Capacitated Vehicle Research Articles

What drives the viability of waste-to-energy? Modelling techno-economic scenarios of anaerobic digestion and energy generation for the Scottish islands

Anaerobic digestion, a technology which converts biowaste into biogas, can address issues of waste utilisation, energy security and reducing emissions. Co-digestion of waste could improve biogas yields and synergies between sectors but requires transport of waste. To improve on existing biowaste-to-energy models which consider simple transport costs, this work combines a techno-economic model with a capacitated vehicle routing problem (CVRP) solver to consider detailed waste transport costs with actual Open Street Map (OSM) road networks. This addresses whether biowaste-to-energy techno-economic modelling is improved with more specific transport costs and more broadly how factors of resource availability, generation technology and transport costs influence the viability of anaerobic digestion and generation plants. The levelised cost of energy (LCOE) is used to compare scenarios of these aspects. The Scottish islands have been modelled as a case study due to high biowaste potential and varied topographies, which both influence transport costs. Number of waste vehicles required is improved by 42.8% and the unit cost of collection varies from £0.1–1670.0/tonne. Local topographies and waste availability significantly affects the viability of individual facilities, which might not be considered by simpler collection cost metrics. Between 14.0 and 20.6% of the regions electricity demand could be met by biogas. While industrial facilities co-located with demand have the cheapest LCOE, this can in some cases be improved with other waste streams, highlighting the need for further research on and policies supporting co-digestion, as well as improving household and business participation rates. Incentives and avoided costs are crucial to supporting biowaste-to-energy if more isolated regions are to benefit from improved waste utilisation.

Combining genetic local search into a multi-population Imperialist Competitive Algorithm for the Capacitated Vehicle Routing Problem

The Vehicle Routing Problem (VRP) is one of the most significant problems in operational research today. VRP has a vast range of application fields such as transportation, logistics, manufacturing, relief systems and communication. To suit the needs of different real-world VRP scenarios, many models of VRP have been developed — CVRP (Capacitated VRP) being the classical form. In this article, a hybrid metaheuristic algorithm, ICAHGS, is proposed for solving CVRP. The present study proposes a refined Imperialist Competitive Algorithm (ICA) as the primary evolutionary and multi-population method for addressing the Capacitated Vehicle Routing Problem (CVRP). In order to further optimize the search process, a Hybrid Genetic Search (HGS-CVRP) algorithm is applied as an enhanced local search and population management strategy within the ICA framework. Additionally, the internal restart step of the HGS-CVRP algorithm is replaced with a multi-step restart mechanism for intensification improvement. One notable aspect of the proposed method is its ability to facilitate parallel processing, with each empire able to be processed on a separate processor. This structure allows for increased computational efficiency in addressing the CVRP. To assess the effectiveness of the proposed algorithm, it has been compared to several state-of-the-art algorithms from the literature. The results of this comparison, which include both classical benchmark instances and real-world applications, demonstrate the competitive performance of the proposed algorithm.

A Two-stage Learning-based method for Large-scale On-demand pickup and delivery services with soft time windows

With the rapid growth of the on-demand logistics industry, large-scale pickup and delivery with soft time windows has become widespread in various time-critical scenarios. This problem has proven to be an NP-hard problem. Hence, the computation time and resources required to solve it increase exponentially with the growth of size. As a result, it is burdensome for the exact algorithm and heuristic method to generate a high-quality solution instantly. Machine learning seems to be a possible option due to the advantage of offline training. However, it is difficult to solve large-scale problems due to the lengthy training time, heavy computational cost, and training instability. Thus, this paper proposes the two-stage learning-based method composed of the clustering stage and the routing stage to tackle this problem. The clustering stage builds upon the attention mechanism by introducing graph convolutional network to the input, which can keep the match of pickup and paired delivery customers and classify them into different vehicles, while the routing stage adopts a well-trained model to generate a route for each capacitated vehicle. Furthermore, the well-trained model is utilized to train another problem inspired by transfer learning. Experiments show that the model, trained on small-scale problems, generalizes well to larger-scale problems, and achieves superior performance compared with the heuristic method and Google OR-Tools, with an extremely short computing time. In addition, the favorable transferability of this model is verified through contrast experiment, which can save a significant amount of training time.

