Vehicle Routing Research Articles

Open Competency Optimization: A Human-Inspired Optimizer for the Dynamic Vehicle-Routing Problem

The vehicle-routing problem (VRP) is a popular area of research. This popularity springs from its wide application in many real-world problems, such as logistics, network routing, E-commerce, and various other fields. The VRP is simple to formulate, but very difficult to solve and requires a great deal of time. In these cases, researchers use approximate solutions offered by metaheuristics. This work involved the design of a new metaheuristic called Open Competency Optimization (OCO), which was inspired by human behavior during the learning process and based on the competency approach. The aim is the construction of solutions that represent learners’ ideas in the context of an open problem. The candidate solutions in OCO evolve over three steps. Concerning the first step, each learner builds a path of learning (finding the solution to the problem) through self-learning, which depends on their abilities. In the second step, each learner responds positively to the best ideas in their group (the construction of each group is based on the competency of the learners or the neighbor principle). In the last step, the learners interact with the best one in the group and with the leader. For the sake of proving the relevance of the proposed algorithm, OCO was tested in dynamic vehicle-routing problems along with the Generalized Dynamic Benchmark Generator (GDBG).

Augmented ɛ‐constraint‐based matheuristic methodology for Bi‐objective production scheduling problems

AbstractMatheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ‐constraint‐based matheuristic methodology (ɛ‐MH) is proposed to apply the idea of ɛ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

Data-driven vehicle rental and routing optimization: An application in online retailing

Due to limited self-owned vehicles, online retailers often struggle to meet high demands for deliveries, especially during large promotions. This study employs machine learning to tackle this challenge by shipping products and renting vehicles in advance. We explore a large amount of historical demand data, enabling accurate forecasting of demand information. It is then combined with an improved meta-heuristic algorithm named the Improved Discrete Whale Optimization Algorithm (IDWOA) to help online retailers make optimal decisions. The algorithm involves a discretization method and an effective perturbation strategy, along with information sharing, Cauchy mutation, and an elimination strategy. Experimental results demonstrate that our method can reduce costs by 14.78% compared to temporary vehicle rentals, and it significantly outperforms other comparative algorithms. Therefore, our study effectively integrates machine learning algorithms with an improved meta-heuristic approach, allowing for increased utilization of data-driven advantages to enhance the precision and efficiency of vehicle rental and routing optimization.

Dynamic collaborative truck-drone delivery with en-route synchronization and random requests

Coordinated truck and drone delivery is gaining popularity in logistics as it can greatly reduce operation costs. However, existing studies on related operations management problems typically ignore the following important features: (i) the random appearance of requests, which require operators to dynamically respond to the requests; and (ii) the decisions of optimal launch and retrieval locations for trucks and drones instead of fixed to customer locations, which can significantly impact the overall time costs. To tackle these challenges, this study investigates the dynamic collaborative truck-drone routing problem with randomly arriving requests and synchronization on routes. We model the problem as a Markov Decision Process (MDP) and solve the MDP via a reinforcement learning (RL) approach. The proposed RL approach determines: (i) whether each request should be serviced upon arrival, (ii) which truck or drone should be assigned for the request, and (iii) the optimal en-route take-off and landing positions for paired trucks and drones. We further employ a framework of decentralized learning and centralized dispatching in RL to increase performance. Numerical experiments are conducted to assess the proposed solution approach on instances generated based on both the Solomon dataset and real-world operational data of a logistics operator in Singapore over several benchmark algorithms under various battery endurance levels of drones and distinct transportation scenarios including node-based dynamic collaborative truck-drone routing problem, dynamic non-collaborative truck and drone routing problem, and dynamic vehicle routing problem. The results show that our RL solution outperforms the benchmark algorithm in total profit by an average of 28.03 %, and our en-route takeoff and landing scenario outperforms the benchmark scenarios in total profit by an average of 8.43 % in multi-day instances. Additionally, compared to the traditional node-based landing scenario, employing our en-route takeoff and landing strategy can save 0.9 h/(drone*day) of waiting time on average.

