Objective Reduction Based on the Least Square Method for Large-Dimensional Multi-objective Optimization Problem

Abstract

In the real-world applications, many multi-objective optimization involve a large number of objective, however, existing evolutionary multi-objective optimization algorithms are applied only to a few number of objective. Because of inconvenience in handling large number of objective, researchers start to deal with how to reduce the redundant objectives. In this paper, we firstly introduce some existing algorithms on transforming high-dimensional to low-dimensional, and then propose a new algorithm, namely large dimensionality reduction based on the least square method. This method fits every objective function to a line, and compares the slope differences between each two lines, finally makes certain which one is redundancy and further reduces this one. This experiment shows, on one hand, there are some redundant objective functions in certain large dimensionality multi-objective optimization problems, and the objective space of non-redundant objective function is accordant with the low-dimensional true Pareto front. On other hand, the experiment result with other similar algorithm shows our algorithm is competitive and the efficacy of the procedure is demonstrated.