A Novel adaptive genetic algorithm for Dynamic Vehicle Routing Problem with Backhaul and Two-dimensional loading constraints, A Case in Tunisian Posta

In this paper, we consider an extension of the Dynamic Vehicle Routing Problem with Backhauls integrated with two-dimensional loading problem called DVRPB with 2D loading constraints (2L-DVRPB). In the VRPB, a vehicle can deliver (Linehaul) then collect goods from customers (backhaul) and bring back to the depot. Once customer demand is formed by a set of two-dimensional items the problem will be treat as a 2L-VRPB. The 2L-VRPB has been studied on the static case. However, in most real-life application, new customer requests can be happen over time of backhaul and thus perturb the optimal routing schedule that was originally invented. This problem has not been analysed sofar in the literature. The 2L-DVRPB is an NP-Hard problem, so, we propose to use a Genetic algorithm for routing and a packing problems. We applied our approach in a real case study of the Regional Post Office of the city of Jendouba in the North of Tunisia. Results indicate that the AGA approach is considered as the best approach in terms of solutions quality for a real world routing system.

Learning-Based Branch-and-Price Algorithms for the Vehicle Routing Problem with Time Windows and Two-Dimensional Loading Constraints

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.

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

This work presents a multi-start algorithm for solving the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP) allowing for the rotation of goods. Researches dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics such as the Constructive Genetic Algorithm (CGA), to construct promising initial solutions; a Tabu Search (TS), to improve the initial solutions on the routing problem; and a Large Neighborhood Search (LNS), for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multi-threading programming to improve the performance. Additionally, memory structures, like hash-tables, were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest of the community involved in symmetry studies, such as, graph algorithms and graph theory.

Advanced loading constraints for 3D vehicle routing problems

Given automated order systems, detailed characteristics of items and vehicles enable the detailed planning of deliveries including more efficient and safer loading of distribution vehicles. Many vehicle routing approaches ignore complex loading constraints. This paper focuses on the comprehensive evaluation of loading constraints in the context of combined Capacitated Vehicle Routing Problem and 3D Loading (3L-CVRP) and its extension with time windows (3L-VRPTW). To the best of our knowledge, this paper considers the currently largest number of loading constraints meeting real-world requirements and reducing unnecessary loading efforts for both problem variants. We introduce an approach for the load bearing strength of items ensuring a realistic load distribution between items. Moreover, we provide a new variant for the robust stability constraint enabling better performance and higher stability. In addition, we consider axle weights of vehicles to prevent overloaded axles for the first time for the 3L-VRPTW. Additionally, the reachability of items, balanced loading and manual unloading of items are taken into account. All loading constraints are implemented in a deepest-bottom-left-fill algorithm, which is embedded in an outer adaptive large neighbourhood search tackling the Vehicle Routing Problem. A new set of 600 instances is created, published and used to evaluate all loading constraints in terms of solution quality and performance. The efficiency of the hybrid algorithm is evaluated by three well-known instance sets. We outperform the benchmarks for most instance sets from the literature. Detailed results and the implementation of loading constraints are published online.