An inverse model-based multiobjective estimation of distribution algorithm using Random-Forest variable importance methods

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 (xn) to objective functions (fm) 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.