MOPC/D: A new Probability Collectives algorithm for Multiobjective Optimisation

Decomposition strategies in Multiobjective optimisation (MOO) are known to be superior to other approaches on a wide variety of problems. Probability Collectives (PC) is a recent distribution-centric optimisation framework that has origins in game-theory and statistical physics. Here, we present a new Probability Collectives MOO algorithm, MOPC/D, based on a decomposition strategy that exploits the search operators which arise naturally from the use of a probabilistic Gaussian Mixture Model formulation. Evaluation of this approach, using the 2- and 3- objective unconstrained problems from the CEC2009 benchmark suite, found MOPC/D to perform competitively with the state of the art (across these problems it would have had the best mean rank and rank variance of 14 algorithms in the CEC2009 competition, e.g. above MOEA/D), and significantly outperform the (only) previously published MOO algorithm in the PC framework. We conclude that the performance of MOPC/D shows considerable promise, and suggest a number of lines for further research.