Joint Approach for Vehicle Routing Problems Based on Genetic Algorithm and Graph Convolutional Network

The logistics demands of industries represented by e-commerce have experienced explosive growth in recent years. Vehicle path-planning plays a crucial role in optimization systems for logistics and distribution. A path-planning scheme suitable for an actual scenario is the key to reducing costs and improving service efficiency in logistics industries. In complex application scenarios, however, it is difficult for conventional heuristic algorithms to ensure the quality of solutions for vehicle routing problems. This study proposes a joint approach based on the genetic algorithm and graph convolutional network for solving the capacitated vehicle routing problem with multiple distribution centers. First, we use the heuristic method to modularize the complex environment and encode each module based on the constraint conditions. Next, the graph convolutional network is adopted for feature embedding for the graph representation of the vehicle routing problem, and multiple decoders are used to increase the diversity of the solution space. Meanwhile, the REINFORCE algorithm with a baseline is employed to train the model, ensuring quick returns of high-quality solutions. Moreover, the fitness function is calculated based on the solution to each module, and the genetic algorithm is employed to seek the optimal solution on a global scale. Finally, the effectiveness of the proposed framework is validated through experiments at different scales and comparisons with other algorithms. The experimental results show that, compared to the single decoder GCN-based solving method, the method proposed in this paper improves the solving success rate to 100% across 15 generated instances. The average path length obtained is only 11% of the optimal solution produced by the GCN-based multi-decoder method.

CMSA based on set covering models for packing and routing problems

AbstractMany packing, routing, and knapsack problems can be expressed in terms of integer linear programming models based on set covering. These models have been exploited in a range of successful heuristics and exact techniques for tackling such problems. In this paper, we show that integer linear programming models based on set covering can be very useful for their use within an algorithm called “Construct, Merge, Solve & Adapt”(CMSA), which is a recent hybrid metaheuristic for solving combinatorial optimization problems. This is because most existing applications of CMSA are characterized by the use of an integer programming solver for solving reduced problem instances at each iteration. We present applications of CMSA to the variable-sized bin packing problem and to the electric vehicle routing problem with time windows and simultaneous pickups and deliveries. In both applications, CMSA based on a set covering model strongly outperforms CMSA when using an assignment-type model. Moreover, state-of-the-art results are obtained for both considered optimization problems.

SWMR Algorithm Approach for the Vendor Managed Inventory Problem when Static Demand Rates

In a two-phase supply chain with Vendor Managed Inventory (VMI) policies, the supplier takes on the duty of keeping its retailers' inventory up to date and making sure they never run out of stock. This is in addition to his inbound inventory. This study aims to combine the retailers in various set partitions or to maximize their distribution and inventory holding costs within the same set partition. This paper focuses on a two-stage supply chain made of a single warehouse and multiple retailers (SWMR) facing a static demand and implementing VMI. We proposed a model for coordinating the system with a two-phase solution method. The first phase is to minimize the overall inventory costs and, in the second phase, a constructive vehicle routing problem (VRP) heuristic is used to optimize the distribution costs by satisfying some additional restrictions. Results of this implementation of VMI in an illustrative supply chain case are shown and discussed in detail.

Optimization of household medical waste recycling logistics routes: Considering contamination risks.

