Multi-objective Vehicle Routing Problem Research Articles

Joint grey time windows and two-dimensional loading design for modelling and solving multi-objective vehicle routing problems

This study defines grey time windows as periods during which customers expect deliveries at a specific time, with an allowance for a certain amount of advance or delay. For model solving, the grey time window is first whitened using the whitening triangle function based on different satisfaction thresholds and corresponding delivery costs. A tightness function is then designed for two-dimensional loading, which measures the effectiveness of different key points and loading postures. Finally, the Iori dataset was utilised to verify the effectiveness of the proposed solution algorithm. To the best of our knowledge, this is the first time the joint design concept of grey time windows and the whitening method have been introduced. Additionally, a grey opportunity-constrained programming model was constructed, with the model transformation and solution methods provided. Simulation results demonstrate that the proposed two-dimensional loading algorithm is both simple and efficient, and that the constructed grey chance-constrained programming model is solvable and has practical application value. Ultimately, this study provides insights for logistics companies on optimising delivery plans under various time window concepts.

An Improved Ant Colony Algorithm with Deep Reinforcement Learning for the Robust Multiobjective AGV Routing Problem in Assembly Workshops

Vehicle routing problems (VRPs) are challenging problems. Many variants of the VRP have been proposed. However, few studies on VRP have combined robustness and just-in-time (JIT) requirements with uncertainty. To solve the problem, this paper proposes the just-in-time-based robust multiobjective vehicle routing problem with time windows (JIT-RMOVRPTW) for the assembly workshop. Based on the conflict between uncertain time and JIT requirements, a JIT strategy was proposed. To measure the robustness of the solution, a metric was designed as the objective. Afterwards, a two-stage nondominated sorting ant colony algorithm with deep reinforcement learning (NSACOWDRL) was proposed. In stage I, ACO combines with NSGA-III to obtain the Pareto frontier. Based on the model, a pheromone update strategy and a transfer probability formula were designed. DDQN was introduced as a local search algorithm which trains networks through Pareto solutions to participate in probabilistic selection and nondominated sorting. In stage II, the Pareto frontier was quantified in feasibility by Monte Carlo simulation, and tested by diversity-robust selection based on uniformly distributed weights in the solution space to select robust Pareto solutions that take diversity into account. The effectiveness of NSACOWDRL was demonstrated through comparative experiments with other algorithms on instances. The impact of JIT strategy is analyzed and the effect of networks on the NSACOWDRL is further discussed.

Multi-Task Multi-Objective Evolutionary Search Based on Deep Reinforcement Learning for Multi-Objective Vehicle Routing Problems with Time Windows

The vehicle routing problem with time windows (VRPTW) is a widely studied combinatorial optimization problem in supply chains and logistics within the last decade. Recent research has explored the potential of deep reinforcement learning (DRL) as a promising solution for the VRPTW. However, the challenge of addressing the VRPTW with many conflicting objectives (MOVRPTW) still remains for DRL. The MOVRPTW considers five conflicting objectives simultaneously: minimizing the number of vehicles required, the total travel distance, the travel time of the longest route, the total waiting time for early arrivals, and the total delay time for late arrivals. To tackle the MOVRPTW, this study introduces the MTMO/DRP-AT, a multi-task multi-objective evolutionary search algorithm, by making full use of both DRL and the multitasking mechanism. In the MTMO/DRL-AT, a two-objective MOVRPTW is constructed as an assisted task, with the objectives being to minimize the total travel distance and the travel time of the longest route. Both the main task and the assisted task are simultaneously solved in a multitasking scenario. Each task is decomposed into scalar optimization subproblems, which are then solved by an attention model trained using DRL. The outputs of these trained models serve as the initial solutions for the MTMO/DRL-AT. Subsequently, the proposed algorithm incorporates knowledge transfer and multiple local search operators to further enhance the quality of these promising solutions. The simulation results on real-world benchmarks highlight the superior performance of the MTMO/DRL-AT compared to several other algorithms in solving the MOVRPTW.

