A capacitated vehicle routing problem with two-dimensional loading constraints is addressed. Associated with each customer are a set of rectangular items, the total weight of the items, and a time window. Designing exact algorithms for the problem is very challenging because the problem is a combination of two NP-hard problems. An exact branch-and-price algorithm and an approximate counterpart are proposed to solve the problem. We introduce an exact dominance rule and an approximate dominance rule. To cope with the difficulty brought by the loading constraints, a new column generation mechanism boosted by a supervised learning model is proposed. Extensive experiments demonstrate the superiority of integrating the learning model in terms of CPU time and calls of the feasibility checker. Moreover, the branch-and-price algorithms are able to significantly improve the solutions of the existing instances from literature and solve instances with up to 50 customers and 103 items. Summary of Contribution: We wish to submit an original research article entitled “Learning-based branch-and-price algorithms for a vehicle routing problem with time windows and two-dimensional loading constraints” for consideration by IJOC. We confirm that this work is original and has not been published elsewhere, nor is it currently under for publication elsewhere. In this paper, we report a study in which we develop two branch-and-price algorithms with a machine learning model injected to solve a vehicle routing problem integrated the two-dimensional packing. Due to the complexity brought by the integration, studies on exact algorithms in this field are very limited. Our study is important to the field, because we develop an effective method to significantly mitigate computational burden brought by the packing problem so that exactness turns to be achievable within reasonable time budget. The approach can be generalized to the three-dimensional case by simply replacing the packing algorithm. It can also be adapted for other VRPs when high-dimensional loading constraints are concerned. Broadly speaking, the study is a typical example of adopting supervised learning to achieve acceleration for operations research algorithms, which expands the envelop of computing and operations research. Hence, we believe this manuscript is appropriate for publication by IJOC.

Abstract The mixed capacitated general routing problem (MCGRP) is defined over a mixed graph, for which some nodes, arcs, and edges must be serviced. The problem consists of determining a set of routes of minimum cost that satisfy the demand. Some problems like salt spreading have a time‐dependent demand which was ignored in the previous studies. This variation of demand is due to the weather or traffic conditions. This study presents a mixed integer programming model without graph transformation to node routing. We use CPLEX to solve small instances and we develop a Slack Induction by String Removals metaheuristic for large instances adapted to this problem. The proposed model and metaheuristic were tested on problems derived from a set of classical instances of the MCGRP with some modifications to include time‐dependent demands.

The rural postman problem with time windows is the problem of serving some required edges with one vehicle; the vehicle must visit these edges during established time windows. This article presents a competitive adaptive large neighborhood search algorithm to solve the problem. Computational experiments are performed on a large set of instances with up to 104 required edges. The results show that this approach is efficient, significantly reducing the computational time on large instances and achieving good solutions: the algorithm is able to solve to optimality 224 of 232 instances. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 44–59 2017

This article studies the snow plow routing problem, which is a modified version of the min–max problem with k‐vehicles for arc routing on a mixed graph with hierarchy. Each arc or edge is given a priority and instead of minimizing the overall finishing time, we minimize the latest finishing time for each priority class. We consider turn restrictions, route balancing, and variable vehicle speeds in a real large‐scale network. To solve the problem, we present a graph transformation from a directed rural postman problem with turn penalties to an asymmetric traveling salesman problem. We then make the following modifications to the metaheuristics to better handle the constraints: development of new neighborhood operators, several applications of the same destruction operators before repair of the solution, and a dynamic arc‐grouping procedure when links are removed or inserted. We tested our methodology on three real networks with 1,626 to 2,146 street segments and 613 to 723 intersections. The results show that our approach can improve the solution, and the grouping procedure is helpful. The results also show that some operators perform better than others; the network topology seems to explain these variations. Finally, we validated our methodology by comparing to some routes planned in the past and to some routes obtained from a commercial solver. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 195–215 2017

Abstract The close‐enough arc routing problem has an interesting real‐life application to routing for meter reading. In this article, we propose a new mathematical formulation for this problem. We analyze our formulation and compare it with two formulations in the literature. We also develop branch‐and‐cut algorithms to solve the problem to optimality. We present computational results for instances based on three types of graphs: directed, undirected, and mixed. Copyright © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(1), 107–118 2014

The Rural Postman Problem with Time Windows for the undirected case is introduced. The problem occurs in the monitoring of roads for black-ice detection. Different formulations are proposed and tested on sets of instances adapted from the literature. A cutting plane algorithm based on valid inequalities for the Traveling Salesman Problem (TSP) with Time Windows and the Precedence Constrained TSP is presented as solution method and tested on a set of real-life networks. Computational results show that this approach is able to solve to optimality instances with up to 104 required edges. At the end of the article the formulations for the undirected case are extended to the directed case. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(3), 169–180 2014

This article describes the problem in which the edges of a network represent customers, and a quantity of material is delivered to them so that each one achieves a desired inventory level while finding the lowest‐cost route of delivery. Routing and inventory decisions are made at the same time. An example of an application of this problem is dust suppression in open‐pit mines. A fleet of trucks spray water along the roads of a mine. Humidity increases the effectiveness of dust‐particle retention. Because the level of humidity decreases, replenishment is done periodically. Other examples of applications include dust suppression in forest roads and plants watering in street medians and sidewalks. We develop a mathematical model that combines two objectives: An inventory objective that minimizes the penalty for the lack of humidity and a routing objective that minimizes watering and traversing costs. Due to the complexity of the mathematical model, we developed an adaptive large neighborhood search algorithm that combines several destroy and repair operators dynamically. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(2), 125–139 2014

This paper presents an optimal constraint programming approach for the open-shop scheduling problem, which integrates recent constraint propagation and branching techniques with new upper bound heuristics. Randomized restart policies combined with nogood recording allow us to search diversification and learning from restarts. This approach is compared with the best-known metaheuristics and exact algorithms, and it shows better results on a wide range of benchmark instances.

Abstract We present a new two‐commodity flow formulation for the traveling salesman problem. Each commodity corresponds to a resource that is either distributed or picked up along the tour of all nodes. This formulation is partcularly well suited to handling time window constraints; the resource used is then the time. This formulation can be extended to the makespan problem. For a n‐node problem, the linear relaxation of the formulation involves only O(n) constraints and O(n2) variables. Implementation issues are discussed and numerical experimentations have been realized for problems of up to 60 nodes. © 1993 by John Wiley & Sons, Inc.