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Weight Vector Arrangement Using Virtual Objective Vectors in Decomposition-based MOEA

This work proposes an arrangement method of weight vectors using virtual objective vectors supplementing the Pareto front estimation. In decomposition-based evolutionary multi-objective optimization, weight vectors decompose the Pareto front. Appropriate weight vector distribution depends on the Pareto front shape, which is generally unknown before the search. Objective vectors of obtained non-dominated solutions become a clue to estimate the Pareto front shape and arrange an appropriate weight vector set. However, a sizeable objective vector set is required for a high-quality Pareto front estimation and weight vector arrangement. The proposed method generates and utilizes a virtual objective vector set based on the objective vectors of obtained non-dominated solutions and an extended weight vector set for the Pareto front estimation. Experimental results using benchmark problems with different Pareto front shapes show that the virtual objective vectors generated from a limited number of actual objective vectors contribute to improving the search performance of decomposition-based evolutionary multi-objective optimization.