In the past few decades, many multiobjective evolutionary optimization algorithms (MOEAs) have been proposed to find a finite set of approximate Pareto solutions for a given problem in a single run, each with its own structure. However, in many real-world applications, it could be desirable to have structure constraints on the entire optimal solution set, which define the patterns shared among all solutions. The current population-based MOEAs cannot properly handle such requirements. In this work, we make the first attempt to incorporate the structure constraints into the whole solution set by a single Pareto set model, which can be efficiently learned by a simple evolutionary stochastic optimization method. With our proposed method, the decision-makers can flexibly trade off the Pareto optimality with preferred structures among all solutions, which is not supported by previous MOEAs. A set of experiments on benchmark test suites and real-world application problems fully demonstrates the efficiency of our proposed method.

翻译：在过去的几十年中，许多多目标进化优化算法（MOEAs）被提出，旨在单次运行中为给定问题找到一组有限的近似帕累托解，每个解具有其自身结构。然而，在许多实际应用中，可能需要对整个最优解集施加结构约束，这些约束定义了所有解之间共享的模式。当前基于种群的MOEAs无法妥善处理此类需求。在本工作中，我们首次尝试通过单个帕累托集模型将结构约束整合到整个解集中，该模型可通过简单的进化随机优化方法高效学习。通过我们提出的方法，决策者可以灵活地在所有解的帕累托最优性与偏好结构之间进行权衡，这是以往的MOEAs所无法支持的。在基准测试套件和实际应用问题上的一系列实验充分证明了我们提出方法的有效性。