A comparative study on the value of accounting for possible relationships between decision variables when solving multi-objective problems

[摘要] ENGLISH ABSTRACT: The cross-entropy method for multi-objective optimisation (MOO CEM)was recently introduced by Bekker & Aldrich (2010) and Bekker (2012).Results presented by both show great promise. The MOO CEM assumesthat decision variables are independent. As a consequence, the questionarises: under which circumstances would an algorithm that accounts forrelationships between decision variables outperform the MOO CEM? Twoalgorithms reported to account for relationships between decision variables,the multi-objective covariance matrix adaptation evolution strategy (MOCMA-ES) and Pareto di erential evolution (PDE), are selected for comparison.In addition, two hybrid algorithms (Hybrid 1 and Hybrid 2) basedon the MOO CEM are created. Theseve algorithms are applied to aset of 46 continuous problems, six instances of the mission-ready resource(MRR) problem, and three instances of a dynamic, stochastic bu er allocationproblem (BAP). Performance is measured using the hypervolumeindicator and Mann-Whitney U-tests. One of the primaryndings is thataccounting for relationships between decision variables is bene cial whensolving small to medium-sized problems. In these cases, the MO-CMA-EStypically outperforms the other algorithms. However, on large problems,Hybrid 1 and the MOO CEM typically perform best.

[发布机构] Stellenbosch University