This paper presents a meta-objective optimization approach, called Bi-Goal Evolution\n(BiGE), to deal with multi-objective optimization problems with many objectives. In multiobjective\noptimization, it is generally observed that 1) the conflict between the proximity\nand diversity requirements is aggravated with the increase of the number of objectives and\n2) the Pareto dominance loses its effectiveness for a high-dimensional space but works\nwell on a low-dimensional space. Inspired by these two observations, BiGE converts a\ngiven multi-objective optimization problem into a bi-goal (objective) optimization problem\nregarding proximity and diversity, and then handles it using the Pareto dominance relation\nin this bi-goal domain. Implemented with estimation methods of individuals� performance\nand the classic Pareto nondominated sorting procedure, BiGE divides individuals into\ndifferent nondominated layers and attempts to put well-converged and well-distributed\nindividuals into the first few layers. From a series of extensive experiments on four\ngroups of well-defined continuous and combinatorial optimization problems with 5, 10\nand 15 objectives, BiGE has been found to be very competitive against five state-of-the-art\nalgorithms in balancing proximity and diversity. The proposed approach is the first step\ntowards a new way of addressing many-objective problems as well as indicating several\nimportant issues for future development of this type of algorithms.
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