Risk control of epidemic in urban cold-chain transportation

The COVID-19 pandemic has severely disrupted the daily running of urban logistics system, thereby increasing the resilience and health requirements in the design of sustainable logistics system. Most scientific contributions have enriched the knowledge of how to deal with viral infection threats from the external environment but ignored the virus transmission from fomites within the logistics system. This study designs an urban cold-chain logistic network with control strategies to reduce the epidemic risk caused by cold-chain fomites while concurrently balancing the total cost and customer satisfaction, which is modeled as a multi-objective vehicle routing problem (MOVRP). The control strategies are modeled by dividing customer points into small groups, and the virus transmission in populations is considered when evaluating epidemic risk. A multi-objective evolutionary algorithm with special initialization (MOEA-SI) is proposed to solve this problem. Simulation results show that all the strategies can efficiently reduce the epidemic risk with reasonable expense of total cost and customer satisfaction. The introduction of special initialization strategy enables the MOEA-SI to have good performance in balancing the three objectives. The above results can enrich the knowledge of how to deal with unexpected epidemics and help the scientific decision-making in sustainable urban management.

Solving Multi-Objective Vehicle Routing Problems with Time Windows: A Decomposition-Based Multiform Optimization Approach

Solving Multi-Objective Vehicle Routing Problems with Time Windows: A Decomposition-Based Multiform Optimization Approach

Conditional Neural Heuristic for Multiobjective Vehicle Routing Problems.

Existing neural heuristics for multiobjective vehicle routing problems (MOVRPs) are primarily conditioned on instance context, which failed to appropriately exploit preference and problem size, thus holding back the performance. To thoroughly unleash the potential, we propose a novel conditional neural heuristic (CNH) that fully leverages the instance context, preference, and size with an encoder-decoder structured policy network. Particularly, in our CNH, we design a dual-attention-based encoder to relate preferences and instance contexts, so as to better capture their joint effect on approximating the exact Pareto front (PF). We also design a size-aware decoder based on the sinusoidal encoding to explicitly incorporate the problem size into the embedding, so that a single trained model could better solve instances of various scales. Besides, we customize the REINFORCE algorithm to train the neural heuristic by leveraging stochastic preferences (SPs), which further enhances the training performance. Extensive experimental results on random and benchmark instances reveal that our CNH could achieve favorable approximation to the whole PF with higher hypervolume (HV) and lower optimality gap (Gap) than those of the existing neural and conventional heuristics. More importantly, a single trained model of our CNH can outperform other neural heuristics that are exclusively trained on each size. In addition, the effectiveness of the key designs is also verified through ablation studies.

A Neural Multi-Objective Capacitated Vehicle Routing Optimization Algorithm Based on Preference Adjustment

The vehicle routing problem (VRP) is a common problem in logistics and transportation with high application value. In the past, many methods have been proposed to solve the vehicle routing problem and achieved good results, but with the development of neural network technology, solving the VRP through neural combinatorial optimization has attracted more and more attention by researchers because of its short inference time and high parallelism. PMOCO is the most state-of-the-art multi-objective vehicle routing optimization algorithm. However, in PMOCO, preferences are often uniformly selected, which may lead to uneven Pareto sets and may reduce the quality of solutions. To solve this problem, we propose a multi-objective vehicle routing optimization algorithm based on preference adjustment, which is improved from PMOCO. We incorporate the weight adjustment method in PMOCO that is able to adapt to different approximate Pareto fronts and to find solutions with better quality. We treat the weight adjustment as a sequential decision process and train it through deep reinforcement learning. We find that our method could adaptively search for a better combination of preferences and have strong robustness. Our method is experimented on multi-objective vehicle routing problems and obtained good results (about 6% improvement compared with PMOCO with 20 preferences).

Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems.

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by the weight decomposition of objectives. This article proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is then built accordingly. Compared with other learning-based methods, our method can greatly shorten the training time of multiple submodels. Due to the rapid and excellent adaptability of the meta-model, more submodels can be derived so as to increase the quality and diversity of the found solutions. The computational experiments on multiobjective traveling salesman problems and multiobjective vehicle routing problems with time windows demonstrate the superiority of our method over most of the learning-based and iteration-based approaches.

