Nearest neighbor prediction of pareto dominance using general regression neural networks

Conventional methods of determining Pareto dominance in multi-objective optimization evaluate and compare objective vectors of candidate solutions, but the computation and (or) experiment of evaluating objective vectors are overwhelmingly costly when computationally expensive multi-objective problems are involved. This study investigates a nearest neighbor prediction method of Pareto dominance using general regression neural networks (GRNN). The decision differential value (D-value) vector of two feasible solutions is used as the input of GRNN, and the objective D-value vector is used as the output. Under the supervision of sample candidate solutions, GRNN is used to predict objective D-value vectors between an observed solution and samples. For an observed candidate, the predicted objective D-Value vectors are used to find out the nearest neighbor samples in objective space. Experimental results show that the nearest neighbor prediction of Pareto dominance relationships using GRNN can obtain acceptable prediction accuracy. The proposed algorithm provides an effective method to relieve the curse of computation cost in computationally expensive multi-objective optimization problems, but without requirement for analytical models of objective functions.