Pareto ant colony optimization with ILP preprocessing in multiobjective project portfolio selection

One of the most important, common and critical management issues lies in determining the "best" project portfolio out of a given set of investment proposals. As this decision process usually involves the pursuit of multiple objectives amid a lack of a priori preference information, its quality can be improved by implementing a two-phase procedure that first identifies the solution space of all efficient (i.e., Pareto-optimal) portfolios and then allows an interactive exploration of that space. However, determining the solution space is not trivial because brute-force complete enumeration only solves small instances and the underlying NP-hard problem becomes increasingly demanding as the number of projects grows. While meta-heuristics in general provide an attractive compromise between the computational effort necessary and the quality of an approximated solution space, Pareto Ant Colony Optimization (P-ACO) has been shown to perform particularly well for this class of problems. In this paper, the beneficial effect of P-ACO's core function (i.e., the learning feature) is substantiated by means of a numerical example based on real world data. Furthermore, the original P-ACO approach is supplemented by an integer linear programming (ILP) preprocessing procedure that identifies several efficient portfolio solutions within a few seconds and correspondingly initializes the pheromone trails before running P-ACO. This extension favors a larger exploration of the search space at the beginning of the search and does so at a low cost.