Variable Neighborhood Descent Algorithm Research Articles

A novel variable neighborhood descent algorithm for service restoration in radial electrical distribution networks

Abstract This paper presents a variable neighborhood descent algorithm for the service restoration problem (SRP) in electrical distribution systems. The restoration problem appears when a permanent fault occurs in the system. The fault must be localized and isolated from the rest of the system. As a consequence of the isolation, the downstream area is de-energized and requires restoration. The variable neighborhood descent algorithm features its ability to solve the SRP for radial distribution systems and introduces a strategy that helps to deal with the system’s radiality. Tests are performed using a 53-node test system. The results show that the proposed algorithm can efficiently solve the SRP in a distribution system, and as a deterministic algorithm, the results can be used to help nondeterministic algorithms.

A reinforcement learning-based multiobjective heuristic algorithm for multiple-truck routing problems with heterogeneous drones

As a result of new technological developments, drone usage has become common in last-mile logistics activities. Owing to the limited flight range of drones, drones may service customers by using trucks as hubs. Although the truck routing problem with drones (TRP-D) has been studied frequently, studies that have addressed this problem in a multiobjective manner are rare. In this study, multiobjective TRP-D is discussed. In this problem, multiple trucks are considered. Each truck is equipped with multiple heterogeneous drones. A multiobjective mixed-integer linear programming (MILP) model is proposed. Since the problem is NP-hard, a reinforcement learning (RL)-based multiobjective heuristic algorithm is proposed to obtain solutions in large-scale cases. A three-phase heuristic feasible-solution-generation algorithm is proposed. The variable neighbourhood descent (VND) algorithm with RL is proposed as a local search algorithm for the multiobjective optimization problem. The results of the proposed heuristic algorithm are compared with the Pareto optimal solutions for small-sized test problems via the augmented ε-constraint (AUGMECON) method and the CPLEX solver. The proposed algorithm is also compared with state-of-the-art multiobjective heuristic algorithms for large-scale problems. According to the results, the proposed algorithm is an efficient multiobjective heuristic algorithm for the addressed problem.

Strategic flood impact mitigation in developing countries’ urban road networks: Application to Hanoi

Due to climate change, the frequency and scale of flood events worldwide are increasing dramatically. Flood impacts are especially acute in developing countries, where they often revert years of progress in sustainable development and poverty reduction. This paper introduces an optimization-based decision support tool for selecting cost-efficient flood mitigation investments in developing countries’ urban areas. The core of the tool is a scenario-based, multi-period, bi-objective Mixed Integer Linear Programming model which minimizes infrastructure damage and traffic congestion in urban road networks. The tool was developed in collaboration with Vietnamese stakeholders (e.g., local communities and government authorities), and integrates data and inputs from other disciplines, including social science, transport economics, climatology and hydrology. A metaheuristic, combining a Greedy Randomized Adaptive Search Procedure with a Variable Neighborhood Descent algorithm, is developed to solve large scale problem instances. An extensive computational campaign on randomly generated instances demonstrates the efficiency of the metaheuristic in solving realistic problems with hundreds of interdependent flood mitigation interventions. Finally, the applicability of the interdisciplinary approach is demonstrated on a real case study to generate a 20-year plan of mitigation investments for the urban area of Hanoi. Policy implications and impacts of the study are also discussed.

An iterative two-phase optimization method for heterogeneous multi-drone routing problem considering differentiated demands

Owing to low cost, high flexibility and delivery efficiency, effectively addressing the challenges of “last-mile” delivery. While collaborative truck-drone delivery systems have been proposed to overcome limitations such as limited battery life and payload capacity, they are not well-suited for large and heavy parcel delivery. To solve the issue, a pioneering heterogeneous multi-drone delivery system. In this system, the mother drone handles the delivery of large and heavy parcels, releasing small drones to manage the delivery of smaller and lighter parcels. To address the complexities of this multi-drone delivery system, we introduce a divide-and-conquer framework consisting of two integral phases. The first phase, the task allocation phase, generates multiple task allocation schemes, while the second phase, the single-drone route planning phase, produces high-quality routes for each individual drone. Two phases are performed in an iterative manner until the predefined stopping criteria are satisfied. In the task allocation phase, we propose a simulated annealing algorithm (SA) to facilitate task allocation among multiple drones, utilizing transfer and recombination operators to generate high-quality solutions. After obtaining the task allocation scheme, a satisfactory route of a mother drone is generated by a variable neighborhood descent algorithm (VND). A desirable route for each single small drone is produced by dynamic programming (DP).Extensive experiments are conducted, demonstrating the outstanding optimization and time efficiency of the proposed two-phase optimization method by the fact that it obtains within a 4.89% gap from the optimal solution generated by CPLEX in 15.48 s for instance up to 125 nodes.

