High dimensional model representation for solving expensive multi-objective optimization problems

Metamodel based evolutionary algorithms have been used for solving expensive single and multi-objective optimization problems where evaluation of functions consume major portion of the running time. The system can be complex, high dimensional, multi-objective and black box function. In this paper, we have proposed a framework for solving expensive multi-objective optimization problems that uses high dimensional model representation (HDMR) as a basic model. The proposed method first explores the region of interest and then exploits them by narrowing the search space. It uses Kriging to interpolate subcomponents of HDMR and NSGA-II to solve the model space. It is compared with basic NSGA-II and multi-objective Kriging method on ZDT, DTLZ and CEC09 test problem suits. The results show that this framework is able to find a good distribution of solutions which are sufficiently converged to Pareto optimal fronts with limited number of solution evaluations.

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