A New Method to Construct the Non-Dominated Set in Multi-Objective Genetic Algorithms

There have been widespread applications for Multi Objective Genetic Algorithm (MOGA) on highly complicated optimization tasks in discontinuous, multi-modal, and noisy domains. Because the convergence of MOGA can be reached with the non-dominated set approximating the Pareto Optimal front, it is very important to construct the non-dominated set of MOGA efficiently. This paper proposes a new method called Dealer's Principle to construct non-dominated sets of MOGA, and the time complexity is analyzed. Then we design a new MOGA with the Dealer's Principle and a clustering algorithm based on the core distance of clusters to keep the diversity of solutions. We show that our algorithm is more efficient than the previous algorithms, and that it produces a wide variety of solutions. We also discuss the convergence and the diversity of our MOGA in experiments with benchmark optimization problems of three objectives.

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