Modeling, landscape analysis, and solving the capacitated single-allocation hub maximal covering problem using the GARVND hybrid algorithm

In this paper, a new variation to the Hub Maximal Covering problem called the Capacitated Single-Allocation Hub Maximal Covering Problem (CSAHMCP) is addressed for the first time and a novel binary-integer mathematical model has been proposed. To analyze the features of the problem’s solution space and to determine the most effective heuristic approach to solve it, a comprehensive Fitness Landscape Analysis is performed which reveals that the problem is of ‘rugged plain’ type and can best be solved using an algorithm with good exploration and exploitation capabilities at the same time. Accordingly, we proposed a new algorithm named GARVND, which is a hybrid of the Genetic Algorithm acting as the main framework for diversification, and a variant of the Variable Neighborhood Descent algorithm called ‘Reduced VND’ acting as a means to improve individual solutions (intensification) by searching in the spaces generated by four types of neighborhood operators. We also introduced two original crossover and mutation operators that can be used for any hub location solution method. The parameters of GARVND are tuned toward less computational times and higher solution quality by using the Taguchi experiment design technique. We solved 114 CSAHMCP instances (several times each) from the Australian Post (AP) dataset using the proposed GARVND, as well as by the Genetic Algorithm, Variable Neighborhood Search, Simulated Annealing, Tabu Search algorithms, and a hybrid algorithm consisting of Grey Wolf Optimizer and Simulated Annealing, in addition to the Gurobi exact solver. Extensive computational results and statistical analyses showed that GARVND yields favorable solutions, outperforming all the compared algorithms by producing smaller gaps with global optimal objective values. In addition, to illustrate the practical value of the CSAHMCP and the GARVND method, we performed a cost-flow sensitivity analysis for the AP Central Sydney network and came up with the best expansion scenarios to be adopted by the management.

Multi-objective simulated annealing algorithm for robotic mixed-model two-sided assembly line balancing with setup times and multiple constraints

Robotic mixed-model two-sided assembly lines (RMTALs) have become increasingly prevalent in manufacturing industries for productivity enhancement. However, only limited attention has been paid to the RMTAL balancing problems that contain both setup times and multiple constraints such as positional constraints, zoning constraints, and synchronism constraints. Given the coexistence of these aspects in real-world scenarios, this study aims to address the RMTAL balancing problem with setup times and the mentioned constraints. To formulate the problem, a mixed integer programming model is proposed to optimize cycle time and total energy consumption. To handle multiple constraints and setup times, a new method based on four-vector encoding is introduced. This method addresses the three constraints during the encoding phase using four intervals and five rules, while setup times are processed during the decoding phase. To solve the problem, a Pareto entropy-based two-mode multi-objective simulated annealing algorithm is developed. The algorithm employs variable neighborhood descent algorithm with switchable objectives to generate the initial Pareto archive. Subsequently, it selects the initial solution with minimal potential in the Pareto archive, alternating between two search modes of exploration and exploitation based on the entropy difference of Pareto solutions. Comparative experiments with four state-of-the-art algorithms on benchmark instances of varying scales demonstrate that the proposed algorithm outperforms the others in over 93% of instances for the hypervolume ratio and inverted generational distance metrics.

