Vehicle routing optimization algorithm based on time windows and dynamic demand

To provide the supplier with the minimizum vehicle travel distance in the distribution process of goods in three situations of new customer demand,customer cancellation service,and change of customer delivery address,based on the ideas of pre-optimization and real-time optimization,a two-stage planning model of dynamic demand based vehicle routing problem with time windows was established.At the pre-optimization stage,an improved genetic algorithm was used to obtain the pre-optimized distribution route,a large-scale neighborhood search method was integrated into the mutation operation to improve the local optimization performance of the genetic algorithm,and a variety of operators were introduced to expand the search space of neighborhood solutions;At the real-time optimization stage,a periodic optimization strategy was adopted to transform a complex dynamic problem into several static problems,and four neighborhood search operators were used to quickly adjust the route.Two different scale examples were designed for experiments.It is proved that the algorithm can plan the better route,and adjust the distribution route in time under the real-time constraints.Therefore,the proposed algorithm can provide theoretical guidance for suppliers to solve the dynamic demand based vehicle routing problem.

Genetic Crossover Operators for the Capacitated Vehicle Routing Problem

We study the capacitated vehicle routing problem(CVRP)which is a well-known NP-hard combinatorial optimization problem(COP).The aim of the problem is to serve different customers by a convoy of vehicles starting from a depot so that sum of the routing costs under their capacity constraints is minimized.Since the problem is very complicated,solving the problem using exact methods is almost impossible.So,one has to go for the heuristic/metaheuristic methods and genetic algorithm(GA)is broadly applied metaheuristic method to obtain near optimal solution to such COPs.So,this paper studies GAs to find solution to the problem.Generally,to solve a COP,GAs start with a chromosome set named initial population,and then mainly three operators-selection,crossover andmutation,are applied.Among these three operators,crossover is very crucial in designing and implementing GAs,and hence,numerous crossover operators were developed and applied to different COPs.There are two major kinds of crossover operators-blind crossovers and distance-based crossovers.We intend to compare the performance of four blind crossover and four distance-based crossover operators to test the suitability of the operators to solve the CVRP.These operators were originally proposed for the standard travelling salesman problem(TSP).First,these eight crossovers are illustrated using same parent chromosomes for building offspring(s).Then eight GAs using these eight crossover operators without any mutation operator and another eight GAs using these eight crossover operators with a mutation operator are developed.These GAs are experimented on some benchmark asymmetric and symmetric instances of numerous sizes and various number of vehicles.Our study revealed that the distance-based crossovers are much superior to the blind crossovers.Further,we observed that the sequential constructive crossover with and without mutation operator is the best one for theCVRP.This estimation is validated by Student’s t-test at 95%confidence level.We further determined a comparative rank of the eight crossovers for the CVRP.

Efficient Network Selection Using Multi-Depot Routing Problem for Smart Cities

Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The suggested study is focused on technological networks for big data-driven systems.With the support of software-defined technologies,a transportation-aided multicast routing system is suggested.By using public transportation as another communication platform in a smart city,network communication is enhanced.The primary objec-tive is to use as little energy as possible while delivering as much data as possible.The Attribute Decision Making with Capacitated Vehicle(CV)Routing Problem(RP)and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research.For the optimum network selection,a Multi-Attribute Decision Making(MADM)method is utilized.For the sake of reducing energy usage,the Capacitated Vehicle Routing Problem(CVRP)is employed.To reduce the transportation cost and risk,Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used.Moreover,a mixed-integer programming approach is used to deal with the problem.To produce Pareto optimal solutions,an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is cre-ated.A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer.Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30%of less energy than the other systems.

