Solving vehicle routing problem by using improved K-nearest neighbor algorithm for best solution

Vehicle routing problem (VRP) is one of the many difficult issues that have no perfect solutions yet. Many researchers over the last few decades have established numerous researches and used many methods with different techniques to handle it. But, for all research, finding the lowest cost is very complex. However, they have managed to come up with approximate solutions that differ in efficiencies depending on the search space. Problem: In this study the problem is as follows: have a number of vehicles which are used for transporting applications to instance place. Each vehicle starts from a main location at different times every day. The vehicle picks up applications from start locations to the instance place in many different routes and return back to the start location in at specific times every day, starting from early morning until the end of official working hours, on the following conditions: (1) Every location will be visited once in each route, and (2) The capacity of each vehicle is enough for all applications included in each route. Objectives: Our paper attempt to find an optimal route result for VRP by using K-Nearest Neighbor Algorithm (KNNA). To achieve an optimal solution for VRP with the accompanying targets: (1) To reduce the distance and the time for all paths this leads to speedy the transportation of customers to their locations, (2) To implement the capacitated vehicle routing problem (CVRP) model for optimizing the solutions. Approach: The approach has been presented based on two phases: firstly, the algorithms have been adapted to solve the research problem, where its procedure is different than the common algorithm. The structure of the algorithm is designed so that the program does not require a large database to store the population, which speeds up the implementation of the program execution to obtain the solution; secondly, the algorithm has proven its success in solving the problem and finds a shortest route. For the purpose of testing the algorithm’s capability and reliability, it was applied to solve the same problem online validated and it achieved success in finding a shorter route. Finding: The findings outcome from this study have shown that: (1) A universal listed of dynamic KNNACVRP; (2) Identified and built up an assessment measure for KNNACVRP; (3) Highlight the strategies, based KNNA operations, for choosing the most ideal way (4) KNNA finds a shorter route for VRP paths. The extent of lessening the distance for each route is generally short, but the savings in the distance becomes more noteworthy while figuring the aggregate distances traveled by all transports day by day or month to month. This applies likewise to the time calculate that has been decreased marginally in view of the rate of reduction in the distances of the paths

Comparison of Randomized Solutions for Constrained Vehicle Routing Problem

In this short paper, we study the capacity-constrained vehicle routing problem (CVRP) and its solution by randomized Monte Carlo methods. For solving CVRP we use some pseudorandom number generators commonly used in practice. We use linear, multiple-recursive, inversive, and explicit inversive congruential generators and obtain random numbers from each to provide a route for CVRP. Then we compare the performance of pseudorandom number generators with respect to the total time the random route takes. We also constructed an open-source library github.com/iedmrc/binary-cws-mcs on solving CVRP by Monte-Carlo based heuristic methods.Comment: 6 pages, 2nd International Conference on Electrical, Communication and Computer Engineering (ICECCE), 12-13 June 2020, Istanbul, Turke

Ant colony optimization and its application to the vehicle routing problem with pickups and deliveries

Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickup and Delivery (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of ACO approach and presents several implementations to various combinatorial optimization problems. Next, VRPPD is described and the related literature is reviewed, Then, an ACO approach for VRPPD is discussed. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature

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

A GRASP Algorithm Based on New Randomized Heuristic for Vehicle Routing Problem

This paper presents a novel GRASP algorithm based on a new randomized heuristic for solving the capacitated vehicle routing problem, which characterized by using a fleet of homogenous vehicle capacity that will start from one depot, to serve a number of customers with demands that are less than the vehicle capacity. The proposed method is based on a new constructive heuristic and a simulated annealing procedure as an improvement phase. The new constructive heuristic uses four steps to generate feasible initial solutions, and the simulated annealing enhances these solutions found to reach the optimal one. We tested our algorithm on two sets of benchmark instances and the obtained results are very encouraging

