Multi-objective Vehicle Routing Problem Research Articles

Solving the multi-objective Vehicle Routing Problem with Soft Time Windows with the help of bees

This paper presents a new model and solution for the multi-objective Vehicle Routing Problem with Soft Time Windows (VRPSTW) using a hybrid metaheuristic technique. The proposed methodology is developed on the basics of a new swarm based Artificial Bee Colony (ABC) algorithm combined with two-step constrained local search for neighborhood selection. VRPSTW involves computing the routes of a set of vehicles with fixed capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. Here, the time window constraints are relaxed into “soft”, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. The solution of routing problems with soft time windows has valuable practical applications. This paper uses a direct interpretation of the VRPSTW as a multi-objective optimization problem where the total traveling distance, number of window violations and number of required vehicles are minimized while capacity and time window constraints are met. Our work aims at using ABC inspired foraging behavior of honey bees which balances exploration and exploitation to avoid local optima and reach the global optima. The algorithm is applied to solve the well known benchmark Solomon׳s problem instances. Experimental results show that our suggested approach is quite effective, as it provides solutions that are competitive with the best known results in the literature. Finally, we present an analysis of our proposed algorithm in terms of computational time.

Multi-objective vehicle routing problem with time windows: Improving customer satisfaction by considering gap time

The vehicle routing problem with time windows is a combinatorial optimisation problem in distribution logistics. It has been infrequently measured as a multi-objective optimisation problem for the benefit of customers. For the purposes of this research, the measurement of multi-objective vehicle routing problem with time windows will be in terms of a minimisation of the total distance travelled by all vehicles, the total number of vehicles used (management beneficial objectives) and the total gap between ready time and issuing time (customer beneficial objective). It is possible to satisfy customers by issuing the goods as close as possible to the customer ready time. This is because possibilities for going out of stock during the above said time gap (by chance of improper inventory maintenance) are reduced with a minimised total time gap, which in turn increases the sales orders for the manufacturing management. An improved genetic algorithm, called the fitness aggregated genetic algorithm, has been implemented to resolve the problem. The proposed algorithm incorporates a fitness aggregation approach and dedicated operators, such as selection based on aggregate fitness value and best cost route crossover, to resolve the multi-objective problem. The algorithm was validated on Solomon’s bi-objective benchmark models for the minimisation of the total distance travelled and total number of vehicles used, and the results formed by proposed algorithm are competitive to best known results. After validating the proposed algorithm on bi-objective models, the third objective – namely, the total time gap between ready time and issuing time – is included in the bi-objective model. The results show that the suggested algorithm creates improved customer-satisfied routes without drastically affecting the total distance travelled and total number of vehicles used.

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.

Multiobjective Vehicle Routing Problems With Simultaneous Delivery and Pickup and Time Windows: Formulation, Instances, and Algorithms

This paper investigates a practical variant of the vehicle routing problem (VRP), called VRP with simultaneous delivery and pickup and time windows (VRPSDPTW), in the logistics industry. VRPSDPTW is an important logistics problem in closed-loop supply chain network optimization. VRPSDPTW exhibits multiobjective properties in real-world applications. In this paper, a general multiobjective VRPSDPTW (MO-VRPSDPTW) with five objectives is first defined, and then a set of MO-VRPSDPTW instances based on data from the real-world are introduced. These instances represent more realistic multiobjective nature and more challenging MO-VRPSDPTW cases. Finally, two algorithms, multiobjective local search (MOLS) and multiobjective memetic algorithm (MOMA), are designed, implemented and compared for solving MO-VRPSDPTW. The simulation results on the proposed real-world instances and traditional instances show that MOLS outperforms MOMA in most of instances. However, the superiority of MOLS over MOMA in real-world instances is not so obvious as in traditional instances.

Routing with time-windows for multiple environmental vehicle types

With the goal of reducing cost, improving customer satisfaction and controlling the environmental pollution, a environmental routing optimization problem with time windows and multiple vehicle types is proposed by considering the concept of low-carbon logistics. A multi-objective vehicle routing problem (VRP) model with soft time-windows for multiple environmental vehicle types is presented, and a hybrid genetic algorithm (GA) is designed. Based on the experiments, the effectiveness of the algorithm is examined. With Pareto analysis, the relationship among the three objectives (distribution cost, customer satisfaction and environmental pollution) is examined. Sensitivity analysis is conducted to identify the influence of different type vehicle on the environmental performance. The results shows that the vehicle speed has strong correlation with the operation cost and environmental pollution, while the load capacity affects the operation cost, customer satisfaction and environmental pollution.

An evolutionary approach for multi-objective vehicle routing problems with backhauls

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes with minimum cost, such that all linehaul and backhaul customers are serviced. A common variant is the VRP with selective backhauls (VRPSB), where the collection from backhaul customers is optional. For most real world applications, the number of vehicles, the total travel cost, and the uncollected backhauls are all important objectives to be minimized, so the VRPB needs to be tackled as a multi-objective problem. In this paper, a similarity-based selection evolutionary algorithm approach is proposed for finding improved multi-objective solutions for VRPB, VRPSB, and two further generalizations of them, with fully multi-objective performance evaluation.

