An Evolutionary Algorithm for Vehicle Routing Problem with Real Life Constraints

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

A parallel memetic algorithm for the NP-hard vehicle routing problem with time windows (VRPTW) is proposed. The algorithm consists of components which are executed as parallel processes. A process runs either a heuristic algorithm or a hybrid of a genetic algorithm and some local refinement procedures. In order to improve the results, processes co-operate periodically using a novel randomized scheme. During each phase of co-operation processes exploit their best solutions found so far. The purpose of the work is to devise the parallel memetic algorithm which determines the VRPTW solutions of the highest possible quality. The experiments on Gehring and Homberger's (GH) benchmarking tests show that the algorithm achieves very good results. By making use of it the best-known solutions to 171 out of 300 GH tests were improved.

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a real-world situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Pareto-optimal solution with the e-constraint method is obtained. Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.

The vehicle routing problem (VRP) is a crucial group of transportation problems, and traditional capacitated VRP (CVRP) directly handles external logistics with a homogeneous vehicle fleet. This paper examines the CVRP from an in-plant logistic view with a heterogeneous fleet in an automotive factory. The homogeneous and heterogeneous vehicle fleets are compared to address the factory's actual in-plant logistics issues. Firstly, simulated annealing (SA), tabu search (TS) algorithms and mathematical modeling were utilized. Then, a hybrid approach was proposed, and all suggested meta-heuristic algorithms were evaluated for homogeneous and heterogeneous vehicle fleets. According to the results, the reduction rates using CVRP with the heterogeneous fleet are 17% and 36% for fleet area and distribution costs, respectively. Also, to examine the effect of the hybrid algorithm parameters on the result, traveling distance was calculated for different scenarios, and multiple regression analyses were applied. According to the multiple regression analysis, the hybrid algorithm's most affected parameter was the cooling coefficient.

Vehicle Routing Problems (VRPs) are usually treated as static routing problem, since all the information is known before the routes been constructed. However, the real world VRPs are dynamic, where information relevant to the routing can change after the initial scheme has been done. This paper treats the dynamic VRPs with real time traffic information. We formulate the mathematic model of the VRPs, and propose a dynamic programming algorithm based on chaos optimization, whereas the route calculating module and dynamic programming module are introduced. Finally, the efficiency of the proposed algorithm is demonstrated by computer simulations.

In this paper, a useful variant of the vehicle routing problem, Vehicle Routing Problem with Time Windows and a limited number of vehicles (m-VRPTW) is given. The problem is to serve a number of customers at minimum cost by using a limited number of vehicles, without violating the time window constraint and the vehicle capacity constraint. The feasible solution of m-VRPTW may contain some unserved customers and third-party vehicles, such as taxies, are hired to serve these unserved customers. The mixed integer programming model of m-VRPTW is proposed and a two-phase algorithm based on insertion algorithm and tabu search algorithm is proposed to solve it. Experimental results show that our algorithm can yield effective and efficient solution and be capable of dealing with the m-VRPTW problems in real life conditions.

Public consciousness on environmental sustainability and industry impact on environment has been increasing for the last few decades. As a result, more and more companies are taking pollution factor into account when planning their logistic activities. Pollution Routing Problem (PRP) is an extension of the classical Vehicle Routing Problem with Time Windows by determining a set of optimal routes and vehicle speed on each route segment for a fleet of vehicles serving a set of customers within specific time windows. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs. Emission levels vary by vehicle type due to differences in curb weight and capacity. Therefore, Heterogeneous Fleet Pollution Routing Problem (HFPRP) has been proposed as an extension of Pollution Routing Problem (PRP). Its goal is to minimize the total costs of fuel, greenhouse gas (GHG) emissions, and vehicle variable cost put together in a more comprehensive objective function. This research developed a mathematical model and proposed a Simulated Annealing (SA) heuristic for HFPRP. The performance of the proposed SA heuristic was first verified using benchmark data of the Pollution Routing Problem. The result shows that SA performs better for 7 instances than previous method. SA was then used to solve HFPRP and the results were compared to those obtained by CPLEX. We found that the consideration of a heterogeneous fleet reduces total costs for all instances.

The heterogeneous fleet vehicle routing problem with light loads and overtime: Formulation and population variable neighbourhood search with adaptive memory

The Vehicle Routing Problem with Time Windows (VRPTW) consists of a homogenous set of vehicles and a set of customer located in a city. In VRPTW all the vehicles starts from the depot visit the customer and end at the depot. Each customer is visited exactly by one vehicle within the specified time window. The objective is to minimize the number of vehicles and total distance travelled simultaneously. This represents the multiobjective Vehicle Routing Problem with Time Windows. The proposed work consists of Hybrid Genetic Search with Diversity Control using the Genetic Algorithm for solving the VRPTW. The Pareto approach is used for finding the set of optimal solutions for achieving the multiobjective. The crossover operator is used for exchanging the best routes, which have shortest distance. Two mutation operators such as relocation mutation operator and split mutation operator were used in this application. In this, it accounts penalty for an infeasible solutions with respect to time-window and duration constrains. The computations are performed using the instances which are obtained from the VRPLIB.