A dynamic incentive mechanism for data sharing in manufacturing industry

Data sharing is a critical component in a blockchain traceability platform. Therefore, creating a reasonable incentive mechanism to ensure that all enterprises participate in data sharing is vital for blockchain platforms. Currently, many researchers employ evolutionary game theory to analyze problems related to data sharing. However, evolutionary game theory typically assumes that the population composed of enterprises is mixed uniformly. Enterprises in the manufacturing industry are not uniformly mixed, as they tend to have specific connections with each other due to the size of enterprises and volume of business. Therefore, a networked evolutionary game is introduced to solve this problem. Firstly, an incentive model for enterprises sharing data is established. Then, a scale-free network is employed to simulate the connections between enterprises. To comprehensively consider the individual and group benefits of enterprises in the game, this study designs a strategy update rule for networked evolutionary game based on Discrete Particle Swarm Optimization and Variable Neighborhood Descent algorithm. To tackle the challenge of determining reasonable incentive values in networked evolutionary games, this study proposes a dynamic incentive mechanism based on the Q-Learning algorithm. Finally, the experiments indicate that this method can successfully facilitate the stable involvement of enterprises in data sharing.

A novel collaborative electric vehicle routing problem with multiple prioritized time windows and time-dependent hybrid recharging

Due to global warming and environmental deterioration, the development of electric vehicles (EVs) is seen as a key measure to promote energy saving and emission reduction in logistics industries. However, EVs’ limited driving range and long recharging time make them unable to be widely applied in logistics distribution activities. Thus, this study establishes a model for a novel collaborative electric vehicle routing problem with multiple prioritized time windows and time-dependent hybrid recharging to address the above difficulties. The model quantifies and incorporates the priority of different time windows into costs to better satisfy customer demands while minimizing the total costs. A time-dependent hybrid recharging strategy that integrates three modes of in-station fast, in-station normal, and en-route battery swapping with collaborative mobile battery swapping vans (BSVs) is presented to reduce the impact of recharging time on route decision-making. The possible queuing time due to the limited capacity of recharging stations is considered to simulate the practical application scenarios. To effectively solve the complex model of synchronous optimization of EV and BSV routes, an extended adaptive large neighborhood search algorithm with two-dimensional coding scheme is proposed. In the proposed algorithm, several removal and insertion operators are integrated to effectively evolve the solutions, and the variable neighborhood descent algorithm is combined with local search operators to further improve the algorithmic performance. Comparison experiments were conducted to verify the effectiveness of the proposed algorithm by comparing with the other baseline algorithms.

Automatic algorithm design of distributed hybrid flowshop scheduling with consistent sublots

The present-day globalized economy and diverse market demands have compelled an increasing number of manufacturing enterprises to move toward the distributed manufacturing pattern and the model of multi-variety and small-lot. Taking these two factors into account, this study investigates an extension of the distributed hybrid flowshop scheduling problem (DHFSP), called the distributed hybrid flowshop scheduling problem with consistent sublots (DHFSP_CS). To tackle this problem, a mixed integer linear programming (MILP) model is developed as a preliminary step. The NP-hard nature of the problem necessitates the use of the iterated F-Race (I/F-Race) as the automated algorithm design (AAD) to compose a metaheuristic that requires minimal user intervention. The I/F-Race enables identifying the ideal values of numerical and categorical parameters within a promising algorithm framework. An extension of the collaborative variable neighborhood descent algorithm (ECVND) is utilized as the algorithm framework, which is modified by intensifying efforts on the critical factories. In consideration of the problem-specific characteristics and the solution encoding, the configurable solution initializations, configurable solution decoding strategies, and configurable collaborative operators are designed. Additionally, several neighborhood structures are specially designed. Extensive computational results on simulation instances and a real-world instance demonstrate that the automated algorithm conceived by the AAD outperforms the CPLEX and other state-of-the-art metaheuristics in addressing the DHFSP_CS.

A Multi-Regional Path-Planning Method for Rescue UAVs with Priority Constraints

This study focuses on the path-planning problem of rescue UAVs with regional detection priority. Initially, we propose a mixed-integer programming model that integrates coverage path planning (CPP) and the hierarchical traveling salesman problem (HTSP) to address multi-regional path planning under priority constraints. For intra-regional path planning, we present an enhanced method for acquiring reciprocating flight paths to ensure complete coverage of convex polygonal regions with shorter flight paths when a UAV is equipped with sensors featuring circular sampling ranges. An additional comparison was made for spiral flight paths, and second-order Bezier curves were employed to optimize both sets of paths. This optimization not only reduced the path length but also enhanced the ability to counteract inherent drone jitter. Additionally, we propose a variable neighborhood descent algorithm based on K-nearest neighbors to solve the inter-regional access order path-planning problem with priority. We establish parameters for measuring distance and evaluating the priority order of UAV flight paths. Simulation and experiment results demonstrate that the proposed algorithm can effectively assist UAVs in performing path-planning tasks with priority constraints, enabling faster information collection in important areas and facilitating quick exploration of three-dimensional characteristics in unknown disaster areas by rescue workers. This algorithm significantly enhances the safety of rescue workers and optimizes crucial rescue times in key areas.

