Incremental lattice design of weight vector set

This paper proposes an alternative method to generate the weight vector set for the decomposition-based evolutionary multi- and many-objective optimization. Since each weight vector specifies an approximation point on the Pareto front, the distribution of the weight vector set has an enormous impact on the total approximation quality of the Pareto front. The conventional simplex-lattice design has scalability on the number of weight vectors by a decomposition parameter and generates a uniformly distributed weight vector set. However, the generated set involves fewer inner weight vectors for the approximation of the central area of the Pareto front. A variant, the two-layered simplex-lattice design, generates an additional layer to introduce inner weight vectors but sacrifices the distribution uniformity. The proposed method, the incremental lattice design, also has scalability on the number of weight vectors by a decomposition parameter and always includes the intermediate weight vector pointing to the center of the Pareto front for any the decomposition parameter while keeping the distribution uniformity. Experimental results show that the proposed method achieves higher approximation quality of the Pareto front than the conventional simplex-lattice and two-layered simplex-lattice designs.