Effective metaheuristics for the latency location routing problem

AbstractThe latency location routing problem (LLRP), a combination of the facility location problem and the cumulative capacitated vehicle routing problem, is a recently proposed variant of location routing problems. It corresponds to a customer‐centric problem, in which the aim is to minimize the sum of the arrival times at the customers. This paper proposes three novel metaheuristic algorithms to solve the LLRP. They use a simulated annealing framework, which after each temperature reduction is intensified through a variable neighborhood descent procedure. Each algorithm uses a different search strategy as intensification. Results on 76 benchmark instances indicate that the proposed metaheurstics outperform the state‐of‐the‐art algorithms, finding new best solutions for all the large‐sized instances (over 100 customers), or the currently known optimal ones for most of the small‐ and medium‐sized instances, in comparable computing times. Furthermore, in more than 80% of the instances the average value of the solutions found by the proposed algorithms is better than or equal to that of the current best known solution.

Resources Relocation Support Strategy Based on a Modified Genetic Algorithm for Bike-Sharing Systems

In recent decades, special attention has been given to the adverse effects of traffic congestion. Bike-sharing systems, as a part of the broader category of shared transportation systems, are seen as viable solutions to these problems. Even if the quality of service in bike-sharing service systems were permanently improved, there would still be some issues that needed new and more efficient solutions. One of these refers to the rebalancing operations that follow the bike depletion phenomenon that affects most stations during shorter or longer time periods. Current work develops a two-step method to perform effective rebalancing operations in bike-sharing. The core elements of the method are a fuzzy logic-controlled genetic algorithm for bike station prioritization and an inference mechanism aiming to do the assignment between the stations and trucks. The solution was tested on traffic data collected from the Citi Bike New York bike-sharing system. The proposed method shows overall superior performance compared to other algorithms that are specific to capacitated vehicle routing problems: standard genetic algorithm, ant colony optimization, Tabu search algorithm, and improved performance compared to Harris Hawks optimization for some scenarios. Since the algorithm is independent of past traffic measurements, it applies to any other potential bike-sharing system.

In-depth analysis of granular local search for capacitated vehicle routing

In-depth analysis of granular local search for capacitated vehicle routing

MOBILITY EMBEDDING FROM CALL DATA RECORD USING WORD2VEC TO SUPPORT NETWORK WITH UNMANNED AERIAL VEHICLE

Call Detail Records (CDRs) are records that provide information about phone conversations and text messages. CDR data has been proved in several studies to give useful information on people's mobility patterns and associations with fine-grained temporal and geographical characteristics. This paper proposes to embed the traces recorded in the CDRs to extract meaningful information. These latter provide insights about the location that may need support to cover or recover the network. After embedding the users' trajectories step, we use the embedding results to recommend the antennas with coordinates and support demand needed to a fleet of Unmanned Aerial Vehicle. Finally, we ended up with a capacitated vehicle routing problem that we solved using a Google open-source software named OR-Tools.

Optimal distribution of perishable foods with storage temperature control and quality requirements: An integrated vehicle routing problem

The quality of food products deteriorates continuously over time at a speed depending on the storage temperature. Therefore, they must be stored at low temperatures to prolong their shelf life, which increases storage costs significantly. In this paper, we study a distribution problem in which a temperature-controlled warehouse is responsible for supplying a perishable food product, using a homogenous fleet of capacitated vehicles, to multiple customers with minimum quality requirements and delivery time windows. The objective is to minimize the sum of the energy cost at the warehouse and the transportation cost to deliver the customer demand. Decisions include the storage temperature at the warehouse and delivery routes. The distribution problem is formulated as a Mixed-Integer Linear Programming (MILP) model. After presenting an analytical study of the problem, a heuristic based on General Variable Neighborhood Search (GVNS) is designed to solve the large-size problem instances. Using the case of a dairy product, the model is solved under various scenarios. It is observed that the distribution and temperature decisions are dependent. Moreover, the optimal distribution plan and storage temperature are significantly impacted by changes in factors related to food quality, such as truck and environmental temperatures and energy price.

The multi-depot pickup and delivery problem with capacitated electric vehicles, transfers, and time windows

The Pickup and Delivery Problem has received increasing attention as a result of the recent growth of third-party delivery companies, and electric vehicles (EVs) are becoming a preferable choice for such large delivery systems due to their environmental benefits. The EVs, however, have limited energy capacity; thus, intra-route facilities are required to recharge them. These facilities can also be visited to transfer requests to other vehicles. In this study, we introduce a novel pickup and delivery problem with electric vehicles and transfers. The traditional constraint that each request should be handled by a single vehicle, is relaxed in this problem with transfers, and additionally, we incorporate other practical considerations such as multi-depots, time-windows, and EVs’ battery and carrying capacity constraints. We develop a mixed-integer linear programming model encompassing all these constraints. To address the computational difficulty of the problem, we propose a hybrid heuristic combining Simulated Annealing (SA) and Large Neighborhood Search (LNS). Experimental results reveal that for small instances where CPLEX can find optimal solutions, our heuristic finds them about 90% faster.