Analysis of multi-objective vehicle routing problem with flexible time windows: The implication for open innovation dynamics

Renewable energy has been a worldwide interest due to a growing energy demand as well as a mounting concern over the hostile impacts from traditional fuels. One of a direction for future renewable energy is the use of biofuel. In this research, we initially apply the K-means algorithm to evaluate the possible locations of collection sites at the upstream of the biofuel supply chain. Next, we propose the multi-objective vehicle routing problem model, in which flexible time windows are synchronized in the model. Additionally, our integrated model evaluates the perspective of socioeconomic by considering total cost – the surrogate criterion for economic aspect as well as the lateness for delivery and the maximum delivery time – the surrogate criteria for social aspect, into account. Finally, we apply a model to a regional case study based on the wood-biomass data of the biofuel supply chain in Thailand, in which the geographic information system is applied.

An improved genetic algorithm for solving the multi-objective vehicle routing problem with environmental considerations

In recent years, the negative impacts of neglecting the environment, particularly global warming caused by greenhouse gases, have gained attention. Many countries and organizations are taking steps to reduce their greenhouse gas emissions and promote sustainable practices. In this paper, we aim to address the gap in the classical Vehicle Routing Problem (VRP) by taking into consideration the environmental effects of vehicles. To find a balance between cost-efficiency and environmental impact, we propose a Hybrid Genetic Algorithm (HGA) to address the Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) and a heterogeneous fleet, taking into account new orders that arrive dynamically during the routing process. This approach takes into consideration the environmental effects of the solutions by optimizing the number and type/size of vehicles used to fulfill both static and dynamic orders. The goal is to provide a solution that is both cost-effective and environmentally friendly, addressing the issue of over-exploitation of energy and atmospheric pollution that threaten our ecological environment. Computational results prove that the hybridization of a genetic algorithm with a greedy algorithm can find high-quality solutions in a reasonable run time.

Stochastic Multi-Objective Vehicle Routing Model in Green Environment With Customer Satisfaction

The Vehicle Routing Problem (VRP) is one of the most studied combinatorial optimization problems in operations research that are classified as NP-hard. Introducing uncertainty to the problem increases the complexity of solving such problems. Sources of uncertainty in a VRP can be travel times, service times, and unpredictable demands of customers. Ignoring these sources may lead to inaccurate modeling of the VRP. Moreover, the area of green logistics and the environmental issues associated received significant attention. This paper aims to study the stochastic multi-objective Vehicle Routing Problem in a green environment. The stochastic Green VRP (GVRP) presented deals with three objectives simultaneously that consider economic, environmental, and social aspects. First, a new hybrid search algorithm to solve the VRP is presented and validated. The algorithm is then employed to solve the stochastic multi-objective GVRP. Pareto fronts were obtained, and trade-offs between the three objectives are presented. Furthermore, an analysis of the effect of customers’ time window relaxation is presented.

A Multipopulation Multiobjective Ant Colony System Considering Travel and Prevention Costs for Vehicle Routing in COVID-19-Like Epidemics

As transportation system plays a vastly important role in combatting newly-emerging and severe epidemics like the coronavirus disease 2019 (COVID-19), the vehicle routing problem (VRP) in epidemics has become an emerging topic that has attracted increasing attention worldwide. However, most existing VRP models are not suitable for epidemic situations, because they do not consider the prevention cost caused by issues such as viral tests and quarantine during the traveling. Therefore, this paper proposes a multi-objective VRP model for epidemic situations, named VRP4E, which considers not only the traditional travel cost but also the prevention cost of the VRP in epidemic situations. To efficiently solve the VRP4E, this paper further proposes a novel algorithm named multi-objective ant colony system algorithm for epidemic situations, termed MOACS4E, together with three novel designs. First, by extending the efficient “multiple populations for multiple objectives” framework, the MOACS4E adopts two ant colonies to optimize the travel and prevention costs respectively, so as to improve the search efficiency. Second, a pheromone fusion-based solution generation method is proposed to fuse the pheromones from different colonies to increase solution diversity effectively. Third, a solution quality improvement method is further proposed to improve the solutions for the prevention cost objective. The effectiveness of the MOACS4E is verified in experiments on 25 generated benchmarks by comparison with six state-of-the-art and modern algorithms. Moreover, the VRP4E in different epidemic situations and a real-world case in the Beijing-Tianjin-Hebei region, China, are further studied to provide helpful insights for combatting COVID-19-like epidemics.

