Empirical Investigations of Reference Point Based Methods When Facing a Massively Large Number of Objectives: First Results

EMO 2017: 9th International Conference on Evolutionary Multi-Criterion Optimization, 19-22 March 2017, Münster, GermanyThis is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Multi-objective optimization with more than three objectives has become one of the most active topics in evolutionary multi-objective optimization (EMO). However, most existing studies limit their experiments up to 15 or 20 objectives, although they claimed to be capable of handling as many objectives as possible. To broaden the insights in the behavior of EMO methods when facing a massively large number of objectives, this paper presents some preliminary empirical investigations on several established scalable benchmark problems with 25, 50, 75 and 100 objectives. In particular, this paper focuses on the behavior of the currently pervasive reference point based EMO methods, although other methods can also be used. The experimental results demonstrate that the reference point based EMO method can be viable for problems with a massively large number of objectives, given an appropriate choice of the distance measure. In addition, sufficient population diversity should be given on each weight vector or a local niche, in order to provide enough selection pressure. To the best of our knowledge, this is the first time an EMO methodology has been considered to solve a massively large number of conflicting objectives.This work was partially supported by EPSRC (Grant No. EP/J017515/1

Many Objective Particle Swarm Optimisation: An Investigation into Strengthening Convergence by Controlling Dominance Area

The application of single and multi-objective particle swarm optimisation (PSO) is widespread, however in many-objective optimisation (problems with four or more competing objectives) traditional PSO has been less well examined. Recent progress on many-objective evolutionary optimisers has lead to the adoption of a variety of non-Pareto quality measures, it is therefore of interest to see how well PSO copes in this domain, and how non-Pareto quality measures perform when integrated into PSO. Here we review the current state of the art in multi- and many-objective PSO optimisation. We compare and contract the performance of canonical PSO, using a wide range of many-objective quality measures, on a number of different parametrised test functions for up to 30 competing objectives. We examine quality measures as selection operators for guides when truncated non-dominated archives of guides are maintained, and maintenance operators, for choosing which solutions should be maintained as guides from one generation to the next. We investigate in detail two Pareto strengthening methods, Controlling Dominance Area of Solutions (CDAS) and Self-Controlling Dominance Area of Solutions (S-CDAS). We find that CDAS and S-CDAS perform exceptionally well as a quality measures to determine archive membership for global and local guides. However, for convergence only at the cost of diversity and spread across the optimal front, single objective canonical PSO run using a linear sum of objectives, has the best performance overall