The escalating generation of household medical waste, a byproduct of industrialization and global population growth, has rendered its transportation and logistics management a critical societal concern. This study delves into the optimization of routes for vehicles within the household medical waste logistics network, a response to the imperative of managing this waste effectively. The potential for environmental and public health hazards due to improper waste disposal is acknowledged, prompting the incorporation of contamination risk, influenced by transport duration, waste volume, and wind velocity, into the analysis. To enhance the realism of the simulation, traffic congestion is integrated into the vehicle speed function, reflecting the urban roads' variability. Subsequently, a Bi-objective mixed-integer programming model is formulated to concurrently minimize total operational costs and environmental pollution risks. The complexity inherent in the optimization problem has motivated the development of the Adaptive Hybrid Artificial Fish Swarming Algorithm with Non-Dominated Sorting (AH-NSAFSA). This algorithm employs a sophisticated approach, amalgamating congestion distance and individual ranking to discern optimal solutions from the population. It incorporates a decay function to facilitate an adaptive iterative process, enhancing the algorithm's convergence properties. Furthermore, it leverages the concept of crossover-induced elimination to preserve the genetic diversity and overall robustness of the solution set. The empirical evaluation of AH-NSAFSA is conducted using a test set derived from the Solomon dataset, demonstrating the algorithm's capability to generate feasible non-dominated solutions for household medical waste recycling path planning. Comparative analysis with the Non-dominated Sorted Artificial Fish Swarm Algorithm (NSAFSA) and Non-dominated Sorted Genetic Algorithm II (NSGA-II) across metrics such as MID, SM, NOS, and CT reveals that AH-NSAFSA excels in MID, SM, and NOS, and surpasses NSAFSA in CT, albeit slightly underperforming relative to NSGA-II. The study's holistic approach to waste recycling route planning, which integrates cost-effectiveness with pollution risk and traffic congestion considerations, offers substantial support for enterprises in formulating sustainable green development strategies. AH-NSAFSA offers an eco-efficient, holistic approach to medical waste recycling, advancing sustainable management practices.

An exact branch-and-price-and-cut algorithm for a practical and large-scale dial-a-ride problem

Vehicle routing problems are encountered in various practical transportation scenarios. One such problem is the dial-a-ride problem (DARP), which involves transporting efficiently passengers from their origin to their destination and whose objective is to design vehicle routes minimizing total costs and accommodating all pickup-and-delivery requests. The solution must also adhere to capacity limitations, time windows, and a maximum ride time for each passenger. This paper proposes an exact branch-price-and-cut algorithm to solve a practical variant of the DARP, where both the passengers and vehicle fleet are heterogeneous, and other practical constraints such as break requirements and maximum route duration are imposed. In this algorithm, column generation which alternates between solving a master problem and subproblems, is used to compute lower bounds in the search tree. We develop a labeling algorithm to efficiently handle these subproblems. The effectiveness of the algorithm is evaluated on a real-world case study involving 849 heterogeneous passengers and more than 70 available vehicles, as well as on 10 smaller instances (with 300 to 820 trips) extracted from another very large real-world dataset. To the best of our knowledge, this 849-trip instance is the largest DARP instance reported to be solved to optimality in the literature.

The Ant Colony Optimization Algorithm Applied in Transport Logistics

The Vehicle Routing Problem belongs to graph optimization and its goal is to find shortest routes visiting a given set of customers with additional constraints present. The article presents the ant colony optimization metaheuristic which solves vehicle routing problems and its real-life application in transport logistics (finding routes for delivery companies). The metaheuristic generated high-quality solutions (superior to compared methods). Our tool is flexible and enables us to solve various variants of routing problems so it is well suited to specific needs of transportation companies.

Stage-Specific Multi-Objective Five-Element Cycle Optimization Algorithm in Green Vehicle-Routing Problem with Symmetric Distance Matrix: Balancing Carbon Emissions and Customer Satisfaction

This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations.

Optimizing a Dynamic Vehicle Routing Problem with Deep Reinforcement Learning: Analyzing State-Space Components

Background: The dynamic vehicle routing problem (DVRP) is a complex optimization problem that is crucial for applications such as last-mile delivery. Our goal is to develop an application that can make real-time decisions to maximize total performance while adapting to the dynamic nature of incoming orders. We formulate the DVRP as a vehicle routing problem where new customer requests arrive dynamically, requiring immediate acceptance or rejection decisions. Methods: This study leverages reinforcement learning (RL), a machine learning paradigm that operates via feedback-driven decisions, to tackle the DVRP. We present a detailed RL formulation and systematically investigate the impacts of various state-space components on algorithm performance. Our approach involves incrementally modifying the state space, including analyzing the impacts of individual components, applying data transformation methods, and incorporating derived features. Results: Our findings demonstrate that a carefully designed state space in the formulation of the DVRP significantly improves RL performance. Notably, incorporating derived features and selectively applying feature transformation enhanced the model’s decision-making capabilities. The combination of all enhancements led to a statistically significant improvement in the results compared with the basic state formulation. Conclusions: This research provides insights into RL modeling for DVRPs, highlighting the importance of state-space design. The proposed approach offers a flexible framework that is applicable to various variants of the DVRP, with potential for validation using real-world data.