New Hybrid Algorithm Based on BicriterionAnt for Solving Multiobjective Green Vehicle Routing Problem

The main objective of this paper is to propose a new hybrid algorithm for solving the Bi objective green vehicle routing problem (BGVRP) from the BicriterionAnt metaheuristic. The methodology used is subdivided as follows: first, we introduce data from the GVRP or instances from the literature. Second, we use the first cluster route second technique using the k-means algorithm, then we apply the BicriterionAntAPE (BicriterionAnt Adjacent Pairwise Exchange) algorithm to each cluster obtained. And finally, we make a comparative analysis of the results obtained by the case study as well as instances from the literature with some existing metaheuristics NSGA, SPEA, BicriterionAnt in order to see the performance of the new hybrid algorithm. The results show that the routes which minimize the total distance traveled by the vehicles are different from those which minimize the CO2 pollution, which can be understood by the fact that the objectives are conflicting. In this study, we also find that the optimal route reduces product CO2 by almost 7.2% compared to the worst route.

Improved ant colony optimization for multi-depot heterogeneous vehicle routing problem with soft time windows

Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.

A Memetic Algorithm With Competition for the Capacitated Green Vehicle Routing Problem

In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor(k NN) based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search(VNS) framework and the simulated annealing(SA) strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station(AFS) adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-ofexperiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP.

Multi-type ant system algorithm for the time dependent vehicle routing problem with time windows

The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.

A metaheuristic method for the multireturn-to-depot petrol truck routing problem with time windows

The petrol truck routing problem is an important part of the petrol supply chain.This study focuses on determining routes for distributing petrol products from a depot to petrol stations with the objective of minimizing the total travel cost and the fixed cost required to use the trucks.We propose a mathematical model that considers petrol trucks returning to a depot multiple times and develop a heuristic algorithm based on a local branch-and-bound search with a tabu list and the Metropolis acceptance criterion.In addition,an approach that accelerates the solution process by adding several valid inequalities is presented.In this study,the trucks are homogeneous and have two compartments,and each truck can execute at most three tasks daily.The sales company arranges the transfer amount and the time windows for each station.The performance of the proposed algorithm is evaluated by comparing its results with the optimal results.In addition,a real-world case of routing petrol trucks in Beijing is studied to demonstrate the effectiveness of the proposed approach.

Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem

Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid ap- proximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimiza- tion (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.

A Survey on the Vehicle Routing Problem and Its Variants

In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. The vehicle routing problem comes under combinatorial problem. Hence, to get solutions in determining routes which are realistic and very close to the optimal solution, we use heuristics and meta-heuristics. In this paper we discuss the various exact methods and the heuristics and meta-heuristics used to solve the VRP and its variants.

GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

Solving material distribution routing problem in mixed manufacturing systems with a hybrid multi-objective evolutionary algorithm

The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.

A Genetic Algorithm for the Split Delivery Vehicle Routing Problem

The Split Delivery Vehicle Routing Problem (SDVRP) allows customers to be assigned to multiple routes. Two hybrid genetic algorithms are developed for the SDVRP and computational results are given for thirty-two data sets from previous literature. With respect to the total travel distance and computer time, the genetic algorithm compares favorably versus a column generation method and a two-phase method.

An improved estimation of distribution algorithm for multi-compartment electric vehicle routing problem

The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles.

A Construction Heuristic for the Split Delivery Vehicle Routing Problem

The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) where customers may be assigned to multiple routes. A new construction heuristic is developed for the SDVRP and computational results are given for thirty-two data sets from previous literature. With respect to the total travel distance, the construction heuristic compares favorably versus a column generation method and a two-phase method. In addition, the construction heuristic is computationally faster than both previous methods. This construction heuristic could be useful in developing initial solutions, very quickly, for a heuristic, algorithm, or exact procedure.

