Understanding clusters of optimal solutions in multi-objective decision problems

Abstract

Multi-objective decisions problems are ubiquitous in requirements engineering. A common approach to solve them is to apply search-based techniques to generate a set of non-dominated solutions, formally known as the Pareto front, that characterizes all solutions for which no other solution performs better on all objectives simultaneously. Analysing the shape of the Pareto front helps decision makers understand the solution space and possible tradeoffs among the conflicting objectives. Interpreting the optimal solutions, however, remains a significant challenge. It is in particular difficult to identify whether solutions that have similar levels of goals attainment correspond to minor variants within a same design or to very different designs involving completely different sets of decisions. Our goal is to help decision makers identify groups of strongly related solutions in a Pareto front so that they can understand more easily the range of design choices, identify areas where strongly different solutions achieve similar levels of objectives, and decide first between major groups of solutions before deciding for a particular variant within the chosen group. The benefits of the approach are illustrated on a small example and validated on a larger independently-produced example representative of industrial problems.