The Optimization of Transportation Costs in Logistics Enterprises with Time-Window Constraints

This paper presents a model for solving a multiobjective vehicle routing problem with soft time-window constraints that specify the earliest and latest arrival times of customers. If a customer is serviced before the earliest specified arrival time, extra inventory costs are incurred. If the customer is serviced after the latest arrival time, penalty costs must be paid. Both the total transportation cost and the required fleet size are minimized in this model, which also accounts for the given capacity limitations of each vehicle. The total transportation cost consists of direct transportation costs, extra inventory costs, and penalty costs. This multiobjective optimization is solved by using a modified genetic algorithm approach. The output of the algorithm is a set of optimal solutions that represent the trade-off between total transportation cost and the fleet size required to service customers. The influential impact of these two factors is analyzed through the use of a case study.

Multi-objective Vehicle Routing Problem with Cost and Emission Functions

Among the logistics activities, transportation, is presented as a major source of air pollution in Europe, generating harmful levels of air pollutants and is responsible for up to 24% of greenhouse gases (GHGs) emissions in the European Union. The growing environmental concern related to the economic activity has been transferred to the field of transport and logistics in recent decades. Therefore, environmental targets are to be added to economic targets in the decision-making, to find the right balance between these two dimensions. In real life, there are many situations and problems that are recognized as multi-objective problems. This type of problems containing multiple criteria to be met or must be taken into account. Often these criteria are in conflict with each other and there is no single solution that simultaneously satisfies everyone. Vehicle routing problems (VRP) are frequently used to model real cases, which are often established with the sole objective of minimizing the internal costs. However, in real life other factors could be taken into account, such as environmental issues. Moreover, in industry, a fleet of vehicles is rarely homogeneous. The need to be present in different segments of the market, forcing many companies to have vehicles that suit the type of goods transported. Similarly, to have vehicles of different load capacities enables a better adaptation to the customer demand. This paper proposes a multi-objective model based on Tchebycheff methods for VRP with a heterogeneous fleet, in which vehicles are characterized by different capacities, costs and emissions factors. Three objective functions are used to minimize the total internal costs, while minimizing the CO2 emissions and the emission of air pollutants such as NOx. Moreover, this study develops an algorithm based on C&W savings heuristic to solve the model when time windows are not considered. Finally, a real case application is analyzed to confirm the practicality of the model and the algorithm.

A New Multi Objective Genetic Algorithm: Fitness Aggregated Genetic Algorithm (FAGA) for Vehicle Routing Problem

This paper presents multi objective vehicle routing problem in which the total distance travelled by the vehicles and total number of vehicles used are minimized. In general, fitness assignment procedure, as one of the important operators, influences the effectiveness of multi objective genetic algorithms. In this paper genetic algorithm with different fitness assignment approach and specialized crossover called Fitness Aggregated Genetic Algorithm (FAGA) is introduced for solving the problem. The suggested algorithm is investigated on large number of popular benchmarks for vehicle routing problem. It is observed from the results that the suggested new algorithm is very effective and the solutions are competitive with the best known results.

Application of the multi-objective cross-entropy method to the vehicle routing problem with soft time windows

The vehicle routing problem with time windows is a widely studied problem with many real-world applications. The problem considered here entails the construction of routes that a number of identical vehicles travel to service different nodes within a certain time window. New benchmark problems with multi-objective features were recently suggested in the literature and the multi-objective optimisation cross-entropy method is applied to these problems to investigate the feasibility of the method and to determine and propose reference solutions for the benchmark problems. The application of the cross-entropy method to the multi-objective vehicle routing problem with soft time windows is investigated. The objectives that are evaluated include the minimisation of the total distance travelled, the number of vehicles and/or routes, the total waiting time and delay time of the vehicles and the makespan of a route.

Disaster relief routing by considering heterogeneous vehicles and reliability of routes using an MADM approach

Article history: Received December 10, 2013 Received in revised format 16 March 2014 Accepted April 29 2014 Available online May 14 2014 A crucial issue in humanitarian relief operations is vehicle routing because there are many difficulties in roads that people face when a disaster is occurred. In such circumstances, selecting more reliable routes could help rescue team act more efficacious. Therefore, we propose a mathematical model that maximizes the reliability of selected routes in disaster relief routing process using a multiple attribute decision making (MADM) technique. Furthermore, the proposed model minimizes the total cost that imposed to system. For this reason, the model is a multi-objective vehicle routing problem (VRP). The problem considered here is NP-hard and its objective is to find near optimal solutions, rather than optimal ones, using the nondominated sorting genetic algorithm. © 2014 Growing Science Ltd. All rights reserved.

