Machine learning based decision support for a class of many-objective optimisation problems

Abstract

There is a growing recognition for the multiple criteria decision making (MCDM) based multi-objective evolutionary algorithms (MOEAs) for tackling many-objective optimisation problems (MaOPs). In that, the aim is to utilise the decision makers’ (DMs’) preferences to guide the search towards a few solutions, as against the whole Pareto-optimal front (POF). This thesis is based on the premise that the practical utility of the MCDM based MOEAs may be impaired due to the lack of–objectivity (a rational basis); repeatability (identical preferences for identical options); consistency (alike preferences across multiple interaction stages); and coherence (alike preferences by multiple DMs) in the DMs’ preferences. To counter these limitations, this thesis aimed at developing offline and online decision support by capturing the preference-structure of the objective functions inherent in the problem model itself. This aim has been realised through the following objectives: • Identification of a criterion for the decision support: in that, preservation of the correlation– structure of the MOEA solutions is found to be a robust criterion in the case of MaOPs. • Development of a machine learning based offline objective reduction framework: it com¬prises of linear and nonlinear objective reduction algorithms, which facilitate the decision support through revelation of: (i) the redundant objectives (if any), (ii) preference-ranking of the essential objectives, (iii) the smallest objective sets corresponding to pre-specified errors, and (iv) the objective sets of pre-specified sizes that correspond to minimum error. • Development of an online objective reduction framework: it addresses a major pitfall associated with the offline framework, that–an essential objective if erroneously eliminated as redundant, has no scope of being reconsidered in the subsequent analysis. This pitfall is countered through a probabilistic retention of all the objectives, and this serves as a self-correcting mechanism that enhances the overall accuracy. • Timing the decision support: it is acknowledged that the revelations by the decision support may vary depending on when the offline or online framework is applied during an MOEA run. This uncertainty on the timing of the decision support is countered through the proposition of an entropy based dissimilarity measure. The efficacy of the proposed frameworks is investigated against a broad range of test problems (scaled up to 50 objectives) and some real-world MaOPs; and, the accuracy of the corresponding decision support is compared against that of an alternative approach based on preserving the dominance relations. The results illustrate that the proposed frameworks and the corresponding decision support bear significant utility for those MaOPs, where not all the objectives are essential, or equally important for describing the true POF. The considered real-world problems also bear evidence of the fact that MaOPs with redundant and disparately important objectives may commonly exist in practice.