Supporting decision making in combinatorially explosive multicriteria situations

Abstract

Several real-world problems, including distributed system design and product design among others, are characterized by combinatorially explosive solution spaces as well as multiple, conflicting criteria. Strategies for finding near-optimal solutions, developed for combinatorial problems, are not applicable in such situations, which require a balance between extensive computation and continual interaction. This makes support or automation of these decisions a difficult task. Current approaches to solve these problems fall in three categories: analytical, genetic algorithm-based approaches and local generators. They frequently assume well-behaved functions and clear understanding of interdependencies among criteria. Many such problems, however, present noisy and discontinuous evaluation functions and contain holistic interdependencies among these functions, rendering these solution approaches inadequate for these problems. We propose a theoretically grounded approach for decision support for this class of problems. The approach combines broad and deep searches with decision-maker feedback that allows the decision-maker to guide and/or stop the search. Specifically, it provides the decision-maker information about (a) the search spaces explored/probed so far, and (b) the search space not yet explored (or may never be explored). We operationalize the approach in a two-phase solution procedure. The first phase — broad characterization of search spaces — requires choices about randomization, sampling and decision space estimation techniques. The second phase — iterative local probes — requires choices about local search heuristics, and fuzzy interpretations based on which the decision-maker can evaluate alternatives and/or stop the search. We demonstrate a specific instantiation of the approach for a multicriteria object assignment problem to verify the feasibility of our approach.