Decomposition Strategies for Vehicle Routing Heuristics

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterization of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: We discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight their strengths and weaknesses, and derive a set of desirable properties. Through an extensive numerical campaign, we investigate the impact of decompositions within two algorithms for the capacitated vehicle routing problem: the Adaptive Large Neighborhood Search of Pisinger and Ropke (2007 ) and the Hybrid Genetic Search of Vidal et al. (2012 ). We evaluate the quality of popular decomposition techniques from the literature and propose new strategies. We find that route-based decomposition methods, which define subproblems by means of the customers contained in selected subsets of the routes of a given solution, generally appear superior to path-based methods, which merge groups of customers to obtain smaller subproblems. The newly proposed decomposition barycenter clustering achieves the overall best performance and leads to significant gains compared with using the algorithms without decomposition. History: Erwin Pesch, Area Editor for Heuristic Search and Approximation Algorithms. Funding: This work was supported by the U.S. Air Force [Grant FA9550-17-1-0234], the Ministerio de Ciencia e Innovación (Juan de la Cierva Formación), H2020 Marie Skłodowska-Curie Actions [Grant 945380], the Ministero dell’Università e della Ricerca [Grant 2015JJLC3E_002], the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 308528/2018-2], and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grant E-26/202.790/2019]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1288 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0048 ) at ( http://dx.doi.org/10.5281/zenodo.7613129 ).

A PTAS for Capacitated Vehicle Routing on Trees

We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.

Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension

In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser in 1959 [ 14 ], we are given a graph G=(V,E) with metric edges costs, a depot r ∈ V , and a vehicle of bounded capacity Q . The goal is to find a minimum cost collection of tours for the vehicle that returns to the depot, each visiting at most Q nodes, such that they cover all the nodes. This generalizes classic TSP and has been studied extensively. In the more general setting, each node v has a demand d v and the total demand of each tour must be no more than Q . Either the demand of each node must be served by one tour (unsplittable) or can be served by multiple tours (splittable). The best-known approximation algorithm for general graphs has ratio α +2(1-ε) (for the unsplittable) and α +1-ε (for the splittable) for some fixed \(ε \gt \frac{1}{3000}\) , where α is the best approximation for TSP. Even for the case of trees, the best approximation ratio is 4/3 [ 5 ] and it has been an open question if there is an approximation scheme for this simple class of graphs. Das and Mathieu [ 15 ] presented an approximation scheme with time n log O(1/ε) n for Euclidean plane ℝ 2 . No other approximation scheme is known for any other class of metrics (without further restrictions on Q ). In this article, we make significant progress on this classic problem by presenting Quasi-Polynomial Time Approximation Schemes (QPTAS) for graphs of bounded treewidth, graphs of bounded highway dimensions, and graphs of bounded doubling dimensions. For comparison, our result implies an approximation scheme for the Euclidean plane with run time n O(log 6 n/ε 5 ) .

Coordinated Operation of Fixed-Route and Demand-Responsive Feeder Transit Services in a Travel Corridor

With the wide use of smartphone travel apps, a new hybrid transit system (HTS) that integrates fixed-route transit (FRT) and app-based demand-responsive feeder transit (DRFT) services have recently emerged in many cities over the world. App-based DRFT services are coordinated with FRT to offer fast, comfortable, and well-connected mobility services to travelers. The study investigates a new variant of HTS, termed flexible HTS (FHTS), allowing FRT to have flexible vehicle departure times and capacitated vehicle loads and DRFT to have flexible feeder stations, so as to further enhance the coordination between FRT and DRFT. The coordinated operation optimization problem of such an FHTS in a travel corridor is formulated as a mixed-integer linear programming model. A novel hybrid metaheuristic algorithm is developed to solve it. In the hybrid algorithm, a constrained compass search method is used to optimize FRT vehicle departure times, and an adaptive large neighborhood search algorithm, coupled with a tailored forward time slack algorithm, is applied to solve the DRFT routing and scheduling problems. A case study in Shucheng County, China is conducted to examine the performance of the model and solution algorithms. Sensitivity analyses on feeder station layout and vehicle size are also conducted. The results show that flexible FRT vehicle departure times and flexible DRFT feeder stations have a great potential of enhancing the coordination of FRT and DRFT services by reducing operators’ costs and passengers’ total travel time. Managerial implications are to set feeder transit stations downstream of an FRT line and to keep a reasonable station spacing.

