AN INTERACTIVE DESIRABILITY FUNCTION BASED APPROACH TO GUIDED PARETO-OPTIMAL FRONT

Abstract

Decision-making involves the use of a rational proceSs for selecting the best of several alternatives. In real life, decisions are often made on the basis of multiple, conflicting and non-commensurable criteria/objectives in uncertain/imprecise environments. Multi-objective evolutionary algorithm (MOEA) usually attempts to find a good approximation to the complete Pareto-optimal front (POF), which then allows the user to decide, among many alternatives. If a single solution is to be selected in a multi-objective optimization problem (MOOP), at some point during the process, the decision maker (DM) has to reveal his/her preferences. Specifying these preferences a priori, i.e., before alternatives are known, often means to ask too much of the DM. On the other hand, searching for all nondominated solutions as most MOEA (a posteriori) do may result in a waste of optimization efforts to find solutions that are clearly unacceptable to the DM. This study introduces an intermediate approach, that asks for partial preference information from the DM as a priori, and then focus the search (using a posteriori) to those regions of the POF that seem most interesting to the DM. In this way, it is possible to provide a larger number of relevant solutions. The DM or user generally, has at least a vague idea about what kind of solutions might be preferred. If such information (preference) is available, it can be used to focus the search, yielding a more fine-grained approximation of the most relevant (from a DM's perspective) areas (regions) of the POF. A novel approach, named as multi-objective evolutionary algorithm based interactive desirability function approach (MOEA-IDFA), to guide the POF into interesting regions is developed. A set of Pareto-optimal solutions is determined via desirability functions (DFs) which reveals DM's preferences regarding different objective regions. The proposed method would be highly effective in generating a compromise solution that is faithful to the DM's preference structure. Theoretical analysis of the methodology is presented to assure the effectiveness of the proposed approach. We apply the proposed approach to numbers of test problems as well as some real life problems having different complexities. It is observed that in almost all cases the proposed approach efficiently guides the population towards the interesting region/regions, allowing a faster convergence and a better coverage of this/these) area/areas of the POF. The idea here is to take the desires of the DM into account more closely when foretelling the biasness onto the set of nondominated solutions. In this way we can create a decision support system (DSS) for the DM to help him/her finding the most satisfactory solution faster. We develop different combination of DFs depending upon the choice of DM and demonstrate these cases with examples. As the approach is MOEA based to validate the proposed approach two different MOEAs: NSGA-II (elitist nondominated sorting genetic algorithm) and MOPSO-CD (multi-objective particle swarm optimization with crowding distance) are presented. An apparent evidence of the efficiency of the proposed ideas is presented via summary of the results of extensive computational tests that have been done in the present thesis. This thesis is described in two parts. The first part deals with development of methodologies (Chapters 2, 3, 4 and 5) and the second part deals with their applications to real world reliability engineering problems (Chapter 6). Conclusions and future scope are summarized in Chapter 7