Fuzzy Filter: a method to solve a dynamic portfolio selection problem with preference incorporation

Abstract

Many real-world optimization problems involve changes related to the passage of time; this characteristic is known as dynamism. In this paper, we approach a dynamic multi-objective project portfolio selection problem with preferences. The objective of the general problem consists of determining the set of projects that optimize a vector of benefits considering the budget constraints. Both benefits and budgets are periodically changing, impacting the definition of the problem. Besides, the problem difficulty increases with the preferences of a decision-maker and more than one objective to satisfy. In this work, we present a new formulation of the described problem and a novel fuzzy method to incorporate the preferences of a decision maker. The method, called Fuzzy Filter (FF), uses fuzzy outranking relations to include controlled intensification and diversification to the solution process. For intensification, it keeps only non-dominated solutions that are in agreement with a decision maker. For diversification, it creates a nadir point from the filtered solutions and generates new solutions from this point. In order to provide an optimization benchmark of a real problem, instances with controlled difficulty were generated, and two algorithms of state of art were adapted to incorporate FF and dynamism. An analysis of extensive experimentation is presented as part of the benchmark.