally, we verify the competitiveness of DISK and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {DISK}^{+}$ </tex-math></inline-formula> via extensive experiments.