The multiobjective traveling salesman–repairman problem with profits: design and implementation of a variable neighborhood descent algorithm for a real scenario

AbstractThis paper introduces a problem that can be seen as a combination of the traveling salesman problem with profits and the traveling repairman problem with profits, coined as the multi‐objective traveling salesman–repairman problem with profits (Mo‐TSRPP). The objective of the Mo‐TSRPP is to simultaneously optimize three objectives: the total cost, total latency, and total profit. Indirectly, the number of nodes visited is also considered although not as an objective itself since it is determined by the size of every efficient solution in the Pareto front. The Mo‐TSRPP emerges as a real‐world problem in which a freelancer, which repairs appliances, wants to plan the daily route. Moreover, the daily plan does not require to visit all customers. To solve the problem, first, a greedy randomized adaptive procedure is designed to generate a set of high‐quality nondominated solutions and then, a variable neighborhood descent algorithm is applied for further improving the initial set. This procedure allows us to attain a good approximation of the Pareto front. To prove the performance of the proposal a comparison is done against three well‐known evolutionary algorithms: NSGA‐II, SPEA‐2, and MOEA/D. Finally, a realistic problem is shown and solved to illustrate the potential of the algorithm.

A simulated annealing with variable neighborhood descent approach for the heterogeneous fleet vehicle routing problem with multiple forward/reverse cross-docks

With a greater awareness of the challenges regarding environmental, societal, political, and economic factors, where reverse logistics has become a significant part of supply chain networks, this paper presents an integrated forward and reverse logistics network, named the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks (HF-VRPMFRCD). We consider a heterogeneous fleet of vehicles with different loading capacities and transportation costs. We also consider multiple cross-docks with two different operations: forward and reverse processes. The former focuses on delivering the demand from suppliers to customers, while the latter aims at returning unsold products from customers to suppliers. We propose a Simulated Annealing with Variable Neighborhood Descent (SAVND) algorithm for solving HF-VRPMFRCD, where Variable Neighborhood Descent (VND) is a local search heuristic embedded in the framework of Simulated Annealing (SA). SAVND outperforms the state-of-the-art algorithm in solving the Heterogeneous Fleet Vehicle Routing Problem with Multiple Cross-Docks (HF-VRPMCD), where the VND heuristic significantly improves the quality of solutions. For HF-VRPMFRCD benchmark instances, SAVND provides optimal solutions for small-scale instances and better solutions than those of the GUROBI solver for remaining larger instances. Lastly, we present and discuss the benefits of integrating the forward and reverse processes.

Logistics in the Sky: A Two-Phase Optimization Approach for the Drone Package Pickup and Delivery System

The application of drones in last-mile distribution has been a contentious research topic in recent years. Existing urban distribution modes mostly depend on trucks. This paper proposes a novel package pickup and delivery mode and system wherein multiple drones collaborate with automatic devices. The proposed mode uses free areas on top of residential buildings to set automatic devices as delivery and pickup points of packages, and employs drones to transport packages between buildings and depots. The integrated scheduling problem of package drop-pickup considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -drones, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -depots, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -customers is crucial for the system. Therefore, we propose a simulated-annealing-based two-phase optimization (SATO) approach to solve this problem. In the first phase, tasks are allocated to depots for serving, such that the initial problem is decomposed into multiple single-depot scheduling problems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -drone. In the second phase, considering the drone capability and task demand constraints, we generated a route-planning scheme for drones in each depot. Concurrently, an improved variable neighborhood descent (IVND) algorithm was designed in the first phase to reallocate tasks, and a local search (LS) algorithm was proposed to search for high-quality solutions in the second phase. Finally, extensive experiments and comparative studies were conducted to verify the effectiveness of the proposed approach.

