A heuristic search approach for solving multiobjective non-order-preserving path selection problems

We consider the problem of routing a vehicle making multiple intermediate stops, assuming a non-order-preserving, multiattribute reward structure. Sub-paths of optimal paths may not be optimal for such a reward structure, which may result from routing a pick-up and delivery vehicle carrying hazardous materials that is routed on the basis of minimizing cost and risk. We assume that a priori bounds exist on the rewards from the vehicle's current position to each of the intermediate destinations and to the depot through all the intermediate destinations that have yet to be visited. Precise calculations of these rewards would require additional computational effort. Two heuristic search algorithms, BU* and DU*, are developed and analyzed. Both algorithms satisfy termination, completeness, and admissibility properties. Results indicate that BU* is guaranteed to perform no worse given better heuristic information, a guarantee that cannot be made for DU*. Computational requirements are illustrated through examples based on a real network in northeast Ohio.