The Vehicle Routing Problem with Profits and Consistency Constraints

This paper models and solves a new transportation problem of practical importance; the Consistent Vehicle Routing Problem with Pro fits. There are two sets of customers, the frequent customers that are mandatory to service and the non-frequent potential customers with known and estimated profit s respectively, both having known demands and service requirements over a planning horizon of multiple days. The objective is to determine the vehicle routes that maximize the net profit, while satisfying vehicle capacity, route duration and consistency constraints. A new mathematical model is proposed that captures the pro fit collecting nature, as well as other features of the problem. For addressing this computationally challenging problem, an Adaptive Tabu Search has been developed, utilizing both short- and long-term memory structures to guide the search process. The proposed metaheuristic algorithm is evaluated on existing, as well as newly generated benchmark problem instances. Our computational experiments demonstrate the effectiveness of our algorithm, as it matches the optimal solutions obtained for small-scale instances and performs well on large-scale instances. Lastly, the trade-off between the acquired pro fits and consistent customer service is examined and various managerial insights are derived

An Adaptive Memory Programming Framework for the Robust Capacitated Vehicle Routing Problem

We present an adaptive memory programming (AMP) metaheuristic to address the robust capacitated vehicle routing problem under demand uncertainty. Contrary to its deterministic counterpart, the robust formulation allows for uncertain customer demands, and the objective is to determine a minimum cost delivery plan that is feasible for all demand realizations within a prespecified uncertainty set. A crucial step in our heuristic is to verify the robust feasibility of a candidate route. For generic uncertainty sets, this step requires the solution of a convex optimization problem, which becomes computationally prohibitive for large instances. We present two classes of uncertainty sets for which route feasibility can be established much more efficiently. Although we discuss our implementation in the context of the AMP framework, our techniques readily extend to other metaheuristics. Computational studies on standard literature benchmarks with up to 483 customers and 38 vehicles demonstrate that the proposed approach is able to quickly provide high-quality solutions. In the process, we obtain new best solutions for a total of 123 benchmark instances

Why to climb if one can jump: a hill jumping algorithm for the vehicle routing problem with time windows

The most common approaches to solve the variants of the well-known vehicle routing problem are based on metaheuristic hill-climbing search. The deficiency of these methods is slow local search based hill climbing that often is restricted to limited local neighborhood. In this paper we suggest a novel new two-phase metaheuristic that escapes the local minima with jumps of varying size, instead of step by step local hill climbing. The initial solution is first generated with a powerful ejection pool heuristic. The key idea of the improvement phase is to combine large neighborhood search with standard guided local search metaheuristic in a novel way, allowing improved search diversification and escape from local minima in more efficient way through jumps. The algorithm has been tested on the standard Gehring and Homberger benchmarks for the vehicle routing problem with time windows and the results indicate very competitive performance. We found 12 new and 43 matched best-known solutions and the best overall results for all problem sizes at comparable computation times