Multi-objective Vehicle Routing Research Articles

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.

Demonstrating the importance of using total time balance instead of route balance on a multi-objective vehicle routing problem with time windows

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

MULTI-OBJECTIVE VEHICLE ROUTING PROBLEM WITH TIMES WINDOWS DENGAN PENDEKATAN GOAL PROGRAMMING UNTUK MENYELESAIKAN MASALAH OPTIMISASI RUTE PERJALANAN BUS PARIWISATA

Determining the route of the tourism bus to visit some tourism object not only to minimaze the distance, but also there are another purpose, such as minimization cost, maximizing tourism object, minimizing trip time, and maximizing the visit time in the tourism object. But, determining the route we should notice the open hours of the tourism object and operational hours for the tourism bus. The matter of determining the rute that involve some purpuse and considering the visit hours in the math is known as multi-objective vehicle routing problem with times windows. Goal programming is one of technique to solve the model with the multi-objective function and assist to find an optimal solution form several an compatible purpose. The purpose of goal programming is to minimize the total of deviation of all the purpose. Based on the case, goal programming will be apply the multi-objective vehicle routing problem with times windows which has been finised with goal programming approachment. Then, from the model it applied for the trip route of tourism agen Purpledia Pictures T&T in Bali island. The completion with LINGO, give an optimal route solution of the tourism bus, as many as three route with total cost IDR 1.269.700,00, as 25 tourism object which has been visited from 49 tourism place, the tour time 14.1 hours in 3 days and the total time to visited of tourism object 27 hours in 3 days.

Algorithms for the multi-objective vehicle routing problem with hard time windows and stochastic travel time and service time

This paper introduces a multi-objective vehicle routing problem with hard time windows and stochastic travel and service times. This problem has two practical objectives: minimizing the operational costs, and maximizing the service level. These objectives are usually conflicting. Thus, we follow a multi-objective approach, aiming to compute a set of Pareto-optimal alternatives with different trade-offs for a decision maker to choose from. We propose two algorithms (a Multi-Objective Memetic Algorithm and a Multi-Objective Iterated Local Search) and compare them to an evolutionary multi-objective optimizer from the literature. We also propose a modified statistical method for the service level calculation. Experiments based on an adapted version of the 56 Solomon instances demonstrate the effectiveness of the proposed algorithms.

A generic fuzzy approach for multi-objective optimization under uncertainty

Abstract Multi-objective optimization under uncertainty has gained considerable attention in recent years due to its practical applications in real-life. Many studies have been conducted on this topic, but almost all of them transformed the problem into a mono-objective one or just neglected the effects of uncertainty on the outcomes. This paper addresses specific uncertain multi-objective problems in which uncertainty is expressed by means of triangular fuzzy numbers. To handle these problems, we introduced a new approach able to solve them without any transformation by considering fuzziness propagation to the objective functions. The proposed approach is composed of two main contributions: First, a fuzzy Pareto dominance is defined for ranking the generated fuzzy solutions. Second, a generic fuzzy extension of well-known evolutionary algorithms is suggested as resolution methods. An experimental study on multi-objective Vehicle Routing Problems (VRP) with uncertain demands is finally carried to evaluate our approach.

Risk based, multi objective vehicle routing problem for hazardous materials: a test case in downstream fuel logistics

Abstract The paper analyses a practical case of study related to the distribution of fuels for the Total Erg Oil Company to the service stations located in the Province of Rome (Italy). The problem is formulated as a capacitated vehicle routing problem with time windows, where several heuristic procedures have been tested, considering both static and dynamic travel times. With respect to the standard operational costs used typically, a multivariable objective function has been proposed which takes into account also a new risk index. The risk index proposed is function of the population density of the zones covered by each path and of the estimated number of road accidents on each road link. In such a way, we take into account the population’s exposure to the risk associated with an incidental event involving a fuel tank. The obtained output is the set of planned routes with minimum service cost and minimum risk. Results demonstrate how an accurate planning of the service saves up to 3 hours and 30 km on a daily basis compared to a benchmark. Moreover, the distribution company can parameterize the configuration of the service, by varying the weight adopted in order to include the risk index. Including the risk index may bring to a higher safety route planning, with an increase of the operating costs of only 2%.

