Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure

THE CHARACTERISTICS STUDY OF SOLVING VARIANTS OF VEHICLE ROUTING PROBLEM AND ITS APPLICATION ON DISTRIBUTION PROBLEM

Vehicle Routing Problem (VRP) is one of the most challenging problems in combinatorial optimization. Objective of VRP is to find minimum length route starts and ends in a depot. There are some additional constraints such as more than one depot, service time, time window, capacity of vehicle, and many more. These are cause of VRP variants. Vehicle Routing Problem with Time Windows (VRPTW) is a variant of VRP with some additional constrains, that are number of requests may not exceed the vehicle capacity, as well as travel time and service time may not exceed the time window. Multi Depot Vehicle Routing Problem (MDVRP) has number of depots serving all customers, a number of vehicles distributing goods to customers with a minimum distance of distribution route without exceeding the capacity of the vehicle. Many researches have presented algorithms to solve VRPTW and MDVRP. This article discusses solution characteristics of VRPTW and MDVRP algorithms, and their performance. VRPTW algorithms reviewed are Tabu Search, Clarke and Wright, Nearest Insertion Heuristics, Harmony Search, Simulated Annealing, and Improved Ant Colony System algorithm. Performance of MDVRP algorithms studied are Self-developed Algorithm, Upper Bound, Clarke and Wright, Ant Colony Optimization, and Genetic Algorithm. Each algorithm is studied on its performance, process, advantages, and disadvantages. This article presents example of distribution problem in VRPTW and MDVRP, based on characteristic of the real problem. A computer program created using Delphi is implemented for VRPTW and MDVRP, to solve distribution problem for any number of vehicles and customer locations. Keywords: VRPTW, MDVRP, Distribution proble

Multi-Objective UAV Mission Planning Using Evolutionary Computation

This investigation purports to develop a new model for multiple autonomous aircraft mission routing. Previous research both related and unrelated to this endeavor have used classic combinatoric problems as models for Unmanned Aerial Vehicle (UAV) routing and mission planning. This document presents the concept of the Swarm Routing Problem (SRP) as a new combinatorics problem for use in modeling UAV swarm routing, developed as a variant of the Vehicle Routing Problem with Time Windows (VRPTW). The SRP removes the single vehicle per target restraint and changes the customer satisfaction requirement to one of vehicle on location volume. The impact of these alterations changes the vehicle definitions within the problem model from discrete units to cooperative members within a swarm. This represents a more realistic model for multi-agent routing as a real world mission plan would require the use of all airborne assets across multiple targets, without constraining a single vehicle to a single target. Solutions to the SRP problem model result in route assignments per vehicle that successfully track to all targets, on time, within distance constraints. A complexity analysis and multi-objective formulation of the VRPTW indicates the necessity of a stochastic solution approach leading to the development of a multi-objective evolutionary algorithm. This algorithm design is implemented using C++ and an evolutionary algorithm library called Open Beagle. Benchmark problems applied to the VRPTW show the usefulness of this solution approach. A full problem definition of the SRP as well as a multi-objective formulation parallels that of the VRPTW method. Benchmark problems for the VRPTW are modified in order to create SRP benchmarks. These solutions show the SRP solution is comparable or better than the same VRPTW solutions, while also representing a more realistic UAV swarm routing solution

Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs

Waste Collection Vehicle Routing Problem: Literature Review

Waste generation is an issue which has caused wide public concern in modern societies, not only for the quantitative rise of the amount of waste generated, but also for the increasing complexity of some products and components. Waste collection is a highly relevant activity in the reverse logistics system and how to collect waste in an efficient way is an area that needs to be improved. This paper analyzes the major contribution about Waste Collection Vehicle Routing Problem (WCVRP) in literature. Based on a classification of waste collection (residential, commercial and industrial), firstly the key findings for these three types of waste collection are presented. Therefore, according to the model (Node Routing Problems and Arc Routing problems) used to represent WCVRP, different methods and techniques are analyzed in this paper to solve WCVRP. This paper attempts to serve as a roadmap of research literature produced in the field of WCVRP

Dynamic vehicle routing with time windows in theory and practice

The vehicle routing problem is a classical combinatorial optimization problem. This work is about a variant of the vehicle routing problem with dynamically changing orders and time windows. In real-world applications often the demands change during operation time. New orders occur and others are canceled. In this case new schedules need to be generated on-the-fly. Online optimization algorithms for dynamical vehicle routing address this problem but so far they do not consider time windows. Moreover, to match the scenarios found in real-world problems adaptations of benchmarks are required. In this paper, a practical problem is modeled based on the procedure of daily routing of a delivery company. New orders by customers are introduced dynamically during the working day and need to be integrated into the schedule. A multiple ant colony algorithm combined with powerful local search procedures is proposed to solve the dynamic vehicle routing problem with time windows. The performance is tested on a new benchmark based on simulations of a working day. The problems are taken from Solomon’s benchmarks but a certain percentage of the orders are only revealed to the algorithm during operation time. Different versions of the MACS algorithm are tested and a high performing variant is identified. Finally, the algorithm is tested in situ: In a field study, the algorithm schedules a fleet of cars for a surveillance company. We compare the performance of the algorithm to that of the procedure used by the company and we summarize insights gained from the implementation of the real-world study. The results show that the multiple ant colony algorithm can get a much better solution on the academic benchmark problem and also can be integrated in a real-world environment

An Improved Whale Optimization Algorithm for Vehicle Routing Problem with Time Windows

The vehicle routing problem with time windows (VRPTW) is a pivotal problem in logistics operation management which attempts to establish routes for vehicles to deliver goods to customers. The objective of VRPTW is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers within time window constraints. As the VRPTW is known to be NP-hard combinatorial problem, it is hard to be solved in reasonable computational time. Therefore, this paper proposes the modification of the whale optimization algorithm with local search to solve the VRPTW. The local search comprised 2-Operator and single insertion for solution improvement. Furthermore, the 2-Operator is used after the exploration phase and single insertion in the exploitation phase. The computational experiments were applied to Solomon’s instance that included small to large size problems. The experiment results show that the average gap of the total distance between the Best Known Solution (BKS) and the proposed solutions is within 5.82%. In addition, the best solution was found 29 out of 56 instances that is better than the PSO at 1.09%. This shows that this proposed provides a minimum value and outperforms other metaheuristics approaches.Keywords: Whale Optimization Algorithm; Vehicle Routing Problem; Time Constraint