Tackling a VRP challenge to redistribute scarce equipment within time windows using metaheuristic algorithms

Abstract

This paper reports on the results of the VeRoLog Solver Challenge 2016–2017: the third solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics Optimization. The authors are the winners of second and third places, combined with members of the challenge organizing committee. The problem central to the challenge was a rich VRP: expensive and, therefore, scarce equipment was to be redistributed over customer locations within time windows. The difficulty was in creating combinations of pickups and deliveries that reduce the amount of equipment needed to execute the schedule, as well as the lengths of the routes and the number of vehicles used. This paper gives a description of the solution methods of the above-mentioned participants. The second place method involves sequences of 22 low level heuristics: each of these heuristics is associated with a transition probability to move to another low level heuristic. A randomly drawn sequence of these heuristics is applied to an initial solution, after which the probabilities are updated depending on whether or not this sequence improved the objective value, hence increasing the chance of selecting the sequences that generate improved solutions. The third place method decomposes the problem into two independent parts: first, it schedules the delivery days for all requests using a genetic algorithm. Each schedule in the genetic algorithm is evaluated by estimating its cost using a deterministic routing algorithm that constructs feasible routes for each day. After spending 80 percent of time in this phase, the last 20 percent of the computation time is spent on Variable Neighborhood Descent to further improve the routes found by the deterministic routing algorithm. This article finishes with an in-depth comparison of the results of the two approaches.

Appendix A: Challenge rules

We summarize the challenge rules, which were originally published in (Dullaert et al. 2017). The challenge consisted of three parts, and the first two ran partially parallel in time.

1.1 Appendix A1: All-time-best challenge

The organizers disclosed 25 instances in December 2016: the “all-time-best instances”. Participants were invited to submit a solution to an instance if it was better than the best solution submitted so far for this instance. Progress, i.e., the cost of the best solution over time, was shown to the participants. This information is still visible on the website, and it shows that different instances are won by different participants.

The all-time-best challenge ran till July 2, 2017 and the participants were rewarded in two ways: for every week during the all-time-best period that their solution was the best, and additionally for having the best solution at the end of the challenge. In this part of the challenge, any means, resources and time, were allowed.

1.2 Appendix A2: Restricted resources challenge

This challenge had a more “traditional” form: the resources were restricted, especially the computing time. The time $T_{\text {limit}}$ (seconds) that each algorithm was allowed to run on the organizers’ single core machine is limited by the formula $T_{\text {limit}}=10+2|R|$. Here |R| is the number of (delivery) requests in the instance. The organizers provided a calibration tool, so that each participant could estimate the equivalent time on his or her local machine. In addition, it was not allowed to use any software that is not freely available for commercial use. In particular, this means that for example the use of commercial MILP solvers was forbidden. Each algorithm had to run on a new set of 25 instances (available since April 1 2017). Furthermore, each solver had to run on each instance, using nine different random seeds, to reduce the variance coming from randomized algorithms. Non-randomized algorithms could also profit from the random seeds: they were known to be between $10^8$ and $10^9$ with a different starting digit for each seed, and hence it was possible to detect this and run 9 different deterministic algorithms. The corresponding results and solver binaries were submitted on May 8, 2017.

The evaluation of algorithms in the restricted resources challenge was done as follows. A rank score was calculated per instance for each solver. First, per instance, the two best solutions and the two worst solutions found by the solver were removed. The remaining five solutions were used to compute the score of the solver. If these five solutions were all feasible, their average counted as the score of the solver. Alternatively, if there were infeasible solutions among the middle 5 solutions, that solver was first ranked with respect to the number of feasible solutions, and secondary by the average cost of the feasible ones. Finalists were announced on June 1.

1.3 Appendix A3: The finals

The finalists’ solvers were run by the organizers on a set of 50 not previously disclosed (the so-called hidden) instances. Again, per solver per instance but equal for each finalist, nine runs with different random seeds were done, again with nine different starting digits. A solver ranking per instance was made with the same rules as above, as well as a ranking of the solvers based on these scores. The winner of the challenge was the participant whose solver had the lowest mean of the ranks.