A tissue P system based evolutionary algorithm for multi-objective VRPTW

Abstract Multi-objective vehicle routing problem with time windows (VRPTW) has important applications in engineering and computer science, and it is a NP-hard problem. In the last decade, numerous new methods for multi-objective VRPTW have sprung up. However, the calculation speed of most algorithms is not fast enough, and on the other hand, these algorithms did not give a complete Pareto optimal front, although their results are excellent. Hence, in this paper, a tissue P system with three cells based MOEA, termed PDVA, is proposed to solve the multi-objective VRPTW. In PDVA, two mechanisms, the discrete glowworm evolution mechanism (DGEM) and the variable neighborhood evolution mechanism (VNEM), are used as sub-algorithms in two cells respectively to balance the exploration and exploitation reasonably. Simultaneously, some special strategies are used to enhance the performance of the proposed algorithm. The following experiments are presented to test the proposed algorithm. First, the influence of the parameters on the performance of the algorithm is investigated. Second, the validity of the algorithm is highlighted when compared to the DGEM-VNEM algorithm. Third, the quality and diversity of the solutions are improved when compared to the other popular algorithms. These results and comparisons on test instances demonstrate the competitiveness of PDVA in solving multi-objective VRPTW in terms of both quantity and speed.

Optimization of multi objective vehicle routing problem using a new hybrid algorithm based on particle swarm optimization and artificial bee colony algorithm considering Precedence constraints

The vehicle routing problem is the basic problem of distribution planning which seeks to find the best route with minimum displacement cost considering the number of customers, their constraints, and number and capacity of the available vehicles. In this study, the traveling salesman problem and vehicle routing models are firstly described and, after that, the multi objective vehicle routing model is proposed to consider the Precedence constraints among customers. There are different meta-heuristic algorithms that can solve such NP-hard problems. In the present study, a solver algorithm is proposed which is based on a combination of the particle swarm optimization and the artificial bee colony algorithms. Additionally, by presenting an operational sample, using data of customers in a region, considering different constraints of the problem and its functions, and using penalty method as well as additional segmentation constraint method, the best vehicle route is obtained and the results of each algorithm together with its hybrid algorithm are demonstrated.

Solving Multi-Objective Vehicle Routing Problem with Time Windows Using Hybrid Ants Optimization and Tabu Search Based on Performance Metrics

In this research, we are studying the possibility of contribution in solving the multi-objective vehicle Routing problem with time windows, that is one of the optimization problems of the NP-hard type, This problem has attracted a lot of attention now because of its real life applications.Moreover, We will also introduce an algorithm called Hybrid Algorithm (HA) which depends on integrates between Multiple Objective Ant Colony Optimisation (MOACO) and Tabu Search (TS) algorithm based on the Pareto optimization, and compare the presented approach is the developer with standard tests to demonstrate the applicability and efficiency.

Robust Dynamic Multi-Objective Vehicle Routing Optimization Method.

For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, and the total distance of routes were normally considered as the optimization objectives. Except for the above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, a corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, a robust dynamic multi-objective vehicle routing method with two-phase is proposed . Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii) The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii) A metric measuring the algorithms robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

A decomposition-based chemical reaction optimization for multi-objective vehicle routing problem for simultaneous delivery and pickup with time windows

A practical variant of the vehicle routing problem (VRP), with simultaneous delivery and pickup and time windows (VRPSDPTW) is a challenging combinatorial optimization problem that has five optimization objectives in transportation and distribution logistics. Chemical reaction optimization has been used to solve mono and multi-objective problems. However, almost all attempts to solve multi-objective problems have included continues problems less than four objectives. This paper studies discrete multi-objective VRPSDPTW using decomposition-based multi-objective optimization chemical reaction optimization. In the proposed algorithm, each decomposed sub-problem is represented by a chemical molecule. All of the molecules are divided into a few groups, with each molecule having several neighboring molecules. To balance the diversity and convergence, we designed operators of on-wall ineffective collision and inter-molecular ineffective collision for a local search, as well as operators of decomposition and synthesis to enhance global convergence. The proposed approach is compared with two different algorithms on hypervolume performance measures. Experimental results show that the proposed algorithm outperform the other algorithms in most benchmarks.

