Multi-depot Vehicle Routing Problem With Time Windows Research Articles

Logistics Distribution Route Optimization With Time Windows Based on Multi-Agent Deep Reinforcement Learning

Multi-depot vehicle routing problem with time windows (MDVRPTW) is a valuable practical issue in urban logistics. However, heuristic methods may fail to generate high-quality solutions for massive problems instantly. Thus, this article presents a novel reinforcement learning algorithm integrated with a multi-head attention mechanism and a local search strategy to solve the problem efficiently. The routing optimization was regarded as a vehicle tour generation process and an encoder-decoder was used to generate routes for vehicles departing from different depots iteratively. A multi-head attention strategy was employed for mining complex spatiotemporal correlations within time windows in the encoder. Then, a decoder with multi-agent was designed to generate solutions by optimizing reward and observing transition state. Meanwhile, a local search strategy was employed to improve the quality of solutions. The experiments results demonstrate that the proposed method can significantly outperform traditional methods in effectiveness and robustness.

Sustainable collaborative strategy in pharmaceutical refrigerated logistics routing problem

The rapid growth of pharmaceutical refrigerated logistics poses sustainability challenges, including elevated costs, energy consumption, and resource inefficiency. Collaborating multiple depots can enhance logistics efficiency when standalone distribution centres have limited transport resources, i.e. refrigerated vehicles. However, the sustainable benefits and performance across different strategies remain unexplored. This study fills this research gap by addressing a refrigerated pharmaceutical routing problem. While many collaborative strategies prioritise economic and environmental benefits, our approach highlights a vital social indicator: maintaining vehicle flow equilibrium at each depot during collaboration. This ensures the stability of transport resources for all stakeholders, promoting sustainable collaborative logistics. The problem is formulated as a multi-depot vehicle routing problem with time windows (MDVRPTW). Three collaborative strategies using Clustering VRP (CLUVRP) and improved Open VRP (OVRP) are proposed and compared. We develop two approaches to address traditional OVRP limitations in ensuring vehicle flow equilibrium at each depot. Our models consider perishable pharmaceuticals and time-dependent travel speeds. Three hybrid heuristics based on Simulated Annealing and Variable Neighborhood Search (SAVNS) are proposed and evaluated for efficacy. Computational experiments and a case study demonstrate distinct sustainable benefits across various strategies, offering valuable insights for decision-makers in the refrigerated logistics market.

An adaptive ant colony algorithm for crowdsourcing multi-depot vehicle routing problem with time windows

Logistics distribution faces difficulties such as increasing delivery demands, demanding delivery time and lower delivery costs. However, the routing optimization for logistic distribution is not a simple vehicle routing problem (VRP). This study focuses on crowdsourcing multi-depot vehicle routing problem with time windows (MDVRPTW) problem, permitting one crowdsourcing driver to deliver multiple customers, which has not been covered yet. To quickly distribute many delivery tasks within a certain time, this paper proposes a two-stage MDVRPTW framework. The first stage is the division stage in which a k-means algorithm based on the elbow method is used to transform the multi-depot problem into several single-depot problems. Then a crowdsourcing VRPTW model is developed, which is a mixed-integer linear programming model. The second stage is the optimization stage, for which an adaptive ant colony (ADACO) algorithm is proposed to determine the most reasonable distribution routes for each distribution center. Solomons classic VRP data is then used to validate the models’ effectiveness, with the results confirming that the crowdsourcing MDVRPTW strategy could save 10.02% costs than traditional MDVRPTW strategy. By comparison, the ADACO algorithm could significantly improve the ACO’s weakness of falling into a local optimum, and would be more suitable for solving large-scale vehicle routing problems than the GUROBI solver.

A bio-inspired approach: Firefly algorithm for Multi-Depot Vehicle Routing Problem with Time Windows

