Solving hybrid-vehicle routing problem using modified simulated annealing

In this paper, we consider the hybrid vehicle routing problem (HVRP) at which the vehicle consumes two types of power: fuel and electricity. The aim of this problem is to minimize the total cost of travelling between customers, provided that each customer is visited only once. The vehicle departs from the depot and returns after completing the whole route. This optimization problem is solved using a modified simulated annealing (SA) heuristic procedure with constant temperature. This approach is implemented on a numerical example and the results are compared with the SA algorithm with decreasing temperature. The obtained results show that using the SA with constant temperature overrides the SA with decreasing temperature. The results indicate that SA with decreasing temperature needs twice the number of iterations needed by the SA with constant temperature to reach a near optimum solution

Low Carbon Logistics Optimization for Multi-depot CVRP with Backhauls - Model and Solution

CVRP (Capacitated Vehicle Routing Problems) is the integrated optimization of VRP and Bin Packing Problem (BPP), which has far-reaching practical significance, because only by taking both loading and routing into consideration can we make sure the delivery route is the most economic and the items are completely and reasonably loaded into the vehicles. In this paper, the CVRP with backhauls from multiple depots is addressed from the low carbon perspective. The problem calls for the minimization of the carbon emissions of a fleet of vehicles needed for the delivery of the items demanded by the clients. The overall problem, denoted as 2L-MDCVRPB, is NP-hard and it is very difficult to get a good performance solution in practice. We propose a quantum-behaved particle swarm optimization (QPSO) and exploration heuristic local search algorithm (EHLSA) in order to solve this model. In addition, three groups of computational experiments based on well-known benchmark instances are carried out to test the efficiency and effectiveness of the proposed model and algorithm, thereby demonstrating that the proposed method takes a short computing time to generate high quality solutions. For some instances, our algorithm can obtain new better solutions

A branch-and-cut algorithm for vehicle routing problems with three-dimensional loading constraints

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if support constraints are enabled in the loading subproblem and call this the incremental feasibility property. Consequently, different infeasible path definitions apply to different 3L-CVRP variants and we introduce several variant-depending lifting steps to strengthen infeasible path inequalities. The loading subproblem is solved exactly using a flexible constraint programming model to determine the feasibility or infeasibility of a route. An extreme point-based packing heuristic is implemented to reduce time-consuming calls to the exact loading algorithm. Furthermore, we integrate a start solution procedure and periodically combine memoized feasible routes in a set-partitioning-based heuristic to generate new upper bounds. A comprehensive computational study, employing well-known benchmark instances, showcases the significant performance improvements achieved through the algorithmic enhancements. Consequently, we not only prove the optimality of many best-known heuristic solutions for the first time but also introduce new optimal and best solutions for a large number of instances.Comment: 33 pages, 13 figures, 7 tables, Submitted to Transportation Scienc

Hybrid Algorithms for the Vehicle Routing Problem with Pickup and Delivery and Two-dimensional Loading Constraints

We extend the classical Pickup and Delivery Problem (PDP) to an integrated routing and two-dimensional loading problem, called PDP with two-dimensional loading constraints (2L-PDP). A set of routes of minimum total length has to be determined such that each request is transported from a loading site to the corresponding unloading site. Each request consists of a given set of 2D rectangular items with a certain weight. The vehicles have a weight capacity and a rectangular two-dimensional loading area. All loading and unloading operations must be done exclusively by movements parallel to the longitudinal axis of the loading area of a vehicle and without moving items of other requests. Furthermore, each item must not be moved after loading and before unloading. The problem is of interest for the transport of rectangular-shaped items that cannot be stacked one on top of the other because of their weight, fragility or large dimensions. The 2L-PDP also generalizes the well-known Capacitated Vehicle Routing Problem with Two-dimensional Loading Constraints (2L-CVRP), in which the demand of each customer is to be transported from the depot to the customer’s unloading site.This paper proposes two hybrid algorithms for solving the 2L-PDP and each one consists of a routing and a packing procedure. Within both approaches, the routing procedure modifies a well-known large neighborhood search for the one-dimensional PDP and the packing procedure uses six different constructive heuristics for packing the items. Computational experiments were carried out using 60 newly proposed 2L-PDP benchmark instances with up to 150 requests

A matheuristic approach to the integration of three-dimensional Bin Packing Problem and vehicle routing problem with simultaneous delivery and pickup

This work presents a hybrid approach to solve a distribution problem of a Portuguese company in the automotive industry. The objective is to determine the minimum cost for daily distribution operations, such as collecting and delivering goods to multiple suppliers. Additional constraints are explicitly considered, such as time windows and loading constraints due to the limited capacity of the fleet in terms of weight and volume. An exhaustive review of the state of the art was conducted, presenting different typology schemes from the literature for the pickup and delivery problems in the distribution field. Two mathematical models were integrated within a matheuristic approach. One model reflects the combination of the Vehicle Routing Problem with Simultaneous Delivery and Pickup with the Capacitated Vehicle Routing Problem with Time Windows. The second one aims to pack all the items to be delivered onto the pallets, reflecting a three-dimensional single bin size Bin Packing Problem. Both formulations proposed—a commodity-flow model and a formulation of the Three-Dimensional Packing Problem must be solved within the matheuristic. All the approaches were tested using real instances from data provided by the company. Additional computational experiments using benchmark instances were also performed.This research was funded by national funds through FCT—Fundação para a Ciência e a Tecnologia, under the projects UIDB/00285/2020, UIDB/00319/2020. This work was supported by the Research Unit on Governance, Competitiveness and Public Policies (UIDB/04058/2020) + (UIDP/04058/2020), funded by national funds through the Foundation for Science and Technology, IP. This work was also funded by FEDER in the frame of COMPETE 2020 under the project POCI-01-0247-FEDER-072638

Unlocking Carbon Reduction Potential with Reinforcement Learning for the Three-Dimensional Loading Capacitated Vehicle Routing Problem

Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a solution to increase efficiency, but challenges remain to make this a possibility. One key challenge is the efficient computation of viable solutions for co-loading and routing. Current operations research methods suffer from non-linear scaling with increasing problem size and are therefore bound to limited geographic areas to compute results in time for day-to-day operations. This only allows for local optima in routing and leaves global optimisation potential untouched. We develop a reinforcement learning model to solve the three-dimensional loading capacitated vehicle routing problem in approximately linear time. While this problem has been studied extensively in operations research, no publications on solving it with reinforcement learning exist. We demonstrate the favourable scaling of our reinforcement learning model and benchmark our routing performance against state-of-the-art methods. The model performs within an average gap of 3.83% to 8.10% compared to established methods. Our model not only represents a promising first step towards large-scale logistics optimisation with reinforcement learning but also lays the foundation for this research stream

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

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A simheuristic for routing electric vehicles with limited driving ranges and stochastic travel times

Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.Peer Reviewe