An Overview and Experimental Study of Learning-Based Optimization Algorithms for the Vehicle Routing Problem

The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contributed significantly to the development of this field,these approaches either are limited in problem size or need manual intervention in choosing parameters.To solve these difficulties,many studies have considered learning-based optimization(LBO)algorithms to solve the VRP.This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches.We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms.Finally,we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

The VRP is classified as an NP-hard problem. Hence exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. To get solutions in determining routes which are realistic and very close to the actual solution, we use heuristics and metaheuristics which are of the combinatorial optimization type. A literature review of VRPTW, TDVRP, and a metaheuristic such as the genetic algorithm was conducted. In this paper, the implementation of the VRPTW and its extension, the time-dependent VRPTW (TDVRPTW) has been carried out using the model as well as metaheuristics such as the genetic algorithm (GA). The algorithms were implemented, using Matlab and HeuristicLab optimization software. A plugin was developed using Visual C# and DOT NET framework 4.5. Results were tested using Solomon’s 56 benchmark instances classified into groups such as C1, C2, R1, R2, RC1, RC2, with 100 customer nodes, 25 vehicles and each vehicle capacity of 200. The results were comparable to the earlier algorithms developed and in some cases the current algorithm yielded better results in terms of total distance travelled and the average number of vehicles used.

Fast and scalable routing protocols for data center networks

Data center networks may comprise tens or hundreds of thousands of nodes,and,naturally,suffer from frequent software and hardware failures as well as link congestions.Packets are routed along the shortest paths with sufficient resources to facilitate efficient network utilization and minimize delays.In such dynamic networks,links frequently fail or get congested,making the recalculation of the shortest paths a computationally intensive problem.Various routing protocols were proposed to overcome this problem by focusing on network utilization rather than speed.Surprisingly,the design of fast shortest-path algorithms for data centers was largely neglected,though they are universal components of routing protocols.Moreover,parallelization techniques were mostly deployed for random network topologies,and not for regular topologies that are often found in data centers.The aim of this paper is to improve scalability and reduce the time required for the shortest-path calculation in data center networks by parallelization on general-purpose hardware.We propose a novel algorithm that parallelizes edge relaxations as a faster and more scalable solution for popular data center topologies.

Development of an Efficient Genetic Algorithm for the Time Dependent Vehicle Routing Problem with Time Windows

This research considers the time-dependent vehicle routing problem (TDVRP). The time-dependent VRP does not assume constant speeds of the vehicles. The speeds of the vehicles vary during the various times of the day, based on the traffic conditions. During the periods of peak traffic hours, the vehicles travel at low speeds and during non-peak hours, the vehicles travel at higher speeds. A survey by TCI and IIM-C (2014) found that stoppage delay as percentage of journey time varied between five percent and 25 percent, and was very much dependent on the characteristics of routes. Costs of delay were also estimated and found not to affect margins by significant amounts. This study aims to overcome such problems arising out of traffic congestions that lead to unnecessary delays and hence, loss in customers and thereby valuable revenues to a company. This study suggests alternative routes to minimize travel times and travel distance, assuming a congestion in traffic situation. In this study, an efficient GA-based algorithm has been developed for the TDVRP, to minimize the total distance travelled, minimize the total number of vehicles utilized and also suggest alternative routes for congestion avoidance. This study will help to overcome and minimize the negative effects due to heavy traffic congestions and delays in customer service. The proposed algorithm has been shown to be superior to another existing algorithm in terms of the total distance travelled and also the number of vehicles utilized. Also the performance of the proposed algorithm is as good as the mathematical model for small size problems.

A GA approach to vehicle routing problem with time windows considering loading constraints

As a new variant of vehicle routing problem( VRP),a finished vehicle routing problem with time windows in finished vehicle logistics( FVRPTW) is modeled and solved. An optimization model for FVRPTW is presented with the objective of scheduling multiple transport routes considering loading constraints along with time penalty function to minimize the total cost. Then a genetic algorithm( GA) is developed. The specific encoding and genetic operators for FVRPTW are devised.Especially,in order to accelerate its convergence,an improved termination condition is given. Finally,a case study is used to evaluate the effectiveness of the proposed algorithm and a series of experiments are conducted over a set of finished vehicle routing problems. The results demonstrate that the proposed approach has superior performance and satisfies users in practice. Contributions of the study are the modeling and solving of a complex FVRPTW in logistics industry.