Solving stochastic multiobjective vehicle routing problem using probabilistic metaheuristic

In this paper we propose a new metaheuristic algorithm for solving stochastic multiobjective combinatorial optimization(SMOCO) problems. Indeed, we find that the various initiatives that have been launched recently on this subject, they propose the classical metaheuristics to solve a stochastic multi-objective problems,but when the stochasticity effects is not taken into account, the choice of an arbitrary value leading to a particular configuration and a high loss of information. To conserve the stochastic nature of SMOCO problems,the pareto ranking should be defined on the random objectives functions directly rather than converted deterministic objectives. From these considerations, the scope of this research should consist of: (i)Proposed novel methodology of stochastic optimality for ranking objective functions characterized by non-continuous and no closed form expression. This novel approach is based on combinatorial probability and can be incorporated in a multiobjective evolutionary algorithm. (ii)Provide probabilistic approaches to elitism and diversification in multiobjective evolutionary algorithms. Finally, The behavior of the resulting Probabilistic Multi-objective Evolutionary Algorithms (PrMOEAs) is empirically investigated on the multi-objective stochastic VRP problem.

A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given Pareto front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter-plots. Experiments are presented for three different combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem and multiobjective vehicle routing problem with time windows. Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

Stochastic partially optimized cyclic shift crossover for multi-objective genetic algorithms for the vehicle routing problem with time-windows

This paper presents a stochastic partially optimized cyclic shift crossover operator for the optimization of the multi-objective vehicle routing problem with time windows using genetic algorithms. The aim of the paper is to show how the combination of simple stochastic rules and sequential appendage policies addresses a common limitation of the traditional genetic algorithm when optimizing complex combinatorial problems. The limitation, in question, is the inability of the traditional genetic algorithm to perform local optimization. A series of tests based on the Solomon benchmark instances show the level of competitiveness of the newly introduced crossover operator.

Bio-Inspired Algorithms Applied to the Multi-Objective Vehicle Routing Problem: Frameworks and Applications

Bio-Inspired Algorithms Applied to the Multi-Objective Vehicle Routing Problem: Frameworks and Applications

Non-dominated sorting differential evolution algorithm for the minimization of route based fuel consumption multiobjective vehicle routing problems

In this paper, three parallel multi-start non-dominated sorting differential evolution algorithms (PMS-NSDEs) are proposed for the solution of four multiobjective route based fuel consumption vehicle routing problems (MRFCVRPs) and their results are compared with the results of a parallel multi-start NSGA II algorithm. All these algorithms use more than one initial population of solutions. In each algorithm a variable neighborhood search algorithm for the improvement of each solution separately is used. The problems that are formulated with two competitive objective functions are the multiobjective symmetric and asymmetric delivery route based fuel consumption vehicle routing problem (MSDRFCVRP and MADRFCVRP) and the multiobjective symmetric and asymmetric pick-up route based fuel consumption vehicle routing problem (MSPRFCVRP and MAPRFCVRP). The objective functions correspond to the optimization of the time needed for the vehicle to travel between two customers or between the customer and the depot and to the route based fuel consumption of the vehicle considering the traveled distance, the load of the vehicle, the slope of the road, the speed and the direction of the wind, and the driver’s behavior when the decision maker plans delivery or pick-up routes. A number of modified Vehicle Routing Problem instances are used in order to measure the quality of the proposed algorithms.

Robust Routes for the Fuzzy Multi-objective Vehicle Routing Problem

This paper considers a multi-objective variant of vehicle routing problems, in which the customer demands are supposed to be triangular fuzzy numbers and the objective functions are also disrupted by fuzziness. However, the propagation of fuzzy demands to the objectives can affect the reliability of generated solutions. To this end, we propose a robustness approach to deal with fuzziness in the multi-objective context. The new approach tries to achieve robust routes that minimize two fuzzy-valued objectives, the total traveled distance and total tardiness time. Additionally, we suggest to refine our previously proposed algorithms for integrating robustness. An experimental study based on a Monte-Carlo simulation is finally carried out to evaluate the obtained results.