A Two-Level Variable Neighborhood Descent for a Split Delivery Clustered Vehicle Routing Problem with Soft Cluster Conflicts and Customer-Related Costs

This paper introduces Split Delivery Clustered Vehicle Routing Problem with Soft cluster conflicts and Customer-related costs (SDCVRPSC) arising in automotive parts of milk-run logistics with supplier cluster distribution in China. In SDCVRPSC, customers are divided into different clusters that can be visited by multiple vehicles, but each vehicle can only visit each cluster once. Penalty costs are incurred when traveling between clusters. The transportation cost of a route is calculated as the maximum direct shipment cost between customers on the route plus the total drop costs. The SDCVRPSC aims to minimize the sum of transportation costs and penalty costs by determining the assignment of customers to vehicles and the visiting order of clusters. We propose an integer linear programming model and a two-level variable neighborhood descent algorithm (TLVND) that includes two-stage construction, intensification at cluster and customer levels, and a perturbation mechanism. Experimental results on designed SDCVRPSC benchmark instances demonstrate that TLVND outperforms the Gurobi solver and two adapted algorithms at the business operation level. Moreover, a real case study indicates that TLVND can bring significant economic savings compared to expert experience decisions. TLVND has been integrated into the decision support system of the case company for daily operations.

Reconfigurable distributed flowshop group scheduling with a nested variable neighborhood descent algorithm

Inspired by a real-world cellular manufacturing system for processing printed circuit boards (PCBs), this study addresses a reconfigurable distributed flowshop scheduling problem (RDFGSP), where the flowline is considered as a cell and a complete process includes two flows through the flowlines. The characteristics of the RDFGSP lie in the reconfigurability of the flowlines and the families with grouped jobs. To solve this problem, at the two flows the family assignment part and sequence part (including family sequence and job sequence) are all required to be addressed. To solve the problem, a mixed integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard property of the problem, a nested variable neighborhood descent (NVND) algorithm is developed. Its core ideas lie in the dynamic solution encoding and decoding strategies and the specially designed nested loops, including the external and internal loops. In the external loop, the solution encoding and decoding only consider the sequence part, and the family assignment part is conceived using the machine property in the decoding process. The internal loop is triggered when a decoding process in the external loop is completed, where the family assignment part and sequence part are all considered. In addition, a collaborative process and a restart strategy are employed to guarantee the global search capability. In the experimental study, the iterated F-Race (I/F-Race) is used to help determine the algorithm parameters with minimum user intervention. Comprehensive computational results demonstrate that the proposed algorithm outperforms the math solver CPLEX and other state-of-the-art metaheuristics.

An efficient iterated local search algorithm for the corridor allocation problem

The corridor allocation problem (CAP) seeks the optimal arrangement of departments along the two sides of a corridor with respect to two key considerations; there should be no gap between two consecutive departments, and both of the rows should start at the same level of the corridor. In this study, a new and comprehensive multi-start iterated local search (ILS) algorithm is developed for CAP to search the solution space more effectively. The proposed algorithm utilizes a variable neighborhood descent (VND) for local search. The VND algorithm employs five neighborhood search mechanisms (swap, insert, inverse, cross, and block insert) and a tabu list to avoid cycling. The performance of the proposed ILS is evaluated on well-known instances of various sizes. Objective function values of 34 out of 82 benchmark instances are improved by the proposed algorithm. The computational results also show that the algorithm is capable of dealing with larger-sized problems with up to eighty departments.

A deep reinforcement learning based approach for dynamic distributed blocking flowshop scheduling with job insertions

The distributed blocking flowshop scheduling problem (DBFSP) with new job insertions is studied. Rescheduling all remaining jobs after a dynamic event like a new job insertion is unreasonable to an actual distributed blocking flowshop production process. A deep reinforcement learning (DRL) algorithm is proposed to optimise the job selection model, and local modifications are made on the basis of the original scheduling plan when new jobs arrive. The objective is to minimise the total completion time deviation of all products so that all jobs can be finished on time to reduce the cost of storage. First, according to the definitions of the dynamic DBFSP problem, a DRL framework based on multi-agent deep deterministic policy gradient (MADDPG) is proposed. In this framework, a full schedule is generated by the variable neighbourhood descent algorithm before a dynamic event occurs. Meanwhile, all newly added jobs are reordered before the agents make decisions to select the one that needs to be scheduled most urgently. This study defines the observations, actions and reward calculation methods and applies centralised training and distributed execution in MADDPG. Finally, a comprehensive computational experiment is carried out to compare the proposed method with the closely related and well-performing methods. The results indicate that the proposed method can solve the dynamic DBFSP effectively and efficiently.

