Towards Decision Support in Dynamic Bi-Objective Vehicle Routing

We consider a dynamic bi-objective vehicle routing problem, where a subset of customers ask for service over time. Therein, the distance traveled by a single vehicle and the number of unserved dynamic requests is minimized by a dynamic evolutionary multi-objective algorithm (DEMOA), which operates on discrete time windows (eras). A decision is made at each era by a decision-maker, thus any decision depends on irreversible decisions made in foregoing eras. To understand effects of sequences of decision-making and interactions/dependencies between decisions made, we conduct a series of experiments. More precisely, we fix a set of decision-maker preferences D and the number of eras n{$<$}inf{$>$}t{$<$}/inf{$>$} and analyze all $|D|\^{n_t}$ combinations of decision-maker options. We find that for random uniform instances (a) the final selected solutions mainly depend on the final decision and not on the decision history, (b) solutions are quite robust with respect to the number of unvisited dynamic customers, and (c) solutions of the dynamic approach can even dominate solutions obtained by a clairvoyant EMOA. In contrast, for instances with clustered customers, we observe a strong dependency on decision-making history as well as more variance in solution diversity.