Improved slime mould algorithm based on hybrid strategy optimization of Cauchy mutation and simulated annealing.

In this article, an improved slime mould algorithm (SMA-CSA) is proposed for solving global optimization and the capacitated vehicle routing problem (CVRP). This improvement is based on the mixed-strategy optimization of Cauchy mutation and simulated annealing to alleviate the lack of global optimization capability of the SMA. By introducing the Cauchy mutation strategy, the optimal solution is perturbed to increase the probability of escaping from the local extreme value; in addition, the annealing strategy is introduced, and the Metropolis sampling criterion is used as the acceptance criterion to expand the global search space to enhance the exploration phase to achieve optimal solutions. The performance of the proposed SMA-CSA algorithm is evaluated using the CEC 2013 benchmark functions and the capacitated vehicle routing problem. In all experiments, SMA-CSA is compared with ten other state-of-the-art metaheuristics. The results are also analyzed by Friedman and the Wilcoxon rank-sum test. The experimental results and statistical tests demonstrate that the SMA-CSA algorithm is very competitive and often superior compared to the algorithms used in the experiments. The results of the proposed algorithm on the capacitated vehicle routing problem demonstrate its efficiency and discrete solving ability.

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

AbstractApproximation of the optimal tour length in a Euclidean traveling salesman problem (TSP) has been studied by many researchers. In a previous study, we used the standard deviation in random tour lengths to approximate the optimal tour length in both Euclidean and non‐Euclidean TSPs and we obtained good estimates. In this paper, we show that the strong power‐law relationship between the standard deviation in random feasible solution values and the optimal solution value also holds for other Euclidean and near‐Euclidean combinatorial optimization problems like the minimum spanning tree (MST) and maximum weight matching (MWM) problems. We then enhance the estimation ability of the model by considering a second predictor: the mean in random feasible solution values. Experimental results show that by using the mean, standard deviation, and randomization, we can accurately predict the optimal solution values for the TSP, MST, MWM, and the capacitated vehicle routing problem (VRP).

Bi-Level Fleet Dispatching Strategy for Battery-Electric Trucks: A Real-World Case Study

Driven by new regulations concerning greenhouse gas (GHG) emissions in the transportation sector, battery-electric trucks (BETs) are considered one of the sustainable freight transportation solutions. In this paper, a dispatching problem of the BET fleet is formulated as a capacitated electric vehicle routing problem (VRP) with pick-up and delivery. As the BET dispatching problem is NP-hard, the performance of existing approaches deteriorates in large instance problems, especially when the customers have different preferences and constraints. This article proposes a bi-level strategy that incorporates routing zone partitioning and metaheuristic-based vehicle routing to solve the large-scale BET dispatching problem, considering the delivery types, limited travel distances, and cargo payloads. We apply this strategy to a real-world fleet dispatching scenario with around 300 customer positions for pickups and drop-offs. The experimental results demonstrate that the proposed bi-level strategy can reduce total travel distance and travel time by 24–31%, compared to the baseline strategy implemented in the real world.

Efficient Network Selection Using Multi-Depot Routing Problem for Smart Cities

Smart cities make use of a variety of smart technology to improve societies in better ways. Such intelligent technologies, on the other hand, pose significant concerns in terms of power usage and emission of carbons. The suggested study is focused on technological networks for big data-driven systems. With the support of software-defined technologies, a transportation-aided multicast routing system is suggested. By using public transportation as another communication platform in a smart city, network communication is enhanced. The primary objective is to use as little energy as possible while delivering as much data as possible. The Attribute Decision Making with Capacitated Vehicle (CV) Routing Problem (RP) and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research. For the optimum network selection, a Multi-Attribute Decision Making (MADM) method is utilized. For the sake of reducing energy usage, the Capacitated Vehicle Routing Problem (CVRP) is employed. To reduce the transportation cost and risk, Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used. Moreover, a mixed-integer programming approach is used to deal with the problem. To produce Pareto optimal solutions, an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is created. A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer. Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30% of less energy than the other systems.