A multiple asset-type, collaborative vehicle routing problem with proximal servicing of demands

This research examines the problem of routing multiple assets of different types over a network to service demands in a collaborative manner. The servicing is collaborative in that, when servicing a demand, the different types of assets must do so nearly simultaneously. Moreover, whereas some asset types must service demands by visiting them, other asset types may provide service proximally. This study sets forth a mixed-integer linear program to model this variant of a vehicle routing problem. In addition to directly solving problem instances via a commercial solver, this research proposes two permutations of a model decomposition heuristic, as well as two preprocessing techniques to impose instance-specific bounds on selected decision variables. Comparative testing on mesh networks evaluates nine combinations of solution methods and preprocessing options to solve a set of 216 instances that vary significant parameters. Results manifest trade-offs between the likelihood of finding a feasible solution with bounded computational effort and the relative quality of solutions identified. For larger networks, the preprocessing technique leveraging a nearest neighbor heuristic in combination with any solution method most frequently identified feasible solutions for the set of test instances (i.e., ∼90% of instances), with lesser solution quality (i.e., within 15% of the best solutions identified, on average). Worst performing for larger networks was a model decomposition technique that first routes assets providing service proximally, and omitting either preprocessing technique; although this combination yielded the best solutions when it identified a feasible solution, it only did so for ∼55% of instances. Other solution method performances exhibit noteworthy nuance, as detailed herein. Further testing of the solution procedures on 216 additional instances for a scenario motivated by a disaster relief using a city road network yielded relatively consistent results; the superlative method leveraged model decomposition and a nearest neighbor preprocessing heuristic, albeit when routing proximally-serving assets first.

A branch-and-price approach for the nurse rostering problem with multiple units

In this paper, we study the nurse rostering problem that considers multiple units and many soft time-related constraints. An efficient branch and price solution approach that relies on a fast algorithm to solve the pricing subproblem of the column generation process is presented. For the nurse rostering problem, its pricing subproblem can be formulated as a shortest path problem with resource constraints, which has been the backbone of several solutions for several classical problems like vehicle routing problems. However, approaches that perform well on these problems cannot be used since most constraints in the nurse rostering problem are soft. Based on ideas borrowed from global constraints in constraint programming to model rostering problems, an efficient dynamic programming algorithm with novel label definitions and dominating rules specific to soft time-related constraints is proposed. In addition, several acceleration strategies are employed to improve the branch and price algorithm. Computational results on two sets of instances ranging from 2 to 4 units over a horizon of 2 or 4 weeks demonstrate the effectiveness of the proposed algorithms. The accelerated dynamic programming algorithm is able to solve pricing subproblems to optimality with the fewest extended labels. When contrasted with Cplex, the branch and price approach yields solutions that are either equivalent or superior across all instances.

A two-phase algorithm for the dynamic time-dependent green vehicle routing problem in decoration waste collection

Transportation activities associated with construction waste generate substantial carbon emissions, an issue that is attracting increasing environmental concern. To raise construction waste transportation efficiency and reduce carbon emission, we address the dynamic time-dependent green vehicle routing problem for decoration waste collection (DTDGVRP-DWC). In the existing literature, many deterministic approaches to the dynamic vehicle routing problem are myopic, as they only react to already arrived requests. In this paper, we propose a stochastic sampling method to tackle with uncertain customer request in the real world. The DTDGVRP-DWC is formulated as an 0-1 programming. In the new model, we consider urban traffic congestion and variable speeds over time, and factors that significantly influence both carbon emissions and fuel costs. To quickly solve the complicated optimization problem, we develop a two-phase algorithm. In the first phase, we embed a competitive simulated annealing algorithm to determine visitation schedules for anticipated and early-request customers. In the second phase, we propose an event-trigger mechanism to decompose the dynamic problem into a series of static sub-problems, and an effective heuristic to solve each sub-problem. Computational results show that as long as the prediction accuracy exceeds a threshold, the forecast routing method consistently performs better than reactive routing. A real-world case demonstrates that an early commitment waiting time strategy benefits timely service requirements, whereas a late or hybrid waiting time strategy takes overall efficiency and customer satisfaction into account.