Multi-Objective Vehicle Routing Problem for Waste Classification and Collection with Sustainable Concerns: The Case of Shanghai City

With the promotion of an ecological civilization philosophy and a sustainable development strategy, solid waste classification and collection has become an emerging issue in China. Based on the three dimensions of sustainable development, namely economy, society, and environment, the route optimization model of waste collection and transportation is constructed. In order to solve the model aiming to maximize the benefits of sanitation companies under the constraints of workload balance, transportation cleanliness, and route changes due to cost factors, we combine the non-dominated sorting genetic algorithm III with simulated annealing. According to the characteristics of the problem, the probabilistic insertion method is incorporated to generate the initial solution, and the adaptive mutation operator is added to improve the population diversity. Finally, a real case in Xuhui District, Shanghai, a megacity taking the lead in 2019 in mandating a separated collection policy, is presented to verify the proposed model’s performance. The results provide a decision solution for dispatching the collection route of vehicles with some references for sanitary companies.

Multiobjective Memetic GRASP to Solve Vehicle Routing Problems with Time Windows Size

The Vehicle Routing Problem with Time Windows is a complete NP combinatorial problem in which product deliveries to customers must be made under certain time constraints. This problem can be solved from a single objective approach, well studied in the state of the art, in which the objective of the total travel distance or the size of the fleet (number of vehicles) is generally minimized. However, recent studies have used a multiobjective approach (Multiobjective Vehicle Routing Problem with Time Windows, MOVRPTW) that solves the problem from a viewpoint closer to reality. This work presents a new multiobjective memetic algorithm based on the GRASP (Greedy Randomized Adaptive Search Procedures) algorithm called MOMGRASP for the minimization of three objectives in MOVRPTW (total travel time, waiting time of customers to be attended, and balance of total travel time between routes). The results of the experimentation carried out with 56 problems proposed by Solomon and 45 problems proposed by Castro-Gutiérrez show that the proposed algorithm finds better solutions in these three objectives and competitive solutions than those reported by Zhou (compared to LSMOVRPTW algorithm and optimizing 5 objectives: number of vehicles, total travel distance, travel time of the longest route, total waiting time due to early arrivals, and total delay time due to late arrivals) and by Baños (versus the MMOEASA algorithm in two scenarios; case 1: total travel distance and balance of distance and case 2: total travel distance and balance of workload).

A hybrid evolutionary multitask algorithm for the multiobjective vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW), as an important logistic problem, has been widely investigated in recent decades. However, it is still a great challenge for most existing approaches to solve multiobjective VRPTWs (MOVRPTWs) with many conflicting objectives. In this study, a hybrid evolutionary multitask algorithm, termed HEMT, is proposed to address MOVRPTWs under the framework of evolutionary multitasking, where multiple MOVRPTWs are optimized simultaneously by leveraging the similarity between them. In particular, HEMT is characterized by three aspects: (1) an exploration stage with knowledge transfer (ESKT) is designed to globally explore the search space by transferring knowledge across different MOVRPTWs; (2) an exploitation stage with knowledge reuse (ESKR) is employed to further promote the quality of solutions by conducting local searches and reusing problem-specific knowledge; and (3) a tradeoff mechanism (TOM) is suggested to adaptively switch the search between ESKT and ESKR. Furthermore, to verify the efficacy of the proposed HEMT, four suites of new multitasking instances are generated based on 45 real-world MOVRPTW benchmarks under different multitask environments. The experimental results show that HEMT not only effectively solves multiple MOVRPTWs simultaneously but also achieves better performances than the traditional single-task counterparts.

Robust Multiobjective Optimization for Vehicle Routing Problem With Time Windows.

