Identifying correlations in understanding and solving many-objective optimisation problems

Abstract

Optimisation problems involving multiple objectives are commonly found in real-world applications. The existence of conflicting objectives produces trade-offs where a solution can be better with respect to one objective but requires a compromise in the other objectives. In many real-world problems the relationship between objectives is unknown or uncertain, and it is common to find problems with non-conflicting objectives. Understanding these relationships has been proven useful in different ways. The search efficiency of a multi-objective optimisation algorithm can benefit if objectives that are not essential to describe the Pareto-optimal front are omitted during the search procedure. Analysts and decision makers might get a better understanding about exiting synergies between the objectives, in turn facilitating the decision-making process of identifying the best solution. One particular useful technique to capture the relationships between objective functions is to rely on correlation measures. This chapter explores the literature of finding correlations among objective functions in solving multi-objective optimisation problems. Particularly, we focus on innovization and objective reduction approaches. We explain different statistical correlation measures and also provide details of benchmark and real-world optimisation problems solved by exploiting the correlations. This chapter provides an insight in solving multi-objective optimisation problems by considering the correlation among objective functions.