Towards a deeper understanding of trade-offs using multi-objective evolutionary algorithms

A multi-objective optimization problem is characterized by multiple and conflicting objective functions. The conflicting nature of the objectives gives rise to the notion of trade-offs. A trade-off represents the ratio of change in the objective function values, when one of the objective function values increases and the value of some other objective function decreases. Various notions of trade-offs have been present in the classical multiple criteria decision making community and many scalarization approaches have been proposed in the literature to find a solution satisfying some given trade-off requirements. Almost all of these approaches are point-by-point algorithms. On the other hand, multi-objective evolutionary algorithms work with a population and, if properly designed, are able to find the complete preferred subset of the Pareto-optimal set satisfying an a priori given bound on trade-offs. In this paper, we analyze and put together various notions of trade-offs that we find in the classical literature, classifying them into two groups. We then go on to propose multi-objective evolutionary algorithms to find solutions belonging to the two classified groups. This is done by modifying a state-of-the-art evolutionary algorithm NSGA-II. An extensive computational study substantiates the claims of the paper.