Multi-objective Vehicle Routing Problem Research Articles

Multi-objective vehicle routing problem with flexible scheduling for the collection of refillable glass bottles: A case study

• Optimization of the collection of refillable glass bottles. • A multi-objective mathematical model based on a VRP with additional considerations. • A decision making tool with indicators to analyze the quality of the solution. • The production of several real data sets inspired by real-life application. Deposit return systems have started making their reappearance as more environmentally conscious consumers seek ways to effectively reduce their carbon footprint. An example is the management of refillable glass bottles which requires a well-organized collection network with inventory management. A collection planning with an efficient algorithm and information system has to be applied. This paper investigates, using integer linear programming, a vehicle routing problem with time constraints to provide flexibility as well as priority rules to avoid inventory saturation at collection points. The model presented, based on a real-life application in the city of Lyon and surrounding areas, includes several objectives with specific assumptions. The result of the optimization is a vehicle routing plan with flexible scheduling based on time slots. Numerical experiments are conducted on instances of different scales making it possible to model the current problem as well as its future evolution. These experiments consider several instances, using a single vehicle among three vehicle types (cargo-bicycle, car and van) and a network composed of 20 stores/clients to collect bottles from. The results show the impacts of the priority rules on the solution obtained and additional indicators are proposed in order to analyze more precisely the quality of the solution in terms of financial cost and environmental impact. The proposed model and program will help make appropriate decisions in planning and scheduling the routes of the vehicles for the refillable glass bottle collection, especially in urban areas.

Multi-Objective Vehicle Routing Problem for a Mixed Fleet of Electric and Conventional Vehicles with Time Windows and Recharging Stations

The vehicle routing problem as a challenging decision problem has been studied extensively. More specifically, solving it for a mixed fleet requires realistic calculation of the performance of electric and combustion vehicles. This study addresses a new variant of the vehicle routing problem for a mixed fleet of electric and combustion vehicles under the presence of time windows and charging stations. A bi-objective mixed-integer programming model is developed which aims at minimizing cost and pollution level concurrently. To accurately quantify travel quantities, such as fuel consumption, emission, and battery charge level, a set of realistic mathematical formulas are used. The model is first converted to a single-objective counterpart using the epsilon-constraint method and a simulated annealing algorithm is tailored to obtain Pareto optimal solutions. A discussion is also made on how the final solution can be selected from the Pareto frontier according to the design objectives. The presented framework can find a set of Pareto optimal solutions as a trade-off between cost and pollution objectives by considering different combinations of electric and combustion vehicles. It was shown that those solutions that involve more electric fleet than combustion fleet, lead to higher total costs and smaller emissions and vice versa.

A complexity task of optimization in logistic distribution: A new approach to the green multi-objective vehicle routing problem

Logistic distribution involves many costs for organizations. Therefore, opportunities for optimization in this respect are always welcome. The purpose of this work is to present a methodology to provide a solution to a complexity task of optimization in Multi-objective Optimization for Green Vehicle Routing Problem (MOOGVRP). The methodology, illustrated using a case study (employee transport problem) and instances from the literature, was divided into three stages: Stage 1, “data treatment”, where the asymmetry of the routes to be formed and other particular features were addressed; Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II); and, finally, Stage 3, “analysis of the results”, with a comparison of the algorithms. Using the same parameters as the current solution, an optimization of 5.2% was achieved for Objective Function 1 (OF{\displaystyle _{1}}; minimization of CO{\displaystyle _{2}} emissions) and 11.4% with regard to Objective Function 2 (OF{\displaystyle _{2}}; minimization of the difference in demand), with the proposed CWNSGA-II algorithm showing superiority over the others for the approached problem. Furthermore, a complementary scenario was tested, meeting the constraints required by the company concerning time limitation. For the instances from the literature, the CWNSGA-II and CWTSNSGA-II algorithms achieved superior results.

A multi-tiered vehicle routing problem with global cross-docking

A new “rich” variation on the multi-objective vehicle routing problem (VRP), called the multi-tiered vehicle routing problem with global cross-docking (MTVRPGC), is introduced in this paper. With respect to previously studied VRPs, the MVRPTGC includes the following novel features: (i) segregation of facilities into different tiers that distinguish them in terms of different processing and storage capabilities, (ii) cross-docking at a pre-specified subset of facilities in the network (a feature referred to as global cross-docking), and (iii) the possibility of spill-over into subsequent planning periods of demand for facility visitation. The problem originated from a real-life application concerning the collection and delivery of pathology specimens in the transportation network of a pathology health-care service provider. Other industrial applications may, however, benefit from this type of VRP, such as mail sorting. A mixed integer linear programming (MILP) model for this VRP is proposed, and tested computationally in respect of seventeen small hypothetical test instances. A multi-objective ant colony optimisation (MACO) algorithm for solving larger real-world instances of the MTVRPGC is also proposed. The solutions returned by the MACO algorithm are compared with those achieved by the MILP in respect to sixteen instances and also compared to actual collection and delivery routes of a real pathology healthcare service provider operating in South Africa and it is found that adopting the routes suggested by the algorithm results in substantial improvements of all the objectives pursued relative to the status quo.