On a Vehicle Routing Problem with Customer Costs and Multi Depots

The Vehicle Routing Problem with Customer Costs (short VRPCC) was developed for railway maintenance scheduling. In detail, corrective maintenance jobs for unexpected occurring failures are planned to a short time horizon. These jobs are geographically distributed in the railway net. Furthermore, dependent on the severity of the failure, it can be necessary to reduce the top speed on the track section in order to avoid safety risks or a too fast deterioration. For fatal failures, it can even be necessary to close the track section. The resulting limitations on railway service lead to penalty costs for the maintenance operator. These must be paid until the track is repaired and the restrictions are removed. By scheduling the maintenance tasks, these penalty costs can be reduced by proceeding corresponding maintenance tasks earlier. However, this may in return lead to increased costs for moving the maintenance machines and crews. For this scheduling problem, the VRPCC was developed. With it, for each maintenance vehicle and crew, a route is defined that describes the order to proceed maintenance tasks. Two kinds of costs are considered: Firstly, travel costs for machinery and crew; and secondly, penalty costs for an unsafe track condition that have to be paid for each day from failure detection to maintenance completion. To model the penalties, the novel customer costs are defined. In detail, for each maintenance activity a customer cost coefficient is given which incur for each day between failure detection and failure repair. The objective function of this problem is defined by the sum of travel costs and time-dependent customer costs. With it, the priority of customers can be taken into account without losing the sight on travel costs. This new vehicle routing problem was introduced in this thesis by a non-linear partition and permutation model. In this model, a feasible solution is defined by a partition of the job set into subsets that represent the allocation of jobs to vehicles and a permutation for each subset that represent the order of processing the jobs. Then, the start times of the jobs were calculated based on the order given by the permutations. It was taken into account that work can only be done in eight hour shifts during the night. Based on the start times, the customer cost value of each job is computed which equals to the paid penalty costs. Then, the costs of a schedule are calculated via the sum of travel costs and customer costs. To solve the VRPCC by a commercial linear programming solver, different formulations of the VRPCC as mixed-integer linear program were developed. In doing so, the start times became decision variables. It turned out that including customer costs led to problems harder to solve than vehicle routing problems where only travel costs are minimized. Further, in the thesis several construction heuristics for the VRPCC were designed and investigated. Also two local search algorithms, first and best improvement, were applied. The computational experiments showed that the solutions generated by the local search algorithm were much better than the solutions of the construction heuristics. The main part of this thesis was to design a Branch-and-Bound algorithm for the VRPCC. For this purpose, new lower bounds for the customer cost part of the objective function were formulated. The computational experiments showed that a lower bound computed from the LP relaxation of a specific bin packing problem had the best trade-off between computational effort and bound quality. For the travel cost part of the objective function, several known lower bounds from the TSP were compared. To design a Branch-and-Bound algorithm, beside efficient lower bound, also suitable branching strategies are necessary to split the problem space into smaller subspaces. In this thesis two branching strategies were developed which are based on the non-linear partition and permutation model to take advantage from the problem structure. To be more precise, new branches are generated by appending or including a job to an uncompleted schedule. Consequently, the start times can be computed directly from the so far planned jobs and more tight lower bounds can be computed for the so far unplanned jobs. By means of computational experiments, the developed Branch-and-Bound algorithms were compared with the classical approach, which means solving a mixed-integer linear program of the VRPCC by a commercial solver. The results showed that both Branch-and-Bound algorithms solved the small instances faster than the classical approach

The Multi-Depot Minimum Latency Problem with Inter-Depot Routes

The Minimum Latency Problem (MLP) is a class of routing problems that seeks to minimize the wait times (latencies) of a set of customers in a system. Similar to its counterparts in the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), the MLP is NP-hard. Unlike these other problem classes, however, the MLP is customer-oriented and thus has impactful potential for better serving customers in settings where they are the highest priority. While the VRP is very widely researched and applied to many industry settings to reduce travel times and costs for service-providers, the MLP is a more recent problem and does not have nearly the body of literature supporting it as found in the VRP. However, it is gaining significant attention recently because of its application to such areas as disaster relief logistics, which are a growing problem area in a global context and have potential for meaningful improvements that translate into reduced suffering and saved lives. An effective combination of MLP\u27s and route minimizing objectives can help relief agencies provide aid efficiently and within a manageable cost. To further the body of literature on the MLP and its applications to such settings, a new variant is introduced here called the Multi-Depot Minimum Latency Problem with Inter-Depot Routes (MDMLPI). This problem seeks to minimize the cumulative arrival times at all customers in a system being serviced by multiple vehicles and depots. Vehicles depart from one central depot and have the option of refilling their supply at a number of intermediate depots. While the equivalent problem has been studied using a VRP objective function, this is a new variant of the MLP. As such, a mathematical model is introduced along with several heuristics to provide the first solution approaches to solving it. Two objectives are considered in this work: minimizing latency, or arrival times at each customer, and minimizing weighted latency, which is the product of customer need and arrival time at that customer. The case of weighted latency carries additional significance as it may correspond to a larger number of customers at one location, thus adding emphasis to the speed with which they are serviced. Additionally, a discussion on fairness and application to disaster relief settings is maintained throughout. To reflect this, standard deviation among latencies is also evaluated as a measure of fairness in each of the solution approaches. Two heuristic approaches, as well as a second-phase adjustment to be applied to each, are introduced. The first is based on an auction policy in which customers bid to be the next stop on a vehicle\u27s tour. The second uses a procedure, referred to as an insertion technique, in which customers are inserted one-by-one into a partial routing solution such that each addition minimizes the (weighted) latency impact of that single customer. The second-phase modification takes the initial solutions achieved in the first two heuristics and considers the (weighted) latency impact of repositioning nodes one at a time. This is implemented to remove potential inefficient routing placements from the original solutions that can have compounding effects for all ensuing stops on the tour. Each of these is implemented on ten test instances. A nearest neighbor (greedy) policy and previous solutions to these instances with a VRP objective function are used as benchmarks. Both heuristics perform well in comparison to these benchmarks. Neither heuristic appears to perform clearly better than the other, although the auction policy achieves slightly better averages for the performance measures. When applying the second-phase adjustment, improvements are achieved and lead to even greater reductions in latency and standard deviation for both objectives. The value of these latency reductions is thoroughly demonstrated and a call for further research regarding customer-oriented objectives and evaluation of fairness in routing solutions is discussed. Finally, upon conclusion of the results presented in this work, several promising areas for future work and existing gaps in the literature are highlighted. As the body of literature surrounding the MLP is small yet growing, these areas constitute strong directions with important relevance to Operations Research, Humanitarian Logistics, Production Systems, and more