Black-box and preference-based optimization algorithms are global optimization procedures that aim to find the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons as possible. In the black-box case, the analytical expression of the objective function is unknown and it can only be evaluated through a (costly) computer simulation or an experiment. In the preference-based case, the objective function is still unknown but it corresponds to the subjective criterion of an individual. So, it is not possible to quantify such criterion in a reliable and consistent way. Therefore, preference-based optimization algorithms seek global solutions using only comparisons between couples of different samples, for which a human decision-maker indicates which of the two is preferred. Quite often, the black-box and preference-based frameworks are covered separately and are handled using different techniques. In this paper, we show that black-box and preference-based optimization problems are closely related and can be solved using the same family of approaches, namely surrogate-based methods. Moreover, we propose the generalized Metric Response Surface (gMRS) algorithm, an optimization scheme that is a generalization of the popular MSRS framework. Finally, we provide a convergence proof for the proposed optimization method.
翻译:黑盒和基于优惠的优化算法是旨在寻找优化问题全球解决办法的全球优化程序,分别使用最少数量的职能评价或可能的抽样比较。在黑盒情况下,目标功能的分析表达方式并不为人所知,只能通过(成本)计算机模拟或实验加以评估。在基于优惠的案例中,目标功能仍然未知,但它与个人的主观标准相对应。因此,不可能以可靠和一致的方式量化这种标准。因此,基于优惠的优化算法寻求全球解决办法,只使用不同样品的夫妇之间的比较,而人类决策者则指出两者中哪一种是首选的。很常见的情况是,黑盒和基于优惠的框架被单独覆盖,并且使用不同的技术来处理。在本文中,我们表明黑盒和基于优惠的优化问题密切相关,并且可以使用相同的方法(即基于套管的方法)加以解决。此外,我们提议采用通用的Metri反应表(GMRS)算法,一个优化方案是通用MSS框架的通用化方法。最后,我们提供了一种提议的统一方法。我们为通用的MSRS框架提供一种一般化的证据。