An improved learnable evolution model for solving multi-objective vehicle routing problem with stochastic demand

The multi-objective vehicle routing problem with stochastic demand (MO-VRPSD) is much harder to tackle than other traditional vehicle routing problems (VRPs), due to the uncertainty in customer demands and potentially conflicted objectives. In this paper, we present an improved multi-objective learnable evolution model (IMOLEM) to solve MO-VRPSD with three objectives of travel distance, driver remuneration and number of vehicles. In our method, a machine learning algorithm, i.e., decision tree, is exploited to help find and guide the desirable direction of evolution process. To cope with the key issue of ”route failure” caused due to stochastic customer demands, we propose a novel chromosome representation based on priority with bubbles. Moreover, an efficient nondominated sort using a sequential search strategy (ENS-SS) in conjunction with some heuristic operations are leveraged to handle the multi-objective property of the problem. Our algorithm is evaluated on the instances of modified Solomon VRP benchmark. Experimental results show that the proposed IMOLEM is capable to find better Pareto front of solutions and also deliver superior performance to other evolutionary algorithms.

Optimization of gas metering maintenance services: A multiobjective vehicle routing problem with a set of predefined overlapping time windows

AbstractOptimization of maintenance services of a company working in the gas metering sector is investigated. In particular, daily tasks of operators are optimized by exploiting the paradigm of vehicle routing problems with a set of predefined time windows that overlap one with the others and four competing objectives to take into account. First, an exact integer formulation is presented that can be solved only for a reduced number of customer sites to visit. Then, a heuristic approach is proposed to find approximate solutions with huge savings on the computational effort, also for high‐dimensional instances. Numerical results on both real and synthetic scenarios showcase the effectiveness of the approach.

Variable Neighborhood Descent for Multi-Compartment and Multi-Objective Vehicle Routing Problem in Refined Product Distribution

Refined product distribution is an application of the Multi-compartment Vehicle Routing Problem (MCVRP), which simultaneously considers the vehicle routing, the assignment of heterogonous vehicles and loading policies of multi-compartment. First, we develop an optimization model with the objective of delivering on-time and minimizing transportation cost. Then we propose a Multi-objective Variable Neighborhood Descent Algorithm (MOVND), where the [Formula: see text]-constraint method transforms the original problem into a series of sub-problems of single objective with constraints. Finally, the efficiency of the proposed algorithm is verified by conducting a large number of small and large instances. Mainly including (i) compared with the classical NSGA-2 algorithm for multi-objective VRP, MOVND provides better performance in terms of convergence, spread and distribution; (ii) the multi-compartment vehicles are able to carry a variety of products simultaneously, which can improve the effective utilization of vehicle space and meet the needs of different customers in a single transportation. In addition, heterogonous vehicles that take full advantage of the characteristics of different vehicles are superior to homogeneous ones in terms of operating cost in the practice of the refined product distribution.

NSGA-II with objective-specific variation operators for multiobjective vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW) is a pivotal problem in logistics domain as it possesses multiobjective characteristics in real-world applications. Literature contains a general multiobjective VRPTW (MOVRPTW) with five objectives along with MOVRPTW benchmark instances that are derived from real-world data. In this paper, we have proposed a nondominated sorting genetic algorithm II (NSGA-II) based approach with objective-specific variation operators to address the MOVRPTW. In the proposed NSGA-II approach, the crossover and mutation operators are designed by exploiting the problem characteristics as well as the attributes of each objective. The performance of the proposed approach is evaluated on the standard benchmark instances of the problem and compared with the state-of-the-art approach available in literature. The computational results demonstrate the superiority of our approach over the state-of-the-art approach for the MOVRPTW.

Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations

<p style='text-indent:20px;'>During military operations, obtaining information on remote battlefields is essential and recent advances in unmanned aerial vehicle technology have led to the use of drones to view battlefields. However, the use of drones in military operations introduces the new problem of determining travel routes for the drones. This type of problem is similar to the well-known classical vehicle routing problem, but the main difference is its objective function. For maintenance purposes, a minimized difference in travel distances is preferred. In addition, obtaining a shorter route in terms of travel distance is important. In this research, we propose a mathematical formulation and an optimal algorithm for the problem and suggest a simple heuristic to handle the large size instance of the problem. The computational results indicate that this algorithm can solve the real-scale instances of the problem, and the heuristic exhibits good performance even when the instance size of the problem is large.</p>

Adaptive inertia weight particle swarm optimisation for a multi-objective capacitated vehicle routing problem with time window in air freight forwarding

Adaptive inertia weight particle swarm optimisation for a multi-objective capacitated vehicle routing problem with time window in air freight forwarding

Research on hot rolling scheduling problem based on Two-phase Pareto algorithm.

Under the background of excess capacity and energy saving in iron and steel enterprises, the hot rolling batch scheduling problem based on energy saving is a multi-objective and multi constraint optimization problem. In this paper, a hybrid multi-objective prize-collecting vehicle routing problem (Hybrid Price Collect Vehicle Routing Problem, HPCVRP) model is established to ensure minimum energy consumption, meet process rules, and maximize resource utilization. A two-phase Pareto search algorithm (2PPLS) is designed to solve this model. The improved MOEA/D with a penalty based boundary intersection distance (PBI) algorithm (MOEA/D-PBI) is introduced to decompose the HPCVRP in the first phase. In the second phase, the multi-objective ant colony system (MOACS) and Pareto local search (PLS) algorithm is used to generate approximate Pareto-optimal solutions. The final solution is then selected according to the actual demand and preference. In the simulation experiment, the 2PPLS is compared with five other algorithms, which shows the superiority of 2PPLS. Finally, the experiment was carried out on actual slab data from a steel plant in Shanghai. The results show that the model and algorithm can effectively reduce the energy consumption in the process of hot rolling batch scheduling.

The parallelization of a two-phase distributed hybrid ruin-and-recreate genetic algorithm for solving multi-objective vehicle routing problem with time windows

Solving multi-objective vehicle routing problem with time windows (MOVRPTW) involves satisfying two or more objectives. However, not many algorithms can achieve a broader set of Pareto optimal front and consistent solutions that have the least difference in magnitude. Therefore, it is rewarding to develop a coveted algorithm that solves these shortcomings. In this paper, we propose the parallelization of a two-phase distributed hybrid ruin-and-recreate genetic algorithm (HRRGA). The algorithms in HRRGA run in either the HRRGA and the hybrid ruin-and-recreate (HRR) phase or the HRR phase. In HRRGA phase, different HRR strategies are used with the hybrid genetic algorithm (HGA) in the near-optimal solution computation. However, in the HRR phase, only the HRR strategies are used. The algorithms in HRRGA are executed in parallel and harness its power of exploitation and exploration. These strategy combinations improve the diversity of the Pareto optimal front while delivering the generated solutions with the least difference in magnitude. Our experiment with Solomon’s benchmark set shows that HRRGA has superior results compared to the recently published hybrid algorithm, has diverse set of Pareto optimal fronts, and achieves several novel Pareto optimal fronts compared to the best-known solutions.

Optimization of Multi Objective Vehicle Routing Problem with Time Windows using Total Time Balance

Vehicle Routing Problem time window (VRPW) used in supply chain management in the physical delivery of goods and services, and the determination of all routes for a fleet of vehicles, starting and ending at a depot and serving customers with known demands by increasing the efficiency and profitability of transportation systems. The main objective of this study is to refutes a multi-objective vehicle routing problem with time windows by minimization of the number of vehicles, the total distance traveled and rout balance not sufficient instead of using 'total time balance'. To test the performance of the objective it considers GA with the fitness Aggregation approach comparing with the related literature based on Solomon’s benchmark instance standard data. The time makespan produced by FAGA and the time makespan mentioned in related literature is compared. From the result, fitness Aggregation approach with genetic algorizim (FAGA) provides better result including the real-time window as compared to previous work .

Metaheuristic algorithm for solving the multi-objective vehicle routing problem with time window and drones

In some special rescue scenarios, the needed goods should be transported by drones because of the landform. Therefore, in this study, we investigate a multi-objective vehicle routing problem with time window and drone transportation constraints. The vehicles are used to transport the goods and drones to customer locations, while the drones are used to transport goods vertically and timely to the customer. Three types of objectives are considered simultaneously, including minimization of the total energy consumption of the trucks, total energy consumption of the drones, and the total number of trucks. An improved artificial bee colony algorithm is designed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector, and the initialization method based on the Push-Forward Insertion Heuristic is embedded. To enhance the exploitation abilities, an improved employed heuristic is developed to perform detailed local search. Meanwhile, a novel scout bee strategy is presented to improve the global search abilities of the proposed algorithm. Several instances extended from the Solomon instances are used to test the performance of the proposed improved artificial bee colony algorithm. Experimental comparisons with the other efficient algorithms in the literature verify the competitive performance of the proposed algorithm.