PHH: Policy-Based Hyper-Heuristic With Reinforcement Learning

Hyper-heuristics have a high level of generality and adaptability, allowing them to effectively solve a wide range of complex optimization problems. With reinforcement learning, hyper-heuristics can use experience and knowledge gained to tackle unforeseen problems, allowing hyper-heuristics to adapt and improve over time. Our paper proposes a framework for using policy-based reinforcement learning to improve the performance of hyper-heuristics. The framework trains hyper-heuristic agents to select the best generalized constructive low-level heuristics to solve combinatorial optimization problems. The framework evaluation was performed using three benchmarking problems: traveling salesman, capacitated vehicle routing, and bin packing problems. The results showed that the proposed framework can outperform existing meta-heuristic and hyper-heuristic-based algorithms for all large problem instances in all problem domains. The proposed framework was also evaluated by applying it to a cost optimization problem for workflow scheduling on a hybrid cloud with a deadline constraint. Eight agents were trained on medium-sized workflows with two deadlines and tested against traditional meta-heuristic and hyper-heuristic methods to solve smaller and larger workflows with unforeseen deadlines. Four workflow applications, three workflow sizes, and three deadlines were used in the evaluation. The results showed that our proposed framework provided significantly better solutions of up to 98% for benchmarking problems, and up to 22% for cost optimization in workflow scheduling. Moreover, trained with small problem instances, the framework performed well for unforeseen larger problem instances implying its generalization. The proposed framework, thus, has the potential to improve both the generality and performance of solving large combinatorial optimization problems.

Two-echelon joint delivery capacitated vehicle routing problem considering carbon emissions of online shopping

Under the environment of a sharing economy and the demand for a low-carbon economy, parcel express companies are compelled to take a fresh view of joint delivery (JD) to enhance horizontal cooperation in the express industry. The purpose of this study is to design an energy-efficient collaborative joint delivery network for different express companies to fulfil the express delivery task. This paper proposes a two-echelon joint delivery capacitated vehicle routing problem (2E-JDCVRP) considering carbon emissions and two distinct fleets of vehicles to optimise the express delivery network in metropolitan areas, while explicitly considering resource sharing between different enterprises. In the 2E-JDCVRP model, the first echelon network requires vehicles at the depots of different express companies to transport the customer demands to satellites that are limitedly shared. The second echelon network concerns the routing of vehicles shared by the satellites to serve all the customers. The objective is to minimise the total cost of the joint distribution of a number of enterprises. A hybrid heuristic algorithm is designed to compute a novel 2E-JDCVRP model that shares idle resources. Computational experiments were conducted to test and verify the efficiency and effectiveness of the proposed 2E-JDCVRP model.

Genetic Crossover Operators for the Capacitated Vehicle Routing Problem

We study the capacitated vehicle routing problem (CVRP) which is a well-known NP-hard combinatorial optimization problem (COP). The aim of the problem is to serve different customers by a convoy of vehicles starting from a depot so that sum of the routing costs under their capacity constraints is minimized. Since the problem is very complicated, solving the problem using exact methods is almost impossible. So, one has to go for the heuristic/metaheuristic methods and genetic algorithm (GA) is broadly applied metaheuristic method to obtain near optimal solution to such COPs. So, this paper studies GAs to find solution to the problem. Generally, to solve a COP, GAs start with a chromosome set named initial population, and then mainly three operators-selection, crossover and mutation, are applied. Among these three operators, crossover is very crucial in designing and implementing GAs, and hence, numerous crossover operators were developed and applied to different COPs. There are two major kinds of crossover operators-blind crossovers and distance-based crossovers. We intend to compare the performance of four blind crossover and four distance-based crossover operators to test the suitability of the operators to solve the CVRP. These operators were originally proposed for the standard travelling salesman problem (TSP). First, these eight crossovers are illustrated using same parent chromosomes for building offspring(s). Then eight GAs using these eight crossover operators without any mutation operator and another eight GAs using these eight crossover operators with a mutation operator are developed. These GAs are experimented on some benchmark asymmetric and symmetric instances of numerous sizes and various number of vehicles. Our study revealed that the distance-based crossovers are much superior to the blind crossovers. Further, we observed that the sequential constructive crossover with and without mutation operator is the best one for the CVRP. This estimation is validated by Student’s t-test at 95% confidence level. We further determined a comparative rank of the eight crossovers for the CVRP.