Solving Multi-Objective Optimization via Adaptive Stochastic Search with Domination Measure

TL;DR

This paper introduces a new domination measure for multi-objective optimization, reformulates the problem into a stochastic single-objective form, and demonstrates an effective, convergent approach that produces well-spread Pareto approximations.

Contribution

It proposes a novel domination measure and a model-based stochastic search method that effectively approximates Pareto sets in multi-objective optimization.

Findings

The approach converges to global optima of the reformulated problem.

It produces uniformly spread Pareto approximations.

It is competitive with existing multi-objective optimization methods.

Abstract

For general multi-objective optimization problems, we propose a novel performance metric called domination measure to measure the quality of a solution, which can be intuitively interpreted as the size of the portion of the solution space that dominates that solution. As a result, we reformulate the original multi-objective problem into a stochastic single-objective one and propose a model-based approach to solve it. We show that an ideal version algorithm of the proposed approach converges to a set representation of the global optima of the reformulated problem. We also investigate the numerical performance of an implementable version algorithm by comparing it with numerous existing multi-objective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multi-objective problem, and is competitive to the tested existing methods.