Improved Multi-Ant-colony algorithm for solving Multi-Objective Vehicle Routing Problems

Classical vehicle routing problems (VRP) involves supply of goods/services from a central depot to geographically scattered customers. Besides the classical objective of minimizing the total travelled distance, the present work also considers simultaneous optimization of two additional objectives namely minimizing make span and minimizing distance imbalance. A mathematical model for this multi-objective version of VRP (MO-VRPTW) has been developed. A meta-heuristic based on multiple ant colony system for solving this MO-VRPTW has also been proposed. Firefly algorithm (FA) has also been applied to avoid local optima. Two new migration operators named Migration-I and Migration-II and multi-pheromone matrices have been developed to further improve the solution set. The proposed algorithm has been tested on a number of benchmark problems and its superiority over other state of art approaches and NSGA-II one of the commonly used method for multi-objective optimization problems is demonstrated.

Multi-objective vehicle routing and loading with time window constraints: a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner.

A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows

In this paper, we present a multi-objective vehicle routing problem with flexible time windows (MOVRPFlexTW). In this problem, a fleet of vehicles can service a set of customers earlier and later than the required time with a given tolerance. This flexibility enables a logistics company to save distribution costs at the expense of customer satisfaction. This paper uses a direct interpretation of the vehicle routing problem with flexible time windows (VRPFlexTW) as a multi-objective problem, where the total distribution costs (including travel costs and fixed vehicle costs) are minimized and the overall customer satisfaction is maximized. We propose a solution strategy based on ant colony optimization and three mutation operators, which incorporates the concept of Pareto optimality for multi-objective optimization. The performance of the proposed approach was evaluated using the well-known benchmark Solomon’s problems. Our experimental results show that the suggested approach is effective, because it provides solutions that are comparative to the best known results in the literatures. Finally, we not only highlight the advantages of MOVRPFlexTW when compared with the single objective VRPFlexTW, but also illustrate its applicability and validation by analyzing a real case.

An Intelligent Water Drop Algorithm for Solving Multi-Objective Vehicle Routing Problems With Mixed Time Windows

This article proposes an Intelligent Water Drop Algorithm for solving Multi-Objective Vehicle Routing Problems by considering the constraints of vehicle volume, delivery mileage, and mixed time windows and minimizing the cost of distribution and the minimum number of vehicles. This article improves the basic Intelligent Water Drop Algorithm and show the improved intelligent water droplet genetic hybrid algorithm is an effective method for solving discrete problems. The authors present a practical example and show the applicability of the proposed algorithm. The authors compare the algorithms with the basic algorithm and show the improved intelligent droplet genetic hybrid algorithm has higher computing efficiency and continuous optimization capability.

Multi Objective Vehicle Routing Problem: A Survey

In the last decades, a lot of research has been done on Multi Objective Vehicle Routing due to its rich real life applications. However, the related literature is yet not being summarized anywhere. This paper presents a broad survey on the considered problem. This paper broadly presents the objectives considered, approaches used to solve multi objective vehicle routing problem. Finally, the survey classifies the main features of recently published literature and also provides some future directions in the considered field.

A Bee Evolutionary Algorithm for Multiobjective Vehicle Routing Problem with Simultaneous Pickup and Delivery

A new closed-loop supply chain logistics network of vehicle routing problem with simultaneous pickups and deliveries (VRPSPD) dominated by remanufacturer is constructed, in which the customers are originally divided into three types: distributors, recyclers, and suppliers. Furthermore, the fuel consumption is originally added to the optimization objectives of the proposed VRPSPD. In addition, a bee evolutionary algorithm guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) with a two-stage optimization mechanism is originally designed to solve the proposed VRPSPD model with three optimization objectives: minimum fuel consumption, minimum waiting time, and the shortest delivery distance. The proposed BEG-NSGA-II could conquer the disadvantages of traditional nondominated sorting genetic algorithm II (NSGA-II) and algorithms with a two-stage optimization mechanism. Finally, the validity and feasibility of the proposed model and algorithm are verified by simulating an engineering machinery remanufacturing company’s reverse logistics and another three test examples.