In this research, an improved bio-inspired metaheuristic named firefly is utilized to solve the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRP-TW) and it is a generalization of Vehicle Routing Problem with Time Windows. This paper discusses the use of biological intelligence in analysis and optimization on MDVRP-TW. The objective of the MDVRP-TW is to minimize the overall distance, means of transportation within a specified time gap, along with other constraints such as limitation of vehicle capacity, restrictions of route duration length to satisfy the customer’s requirements. The routes must be designed where each customer is visited only once in a particular time gap with one vehicle and all the routes must originate and end at the same depot. The overall demand should not go beyond the vehicle’s capacity on each route. Multi-objective problems have attracted the attentions of many researchers in recent years, as they are more closely related to real-world situations. However, transportation is a significant factor for the current society, exhibiting and planning a complicated transport system was a very thought-provoking task. Many research studies have shown several successful metaheuristics and heuristic methodologies to solve MDVRP-TW in which, instead of a single depot, numerous depots with varying locations. In this work considered both the earliest time and latest arrival time window (double-sided time window). It is assumed that if an arrival time is more significant than the latest time, it will lead to an infeasible solution whereas, if an arrival time is lesser than the earliest time, then it will lead to a waiting time. However, due to its challenging task and multi-objective and limitations, there is still a space to solve it. In this work, a novel technique that combines an improved firefly algorithm (IFA), which uses different mechanisms, namely, inter-depot approach in assignment phase, Clarke & wright algorithm, and local search method in routing and scheduling phase were applied. The suggested technique has been evaluated using Cordeau standard benchmark instances and proved the technique’s novelty and feasibility. In a few circumstances, the modified firefly algorithm outperforms other algorithms, and optimal benchmark solution in terms of results and competence.

Optimizing nonlinear charging times of electric vehicle routing with genetic algorithm

With the rising share of electric vehicles used in the service industry, the optimization of their specific constraints is gaining importance. Lowering energy consumption, time of charging and the strain on the electric grid are just some of the issues that must be tackled, to ensure a cleaner and more efficient industry. This paper presents a Two-Layer Genetic Algorithm (TLGA) for solving the capacitated Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW) and Electric Vehicles (EV) with partial nonlinear recharging times (NL) – E-MDVRPTW-NL. Here, the optimization goal is to minimize driving times, number of stops at electric charging stations and time of recharging while taking the nonlinear recharging times into account. This routing problem closes the gap between electric vehicle routing problem research on the one hand and its applications to several problems with numerous real-world constraints of electric vehicles on the other. Next to the definition and the formulation of the E-MDVRPTW-NL, this paper presents the evolutionary method for solving this problem using the Genetic Algorithm (GA), where a novel two-layer genotype with multiple crossover operators is considered. This allows the GA to not only solve the order of the routes but also the visits to electric charging stations and the electric battery recharging times. Various settings of the proposed method are presented, tested and compared to competing meta-heuristics using well-known benchmarks with the addition of charging stations.

Investigation of Convergence Properties of Ant Colony Based Algorithms

The paper presents the Ant Colony Optimization (ACO) algorithms, and investigates their convergence properties. Our investigation is limited to the following ACO algorithms: Ant System, MAX-MIN Ant System, Elitist Strategy of Ant System and Rank Based Version of Ant System. In the literature can be seen, that a novel of optimization problems are solved with ACO algorithms. In our investigation, we limited the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW), which is an NP-hard discrete optimization problem. The paper presents a literature review in connection with ACO algorithms, and Vehicle Routing Problem (VRP). After that, the mathematical model is written. The paper also presents the implemented algorithms, and the test results based on benchmark data.

A Survey for Vehicle Routing Problems and Its Derivatives

Based on the research of recent papers on routing optimization, this paper classifies routing problem into traditional vehicle routing problem and its derivatives, such as CVRP (Capacity Vehicle Routing Problem), HVRP (Heterogeneous Vehicle Routing Problem), MDVRP (Multi-warehouse Vehicle Routing Problem, VRPTW (Vehicle Routing Problem with Time Window). Optimization problem, MDVRPTW (multi-depot vehicle routing problem with time windows), MDHVRPTW (multi-depot heterogeneous vehicle routing problem with time windows). The characteristics of the above problems are summarized and analyzed, and the innovative solution methods are proposed. Finally, the further research trends and hot spots of the path optimization problem are prospected.

Multi-depot vehicle routing problem with time windows considering delivery and installation vehicles

We extend the multi-depot vehicle routing problem with time windows (MDVRPTW), a practical and challenging problem in logistics and supply chain management, to a study of service vehicles used for delivery and installation of electronics. This study shows that MDVRPTW results can be used to minimize fixed costs of the depots and the delivery and installation vehicles as well as expenses related to travel distances and labor. Along with a mixed integer programming model, we develop a heuristic and a genetic algorithm to identify a near-optimal solution. Computational results demonstrate that the proposed algorithms can efficiently be used to solve relatively large problems.