In this article, we focus on the vehicle routing problem (VRP) with time windows under uncertainty. To capture the uncertainty characteristics in a real-life scenario, we design a new form of disturbance on travel time and construct robust multiobjective VRP with the time window, where the perturbation range of travel time is determined by the maximum disturbance degree. Two conflicting objectives include: 1)the minimization of both the total distance and: 2)the number of vehicles. A robust multiobjective particle swarms optimization approach is developed by incorporating an advanced encoding and decoding scheme, a robustness measurement metric, as well as the local search strategy. First, through particle flying in the decision space, the problem space characteristic under deterministic environment is fully exploited to provide guidance for robust optimization. Then, a designed metric is adopted to measure the robustness of solutions and help to search for the robust optimal solutions during the particle flying process. In addition to the updating process of particle, two local search strategies, problem-based local search and route-based local search, are developed for further improving the performance of solutions. For comparison, we develop several robust optimization problems by adding disturbances on selected benchmark problems. The experimental results validate our proposed algorithm has a distinguished ability to generate enough robust solutions and ensure the optimality of these solutions.

Multi-objective evolutionary algorithm based on RBF network for solving the stochastic vehicle routing problem

Solving the multi-objective vehicle routing problem with stochastic demand (MO-VRPSD) is challenging due to its non-deterministic property and conflicting objectives. Most multi-objective evolutionary algorithm dealing with this problem update current population without any guidance from previous searching experience. In this paper, a multi-objective evolutionary algorithm based on artificial neural networks is proposed to tackle the MO-VRPSD. Particularly, during the evolutionary process, a radial basis function network (RBFN) is exploited to learn the potential knowledge of individuals, generate hypothesis and instantiate hypothesis. The RBFN evaluates individuals with different scores and generates new individuals with higher quality while taking into account the non-dominated relationship between individuals. Moreover, integrated with a specific non-dominated sorting strategy, i.e., ENS-SS, along with several effective heuristic operations, the proposed algorithm performs favorably for solving the MO-VRPSD. The experimental results based on the modified Solomon benchmark instances verified the effectiveness of the respective components, and the superiority to other multi-objective evolutionary algorithms.

Uncertainty modeling in multi-objective vehicle routing problem under extreme environment

Uncertainty modeling in multi-objective vehicle routing problem under extreme environment

Metaheuristic Algorithms Based on Compromise Programming for the Multi-Objective Urban Shipment Problem.

The Vehicle Routing Problem (VRP) and its variants are found in many fields, especially logistics. In this study, we introduced an adaptive method to a complex VRP. It combines multi-objective optimization and several forms of VRPs with practical requirements for an urban shipment system. The optimizer needs to consider terrain and traffic conditions. The proposed model also considers customers’ expectations and shipper considerations as goals, and a common goal such as transportation cost. We offered compromise programming to approach the multi-objective problem by decomposing the original multi-objective problem into a minimized distance-based problem. We designed a hybrid version of the genetic algorithm with the local search algorithm to solve the proposed problem. We evaluated the effectiveness of the proposed algorithm with the Tabu Search algorithm and the original genetic algorithm on the tested dataset. The results show that our method is an effective decision-making tool for the multi-objective VRP and an effective solver for the new variation of VRP.

A hybrid multi-objective evolutionary algorithm for open vehicle routing problem through cluster primary-route secondary approach

ABSTRACT This study focuses on the cluster primary-route secondary approach to solve the multi-objective open green vehicle routing problem under a sustainable environment. An open green vehicle routing problem involves distributing products or services from a single depot to several customers placed at different geographical locations using third-party logistics to reduce pollution. The proposed model considers two conflicting realistic objectives: minimizing the operating costs and minimizing the carbon emission due to fuel consumption by the service vehicles. Unlike existing multi-objective problems, this multi-objective model chooses an optimal route based on the decision maker’s choice from the set of alternative solutions. Initially, it clusters all the customers by applying a modified -means algorithm. Each cluster is served by one vehicle only. Then a multi-objective evolutionary algorithm is employed to search for the best subroute to cover all the customers belonging to a cluster. We employ the extended Strength Pareto Evolutionary Algorithm (SPEA2) and Non-dominated Sorting-based Genetic Algorithm (NSGA-II) separately to obtain different approximate fronts. The VIKOR method is used to identify the decision maker’s choice-based solution for each cluster. In the next step, all the compromise solutions are combined to produce the final result of the proposed problem. Some statistical analyses are performed to compare the performance of SPEA2 and NSGA-II. SPEA2 has shown better results compared to NSGA-II.