Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive training time of surrogate models, or the optimal use of many-core computers to approximate efficiently multiple objectives simultaneously. Thinking out of the box, complexity can also be shifted from approximating the individual objective functions to approximating the entire Pareto front. This leads to further complexities, namely, how to validate statistically and apply the techniques developed to real-world problems. In this paper, we discuss emerging complexity-related topics in surrogate-assisted multicriteria optimization that may not be prevalent in nonsurrogate-assisted single-objective optimization. These complexities are motivated using several real-world problems in which the authors were involved. We then discuss several promising future research directions and prospective solutions to tackle emerging complexities in surrogate-assisted multicriteria optimization. Finally, we provide insights from an industrial point of view into how surrogate-assisted multicriteria optimization techniques can be developed and applied within a collaborative business environment to tackle real-world problems.

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代理辅助的多标准优化：复杂性，预期解决方案和业务案例

解决现实世界中多标准优化问题的复杂性通常源于以下事实：使用复杂，昂贵和/或耗时的仿真工具或物理实验来评估问题的解决方案。在这种情况下，通常使用有效的计算模型（通常称为代理模型或元模型）来近似模拟或物理实验的结果（目标或约束函数值）。多个目标函数的存在为代理辅助优化带来了额外的复杂性。例如，复杂性可以涉及元模型的用于各个目标函数，替代模型的广泛的训练时间，或最佳使用的众核计算机同时近似有效多个目的适当的选择。开箱即用的思维方式，也可以将复杂性从近似单个目标函数转换为近似整个Pareto前沿。这导致了进一步的复杂性，即如何进行统计验证以及将开发的技术应用于实际问题。在本文中，我们讨论了替代辅助的多准则优化中新兴的与复杂性相关的主题，这些主题在非替代辅助的单目标优化中可能并不普遍。这些复杂性是由涉及作者的几个实际问题激发的。然后，我们讨论了一些有希望的未来研究方向和前瞻性解决方案，以解决代理辅助的多准则优化中出现的复杂性。最后，