Heterogeneous multi-drone routing problem for parcel delivery

With the rapid development of drone technology, logistics giants like Amazon and SF Express have applied drones to parcel delivery. Drone delivery could eliminate delivery delays caused by traffic lights and traffic jams on ground vehicles, and it can deliver parcels in case of road damage caused by natural disasters. Based on this motivation, we study a new logistics delivery problem using heterogeneous multi-drone, namely, HDDP, where a large drone carries multiple small drones to distribution regions. The new features of HDDPs are multifold. First, the large drone does not directly deliver parcels, but rather launches small drones to deliver parcels. Second, the HDDP allows each small drone to deliver multiple parcels in a flight considering energy consumption according to its payload and endurance. Third, the small drone is launched from the large drone and lands at the automatic airport. In addition, we design a three-stage-based iterative optimization algorithm to reduce the complexity of the HDDP. Specifically, at the first stage, a fuzzy c-means cluster algorithm considering the small drone’s payload is designed to cluster customers; at the second stage, an improved variable neighborhood descent algorithm is developed to plan the route of the large drone; at the third stage, the dynamic programming algorithm is adopted to plan the routes of the small drones. These three stages are iteratively optimized until the termination criterion is met. Additionally, numerical experimental results indicate that the proposed algorithm for HDDP is superior to the comparison algorithms in terms of delivery time and delivery cost, and the impacts of three crucial factors are analyzed and some constructive conclusions are given.

An Efficient Two-Layer Framework for Tour Sense Recommendation

The paper shows a cutting edge prototype system, which can recommend most comprehensive travel plans that include brand new, diverse latest interest factors (POIs). It systematically gathers and analyzes data on thousands of cutting-edge tourism destinations and geographical nodes. Tour feel is a recommendation framework which examines the preference information modern day diverse tourists based totally on the transport records collected from various towns. Humans can get properly-in shape path plans, which consist of a sequence brand new points cutting-edge interest (POIs) primarily based on vacationers' constraints and goals, way to the advancement ultra-modern excursion recommendation. Multiple scenic spots and entrances are common in big-scale POIs, which are known as brilliant-POIs in this article. Maximum contemporary excursion advice algorithms, alternatively, forget the big expertise determined inside super POIs. A layer machine, which takes into account the ultra-modern route architecture (outer model) and panoramic routes within outstanding POIs (internal model). A full-on-integration-based Embedded Keep VND algorithm is used to merge templates. A greedy randomized adjustable path advent system (grasp) for local improvements in the internal version of the outer version and variable neighborhood descent (VND). The first rate-POI is considered "meta node" in the development of trendy outer routes. Dijkstra Algorithm with Pruning dynamically reviews the most satisfying path within the exquisite POI in the internal model to conform to the outer direction. The obtained end results provide the traveller with the ultimate quality route and the focus point chosen by the users.

The electric vehicle routing problem with drones: An energy minimization approach for aerial deliveries

This paper introduces the Electric Vehicle Routing Problem with Drones (EVRPD), the first VRP combining electric ground vehicles (EVs) with unmanned aerial vehicles (UAVs), also known as drones, in order to deliver packages to customers. The problem’s objective is to minimize the total energy consumption, focusing on the main non-constant and controllable factor of energy consumption on a delivery vehicle, the payload weight. The problem considers same-sized packages, belonging to different weight classes. EVs serve as motherships, from which drones are deployed to deliver the packages. Drones can carry multiple packages, up to a certain weight limit and their range is depended on their payload weight. For solving the EVRPD, four algorithms of the Ant Colony Optimization framework are implemented, two versions of the Ant Colony System and the Min–Max Ant System. A Variable Neighborhood Descent algorithm is utilized in all variants as a local search procedure. Instances for the EVRPD are created based on the two-echelon VRP literature and are used to test the proposed algorithms. Their computational results are compared and discussed. Practical, real-life scenarios of the EVRPD application are also presented and solved.