IJARCCE - Computer and Communication Engineering

2 Abstract- We present a novel Ordered Distance Vector (ODV) based Equi-begin with Variable-diversity (EV) Technique for the exact solution of a variation of the vehicle routing problem with time windows in which the transportation fleet is made by vehicles with different capacities and fixed costs, based on different depots. The Multi- Depot Vehicle Routing Problem with Time Windows (MDVRPTW) is a generalization of the standard Vehicle Routing Problem (VRP). The VRPTW is NP-Complete. The MDVRPTW problem is addressed using an efficient Genetic Algorithm (GA). Genetic algorithm is a powerful optimization technique to solve NP-Complete problems. In GA different initial population seeding techniques were used to find out the performance of an individual. In this paper, we are analyzing the performance of Gene Bank technique with a proposed novel Ordered Distance Vector (ODV) based EV Technique in terms of convergence rate (%), quality solution and convergence diversity. Different authors provided different bench mark instances for MDVRPTW in neo research group. In order to compare the effectiveness and performance of the proposed population seeding technique, we are using Cordeaus benchmark instances; it contains 20 different instances of MDVRPTW obtained from VRPLIB were experimented using MATLAB software.

Multi-phase modified shuffled frog leaping algorithm with extremal optimization for the MDVRP and the MDVRPTW

In this work, a novel multi-phase modified shuffled frog leaping algorithm (MPMSFLA) framework is presented to solve the multi-depot vehicle routing problem (MDVRP) more quickly. The presented algorithm adopts the K-means algorithm to execute the clustering analyses for all customers, generates a frog population according to the result of the clustering analyses, and then proceeds to the three-phase process. In the first phase, a cluster MSFLA local search is carried out for each cluster. In the second phase, the algorithm selects good individuals through a binary tournament to construct a new population and then performs a global optimization for all customers and depots using the global MSFLA. In the third phase, a cluster adjustment is implemented for the population to generate new clusters. These procedures continue until the convergence criterion is satisfied. The experimental results show that our algorithm can achieve a high quality solution within a short runtime for the MDVRP, the MDVRP with time windows (MDVRPTW) and the capacitated vehicle routing problem (CVRP). The proposed algorithm is suitable for solving large-scale problems.

Metaheuristic for solving routing problem in logistics management

Multi Depot Vehicle Routing Problem with Time Windows (MDVRPTW) is one of the major logistics problems In this paper a two phase heuristics is proposed in which the customers are assigned to the depot in the first phase The routes are constructed with modified ant colony optimisation procedure and are improved using 2-Opt procedure in phase two The proposed heuristic has been applied to Cordeau MDVRPTW benchmark problems It is found that the proposed heuristic gives promising and better results, on an average, as compared to those solutions given by the existing heuristic for the MDVRPTW.

Combination of Multiple Ant Colony System and Simulated Annealing for the Multidepot Vehicle-Routing Problem with Time Windows

The vehicle-routing problem (VRP) is an important management problem in the field of physical distribution and logistics. In practice, the logistics system usually includes more than one depot, and the start of the service at each customer must be within a given time window. Hence, the multidepot vehicle-routing problem with time windows (MDVRPTW) is an important variant of the VRP. The MDVRPTW is a difficult combinatorial optimization problem due to the many complex constraints involved. The research presented in this paper proposes a multiple ant colony system (MACS) to solve the problem. In addition, two hybrid algorithms, which combine the strengths of MACS and simulated annealing, are developed to improve solution quality. The performance of the proposed algorithms is tested on several benchmark instances and compared with that of other algorithms in the literature. The results indicate that the proposed algorithms are effective in solving the MDVRPTW, and six new best solutions are found.

New measures of proximity for the assignment algorithms in the MDVRPTW

This paper proposes new proximity measures for assignment algorithms for the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW). Given the intrinsic difficulty of this problem class, two-step approximation methods of the type ‘cluster first, route second’ seem to be the most promising for practical size problems. The focus is on the clustering phase, the assignment of customers to depots. Our approach is to extend the existing metrics with time windows. New measures that include time windows and distances are added to two assignment heuristics, that previously only used distance to evaluate proximity between customers and depots. A computational study of their performance is presented, which shows that the inclusion of time windows in the measures of proximity gives better results, in terms of routing, than only using the distance.

New assignment algorithms for the multi-depot vehicle routing problem

This paper considers the design and analysis of algorithms for the multi-depot vehicle routing problem with time windows (MDVRPTW). Given the intrinsic difficulty of this problem class, approximation methods of the type ‘cluster first, route second’ (two-step approaches) seem to offer the most promise for practical size problems. After describing six heuristics for the cluster part (assignment of customers to depots) an initial computational study of their performance is conducted. Finding, as expected, that the heuristics with the best results (in terms of the routing results) are those with the largest computational efforts.