Solving High-Dimensional Multi-Objective Optimization Problems with Low Effective Dimensions

• DOI: 10.1609/aaai.v31i1.10664
• Publication Date: 2022-06-24T18:44:22Z
• Authors: Hong Qian; Yang Yu
• Keywords: High dimensional

Multi-objective (MO) optimization problems require simultaneously optimizing two or more objective functions. An MO algorithm needs to find solutions that reach different optimal balances of the functions, i.e., Pareto front, therefore, high dimensionality solution space can hurt much severer than single-objective optimization, which was little addressed in previous studies. This paper proposes a general, theoretically-grounded yet simple approach ReMO, scale current derivative-free algorithms high-dimensional non-convex functions with low effective dimensions, using random embedding. We prove conditions under an function has dimension, and for such we ReMO possesses desirable properties front preservation, time complexity reduction, rotation perturbation invariance. Experimental results indicate is even where all dimensions are but most only have small bounded effect on value.