Routing and charging scheduling for the electric carsharing system with mobile charging vehicles

Electric carsharing systems are expected to be an optional alternative to private vehicles for decreasing the urban traffic congestion and emissions. However, the temporal and spatial imbalance of the charging demand of shared electric vehicles adds to the managerial complexity of electric carsharing systems. This paper integrates mobile charging vehicles into the electric carsharing system to address this imbalance. Mobile charging vehicles can dwell at stations to provide elastic charging capacity, and thereby decrease both the waiting time of shared electric vehicles at busy stations and the investments in fixed charging piles at suburban stations. In this paper, a mixed integer linear programming formulation is proposed based on a time-space network, in which the routes of shared electric vehicles, charging schedules of shared electric vehicles, and routes of mobile charging vehicles are optimized simultaneously. Then, an algorithm based on Lagrangian relaxation is proposed. Specifically, the proposed formulation is decomposed into three independent subproblems. We propose three exact algorithms for these subproblems, and a tailored multistep repair algorithm is designed to generate feasible solutions. A case study in Hefei, China demonstrates the performance of the proposed algorithm and the effects of the number of SEVs, the number of MCVs, the number of fixed charging piles, trip component, battery capacity, and revenue on the operation of the electric carsharing system.

Robust convoy movement problem under travel time uncertainty

A convoy represents a collection of vehicles traveling with a spacing of 50–100 m between them for tactical purposes. The convoy movement problem is a variant of the vehicle routing problem, an NP-hard problem aimed at determining the paths and schedules of convoys. Given the uncertainties in travel times during wartime, attributable to various factors such as road conditions and enemy threats, it is essential to consider uncertain travel times when determining convoy paths and schedules. Therefore, this study introduces a robust convoy movement problem under travel time uncertainty. A polyhedral set for uncertain travel times is used to derive a robust counterpart for the problem. To solve the proposed problem, we establish an exact algorithm that determines optimal solutions by iteratively generating and integrating multiple paths of convoys. This algorithm involves four steps: generation of k-th robust shortest paths, construction of path combinations, adjustment of departure times, and conduction of optimality check. These steps are iterated sequentially until the optimal solution is obtained. In computational experiments, the exact algorithm demonstrates superior performance and reduced computation time compared with the commercial solver CPLEX on both real instances and randomly generated instances. In addition, we conduct a sensitivity analysis for several parameters related to the problem, providing valuable managerial insights for decision-makers.

A quadratically constrained mixed-integer non-linear programming model for multiple sink distributions

Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 ($1,638.91) to GH¢14,676 ($1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.

A branch-cut-and-price approach for the two-echelon vehicle routing problem with drones

We present a new set-partitioning model for the two-echelon vehicle routing problem with drones (2E-VRP-D). In this model, partial routes corresponding to drone movements are enumerated by an efficient dynamic program. A state-of-the-art exact branch-cut-and-price algorithm solves the model using a labeling algorithm for the pricing problems. We further propose an adaptation of the well-known rounded capacity cuts, specifically tailored to address this problem, as well as pre-processing methods designed to enhance the algorithm’s efficiency. In addition, we propose an effective heuristic branch-cut-and-price based on the exact algorithm. Computational experiments demonstrate that the exact algorithm solves all instances from the 2E-VRP-D literature and significantly increases the size of optimally solved clustered instances. Finally, a sensitivity analysis is conducted to assess the impact of the proposed enhancements.

A Parallel Genetic Algorithm With Variable Neighborhood Search for the Vehicle Routing Problem in Forest Fire-Fighting

A Parallel Genetic Algorithm With Variable Neighborhood Search for the Vehicle Routing Problem in Forest Fire-Fighting