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

Many real-world optimization problems are dynamics. A solution proposal is approached for the dynamic problem of selecting project portfolios with multiple objectives and decision makers' preferences. The objective is to determine the projects that optimize benefits considering the budgetary restrictions that change periodically. It is well-known that the problem's difficulty increases with the preferences of the decision maker and more than one objective to satisfy. This work presents a new formulation of the problem and a fuzzy method to incorporate the preferences, named fuzzy filter (FF). This method uses fuzzy outranking relations to include controlled intensification and diversification to the solution process. It keeps only non-dominated solutions in agreement with a decision maker for intensification. For diversification, it creates a nadir point from the filtered solutions and generates new solutions from this point. Two state-of-the-art algorithms were adapted to incorporate the proposed FF method. To validate this proposal, instances with controlled difficulty were generated from easy to difficult. The experimentation showed that the FF improves the ability of algorithms to approach the region of interest of the decision maker when compared against their dynamic version without preferences.