Section: New Results

Decomposition-Based Algorithms for Multiobjective Optimization

Participants : Dimo Brockhoff, Bilel Derbel, Arnaud Liefooghe, Gauvain Marquet, El-Ghazali Talbi.

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. Those algorithms decompose a multiobjective optimization problem into several single-objective optimization problems by using so-called scalarizing functions which are then simultaneously optimized by single-objective algorithms in a cooperative manner.

Our contributions to decomposition-based algorithms in 2014 has been three-fold. Firstly, we investigated in [28] the general impact of different scalarizing functions and their parameters on the search performance. We thereby abstracted from any specific algorithm and only considered the difficulty of the single scalarized problems in terms of the search ability of a (1+lambda)-EA on bi-objective NK-landscapes. Secondly, in [16] , we proposed a new distributed heuristic for approximating the Pareto set of bi-objective optimization problems. Given a number of computing nodes, we self-coordinate them locally, in order to cooperatively search different regions of the Pareto front. As local information, every node uses only the positions of its neighbors in the objective space and evolves its local solution adaptively, based on what we term a `localized fitness function'. We deployed our distributed algorithm using a computer cluster of hundreds of cores. At last, we enhanced the algorithm MOEA/D, a prominent example of a decomposition-based algorithm from the literature, by investigating the idea of evolving the whole population simultaneously at once. We thereby proposed new alternative selection and replacement strategies that can be combined in different ways within a generic and problem-independent framework [36] .