Vehicle Routing Problem with Time Windows (VRPTW) is a constrained NP-hard problem that designs the least cost routes from one depot to a set of geographically scattered points. Most of traditional techniques are difficult to solve this kind of problem. In this paper, we explored the validity of another swarm-intelligence-based model-Bacterial Foraging Optimization (BFO) for VRPTW solving. Original BFO, BFO with linear decreasing chemotaxis step (BFO-LDC) and BFO with non-linear decreasing chemotaxis step (BFO-NDC) are used to obtain the best solutions of a given VRPTW problem, respectively. The experimental results demonstrated that the proposed BFO algorithms have the potential to solve Vehicle Routing Problem with Time Windows (VRPTW) with rapid convergence rate and the good result accuracy.

The growth in e-commerce sales has been constant and, driven by the Covid-19 pandemic, has exceeded previous expectations. Owing to social isolation, parcel lockers - systems for goods collection - have become widely used to reduce physical contact between people involved in the delivery process. This resource has also become an important strategy for reducing costs, as it enables deliveries from multiple customers to be consolidated in the same location. In the context of smart cities, in which the optimization of urban transport plays a key role in building more sustainable and efficient environments, the inclusion of parcel lockers is essential. Thus, research in this area that considers their use aligns with the concept of smart cities, promoting the use of innovative technologies to improve mobility and urban logistics. Specifically in this context, the Vehicle Routing Problem With Parcel Lockers (VRPPL) is an extension of the Vehicle Routing Problem with TimeWindows (VRPTW), introducing the use of lockers, with the objective to reduce the total distance traveled. In this study, an algorithm based on Iterated Greedy (IG) and Random Variable Neighborhood Descent (RVND) was developed to reduce the costs and computational times presented in the literature. We selected a set of 168 well-known instances for the problem. Computational experiments and comparative analyses were performed. The developed algorithm achieved better results in 167 instances, with an average gap of −1.315%. The best execution times were obtained for all instances, thereby reducing the mean execution time from 240.293s to 0.104s.

This paper investigates a well-known complex combinatorial problem known as the vehicle routing problem with time windows (VRPTW). Unlike the standard vehicle routing problem, each customer in the VRPTW is served within a given time constraint. This paper solves the VRPTW using an improved artificial bee colony (IABC) algorithm. The performance of this algorithm is improved by a local optimization based on a crossover operation and a scanning strategy. Finally, the effectiveness of the IABC is evaluated on some well-known benchmarks. The results demonstrate the power of IABC algorithm in solving the VRPTW.

Vehicle routing problem is a typical NP hard problem in combinatorial optimization. This paper proposes an improved algorithm, namely Immune Ant Colony Algorithm to solve the problem of vehicle routing problem. The algorithm is based on the intelligent optimization idea- Ant Colony Algorithm and Artificial Immune Algorithm. In this paper, in order to solve the problem of vehicle routing problem effectively four aspects are modified to improve the basic ant colony algorithm. And the improved Artificial Immune Algorithm is used to solve the problem of Ant Colony Algorithm to be apt to plunge into as the local optimum solution. On the basis of these improvements, the framework of the new algorithm—Immune Ant Colony Algorithm is given. Finally, it was proved that Immune Colony Algorithm can quicken the convergence rate to obtain optimal solution and decrease computing time. In addition, the computing simulation examples show its validity.

This paper addresses the issue of ship routing design for collecting and transporting the oily liquid waste from a number of ports to a waste treatment center. The aim is simultaneously to construct a set of ship routes and to determine the number and the types of ships in a fleet at the minimum total cost. The problem is considered as a vehicle routing problem with heterogeneous fleet of vehicles and multiple trips (VRPHMT). The VRPHMT is a combination of two variants of the classical vehicle routing problem (VRP) by including two additional features. The first is the heterogeneous fleet of vehicles where number and types of vehicles have to be determined, and the second is multiple trips where vehicles may perform more than one route or trip as long as the total duration of each vehicles does not exceed the planning period.

Path optimization is a critical issue in vehicle routing problems (VRPs). This study tends to solve a VRP with time windows (VRPTW), which is an important version of VRP. Its principal objective is to find out the minimum cost routes to serve the customers within service time intervals, by a fleet of vehicles having confined capacity. An improved ant colony optimization (ACO) is applied to the problem, which uses a new pheromone reset and update function to enhance the route searching and a 2-opt method to improve the optimized path. The proposed ACO is tested on standard benchmarks of VRPTW. The results verifies the effectiveness of the algorithm and confirms it as better path optimizing method for VRPTW, in comparison to the traditional ACO and other heuristics.