A non-dominance-based online stopping criterion for multi-objective evolutionary algorithms

• Published in: International journal for numerical methods in engineering 2010-11, Vol.84 (6), p.661-684
• Main Authors: Goel, Tushar, Stander, Nielen
• Format: Article
• Language: English
• Subjects: Computational efficiency; Convergence; Crashworthiness; evolutionary algorithm; Evolutionary algorithms; Exact sciences and technology; Fundamental areas of phenomenology (including applications); genetic algorithms; Inelasticity (thermoplasticity, viscoplasticity...); Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); multi-objective; Numerical analysis; Numerical analysis. Scientific computation; Optimization; Physics; Sciences and techniques of general use; Searching; Solid mechanics; stopping criterion; Structural and continuum mechanics
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.2909

A non‐dominance criterion‐based metric that tracks the growth of an archive of non‐dominated solutions over a few generations is proposed to generate a convergence curve for multi‐objective evolutionary algorithms (MOEAs). It was observed that, similar to single‐objective optimization problems, there were significant advances toward the Pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured. This convergence curve was used to terminate the MOEA search to obtain a good trade‐off between the computational cost and the quality of the solutions. Two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric. Copyright © 2010 John Wiley & Sons, Ltd.