Solving Multi-objective Vehicle Routing Problem with Time Windows by FAGA

The vehicle routing problem with time windows (VRPTW) is a complex transportation issue. In this paper, multi objective VRPTW is considered in which the total distance travelled, total number of vehicles used and route balance are minimized. Genetic algorithm with fitness aggregation approach and specialized operators like selection based on aggregate fitness value, best cost route crossover called Fitness Aggregated Genetic Algorithm (FAGA) is introduced for solving the multi objective problem. The algorithm was tested on large number of Solomon's benchmarks for bi-objective model that is minimization of total distance travelled and total number of vehicles used. The results produced by FAGA are highly competitive to best known results reported in the literature. After validation the third objective that is route balance is incorporated into bi-objective model and it is observed that FAGA produces better balanced routes without affecting the total distance travelled and total number of vehicles used.

A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.

A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows

The Capacitated Vehicle Routing Problem with Time Windows is an important combinatorial optimization problem consisting in the determination of the set of routes of minimum distance to deliver goods, using a fleet of identical vehicles with restricted capacity, so that vehicles must visit customers within a time frame. A large number of algorithms have been proposed to solve single-objective formulations of this problem, including meta-heuristic approaches, which provide high quality solutions in reasonable runtimes. Nevertheless, in recent years some authors have analyzed multi-objective variants that consider additional objectives to the distance travelled. This paper considers not only the minimum distance required to deliver goods, but also the workload imbalance in terms of the distances travelled by the used vehicles and their loads. Thus, MMOEASA, a Pareto-based hybrid algorithm that combines evolutionary computation and simulated annealing, is here proposed and analyzed for solving these multi-objective formulations of the VRPTW. The results obtained when solving a subset of Solomon’s benchmark problems show the good performance of this hybrid approach.

Constraint Cellular Ant Algorithm for the Multi-Objective Vehicle Routing Problem

Constraint Cellular ant algorithm is a new optimization method for solving real problems by using both constraints method, the evolutionary rule of cellular, graph theory and the characteristics of ant colony optimization. Multi-objective vehicle routing problem is very important and practical in logistic research fields, but it is difficult to model and solve because objectives have complicated relationship and restriction. Constraint Cellular ant algorithm has more obvious advantages to solve such kind of combinatorial optimization problems than many other algorithms. The test results show that the constraint cellular ant algorithm is feasible and effective for the MOVRP. The clarity and simplicity of the constraint cellular ant algorithm is greatly enhanced to ant colony optimization.

Multiobjective Vehicle Routing Problem with Route Balance Based on Genetic Algorithm

This study proposes a genetic algorithm to solve the biobjective vehicle routing problem with time windows simultaneously considering total distance and distance balance of active vehicle fleet. A new complex chromosome is used to present the active vehicle route. Through tournament selection, one-point crossover, and migrating mutation operator, the solution of the problem is solved. In experiment on Solomon’s benchmark problems, considering the total distance and distance balance, the results are improved in all classes of problems. According to the experimental results, the suggested approach is sufficient and the average GA performance is good.

Cellular Ant Algorithm for the Multi-Objective Vehicle Routing Problem

Cellular Ant Algorithm for the Multi-Objective Vehicle Routing Problem

Multiobjective vehicle routing problem with fixed delivery and optional collections

We present an adaption on the formulation for the vehicle routing problem with fixed delivery and optional collections, in which the simultaneous minimization of route costs and of collection demands not fulfilled is considered. We also propose a multiobjective version of the iterated local search (MOILS). The performance of the MOILS is compared with the \(\epsilon \)-constrained (\(P_{\epsilon }\)) ILS, the NSGA-II and the indicator-based multi-objective local search methods in the solution of 14 problem instances containing between 50 and 199 customers plus the depot. The results indicate that the MOILS outperformed the other approaches, obtaining significantly better average values for coverage, hypervolume and cardinality.

Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction

The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self‐adaptive grid multi‐objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due‐time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.

A decomposition-based hierarchical optimization algorithm for hot rolling batch scheduling problem

In this paper, the hot rolling batch scheduling problem is formulated as a multi-objective vehicle routing problem with double time windows model, in which the first time window deals with the surface grade constraint and the second one is for the linkage modes. In view of the complexity of the proposed model and the priority of considered objectives in practical production, a decomposition-based hierarchical optimization algorithm is proposed to solve the model. Firstly, the model is decomposed into two sub-problems: vehicle routing problem with time windows (VRPTW) and single vehicle routing problem with time windows (SVRPTW). Secondly, MACS-VRPTW is used to optimize the VRPTW sub-problem, in which the first objective is prior to the second one. Then, dynamic programming and genetic algorithm are used to optimize the SVRPTW sub-problem so as to reach a higher hot charge temperature. Experimental results based on the practical production instances have indicated that the proposed model and algorithm are effective and efficient.