Most existing methods of multiobjective estimation of distributed algorithms apply the estimation of distribution of the Pareto-solution on the decision space during the search and little work has proposed on making a regression-model for representing the final solution set. Some inverse-model-based approaches were reported, such as inversed-model of multiobjective evolutionary algorithm (IM-MOEA), where an inverse functional mapping from Pareto-Front to Pareto-solution is constructed on nondominated solutions based on Gaussian process and random grouping technique. But some of the effective inverse models, during this process, may be removed. This paper proposes an inversed-model based on random forest framework. The main idea is to apply the process of random forest variable importance that determines some of the best assignment of decision variables (x_n) to objective functions (f_m) for constructing Gaussian process in inversed-models that map all nondominated solutions from the objective space to the decision space. In this work, three approaches have been used: classical permutation, Naïve testing approach, and novel permutation variable importance. The proposed algorithm has been tested on the benchmark test suite for evolutionary algorithms [modified Deb K, Thiele L, Laumanns M, Zitzler E (DTLZ) and Walking Fish Group (WFG)] and indicates that the proposed method is a competitive and promising approach.

中文翻译：

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使用随机森林变量重要性方法的基于逆模型的多目标分布算法估计

大多数现有的分布式算法的多目标估计方法在搜索过程中应用帕累托解在决策空间上的分布估计，并且很少有工作提出建立回归模型来表示最终解集。报告了一些基于逆模型的方法，例如多目标进化算法的逆模型（IM-MOEA），其中基于高斯过程和随机分组的非支配解构建从帕累托前沿到帕累托解的逆函数映射技术。但是在这个过程中，一些有效的逆模型可能会被删除。本文提出了一种基于随机森林框架的逆模型。x _n ) 到目标函数 ( f _m ) 用于在反模型中构建高斯过程，该模型将所有非支配解从目标空间映射到决策空间。在这项工作中，使用了三种方法：经典置换、朴素测试方法和新颖的置换变量重要性。所提出的算法已经在进化算法的基准测试套件上进行了测试[修改了 Deb K、Thiele L、Laumanns M、Zitzler E (DTLZ) 和 Walking Fish Group (WFG)]，并表明所提出的方法是一种有竞争力和有前途的方法.