Group Preference-based Evolutionary Multi-objective Optimization with Non-Equally Important Decision Makers: Application to the Portfolio Selection Problem

Abstract

Recently, Evolutionary Multi-objective Optimization (EMO) researchers have addressed the task of incorporating Decision Maker’s (DM’s) preferences in EMO Algorithms (EMOAs) in order to guide the search towards the preferred region of the Pareto front which is called Region Of Interest (ROI). In fact, the DM is not interested in discovering the whole Pareto front especially with the increase of the number of objectives. Once the ROI is well-approximated, the DM can subsequently select the final solution to realize. Unfortunately, most of the proposed studies assume the uniqueness of the DM which is not the case for several decision making situations. Few preference-based EMOAs have addressed this task by guiding the search based on several reference points each corresponding to a particular DM then searching for an average ROI. However, this method does not resolve the problem and most DMs are still dissatisfied since the EMOA cannot achieve a consensus between the different negotiators. Additionally, DMs are not equally important from a hierarchical viewpoint. In this study, we address this problematic differently by providing the non-equally important DMs with a negotiation support system based on software agent paradigm to aggregate their conflicting preferences before the beginning of the evolutionary process. This negotiation system helps the DMs to confront and adjust their preferences through a number of negotiation rounds. The output of the system is a set of social preferences which will be injected subsequently in the EMOA in order to guide the search towards a satisfying social ROI. The proposed system is demonstrated to be helpful for such group decision making situation through a case study in addition to a practical instance of the Portfolio selection problem.