An adaptive large neighborhood search heuristic for multi-commodity two-echelon vehicle routing problem with satellite synchronization

<p style='text-indent:20px;'>In considering route optimization from multiple distribution centers called depots via some intermediate facilities called satellites to final customers with multiple commodities request, we introduce the Multi-Commodity Two-Echelon Vehicle Routing Problem with Satellite Synchronization (MC-2E-VRPSS). The MC-2E-VRPSS involves the transportation from multiple depots to satellites on the first echelon and the deliveries from satellites to final customers on the second echelon. The MC-2E-VRPSS integrates satellite synchronization constraints and time window constraints for satellites on the two-echelon network and aims to determine cost-minimizing routes for the two echelons. The satellite synchronization constraints which trucks from the multiple depots to some satellites need to be coordinated guarantee the efficiency of the second echelon network. In this study, we develop a mixed-integer programming model for the MC-2E-VRPSS. For validating the model formulation, we conduct the computational experiments on a set of small-scale instances using GUROBI and an adaptive large neighborhood search (ALNS) heuristic which we develop for the problem. Furthermore, the computation experiments for evaluating the applicability of the ALNS heuristic compared with large neighborhood search (LNS) on a set of large-scale instances are also conducted, which proved the effectiveness of the ALNS.</p>

Adaptive large neighborhood search for mixed integer programming

Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver adaptively concentrates its limited computational budget by learning which LNS heuristics work best for the MIP problem at hand. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts as a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search spaces, which we call auxiliary problems. The decision which auxiliary problem should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available auxiliary problems based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing prioritization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some LNS problems which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP.

Preference-Based Multi-Objective Optimization for Synchromodal Transport Using Adaptive Large Neighborhood Search

Decision-makers in synchromodal transport (ST) have different preferences toward different objectives, such as cost, time, and emissions. To solve the conflicts among objectives and obtain preferred solutions, a preference-based multi-objective optimization model is developed. In ST, containers need to be transferred across modes, therefore the optimization problem is formulated as a pickup and delivery problem with transshipment. The preferences of decision-makers are usually expressed in linguistic terms, so weight intervals, that is, minimum and maximum weights, are assigned to objectives to represent such vague preferences. An adaptive large neighborhood search is developed and used to obtain non-dominated solutions to construct the Pareto frontier. Moreover, synchronization is an important feature of ST and it makes available resources fully utilized. Therefore, four synchronization cases are identified and studied to make outgoing vehicles cooperate with changes of incoming vehicles’ schedules at transshipment terminals. Case studies in the Rhine-Alpine corridor are designed and the results show that the proposed approach provides non-dominated solutions which are in line with preferences. Moreover, the mode share under different preferences is analyzed, which signals that different sustainability policies in transportation will influence the mode share.