Heuristic algorithms for aggregation of incomplete rankings in multiple criteria group decision making

Abstract

We propose heuristics for constructing a compromise incomplete ranking based on partial rankings admitting incomparability. We consider the utilitarian and egalitarian perspectives oriented toward minimizing an average or a maximal distance from any input ranking. The proposed algorithms incorporate genetic algorithms, simulated annealing, tabu search, local search, and intuitive, dedicated procedures. We demonstrate their efficiency in a real-world case study concerning the ranking of insulating materials based on the conflicting, incomplete preferences of a few tens of Decision Makers (DMs). For each DM, we consider a single representative ranking consistent with his/her preferences or thousands of such rankings following incorporation of the robustness concern. The experimental comparison is generalized to artificially generated problems that differ in terms of the numbers of alternatives and input rankings, and diversity levels. The results are quantified with the quality of obtained rankings and computation time.