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sweep algorithm for Solving Discrete Optimal Control Problems with Three-point Boundary Conditions

JOURNAL OF AUTOMATION AND INFORMATION SCIENCES 2008年第7期40卷 48-58页

作者： Aliev, F. A. Zulfugarova, R. T. Mutallimov, M. M. Azerbaijan Acad Sci Baku Azerbaijan Baku State Univ Azerbaijan Res Inst Appl Math Baku Azerbaijan

The sweep algorithm for solving optimal control problem with three-point boundary conditions is offered. According to this algorithm the search for initial conditions is reduced to solution of the corresponding system... 详细信息

关键词： sweep algorithm three-point boundary conditions initial conditions system of linear algebraic equations

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sweep algorithm for solving optimal control problem with multi-point boundary conditions

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ADVANCES IN DIFFERENCE EQUATIONS 2015年第1期2015卷 1-13页

作者： Mutallimov, Mutallim Zulfugarova, Rena T. Amirova, Leyla I. Baku State Univ Inst Appl Math Baku Azerbaijan

The sweep algorithm for solving optimal control problem with multi-point boundary conditions is offered. According to this algorithm, the search of initial conditions is reduced to the solution of the corresponding sy... 详细信息

关键词： sweep algorithm multi-point boundary conditions initial conditions sbystem of linear algebraic equations

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Some extensions to the sweep algorithm

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2011年第9-12期56卷 1057-1067页

作者： Na, Byungsoo Jun, Yeowoon Kim, Byung-In Pohang Univ Sci & Technol POSTECH Dept Ind & Management Engn Pohang 790784 South Korea Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

The sweep algorithm has been widely used for the vehicle routing problem and its variants since it was published in 1971. It clusters a group of stops into a route according to the polar angle between the stops and the depot. In this paper, we point out the weakness of grouping stops solely by the polar angle in the sweep algorithm and propose some extensions to the algorithm. The sweep nearest algorithm and the usage of various reference points are proposed. The effectiveness of the extensions is demonstrated by computational results on the benchmark problems of the capacitated vehicle routing problem.

关键词： Vehicle routing Heuristics Logistics sweep algorithm

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Comments on 'sweep algorithm for solving optimal control problem with multi-point boundary conditions' by M Mutallimov, R Zulfuqarova, and L Amirova

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ADVANCES IN DIFFERENCE EQUATIONS 2016年第1期2016卷 1页

作者： Aliev, Fikret A. Baku State Univ Inst Appl Math Baku Azerbaijan

A counter example is given for the solution of the linear-quadratic optimization problem with three-point boundary conditions. The example shows that the solution obtained in (Mutallimov et al. in Adv. Differ. Equ. 20... 详细信息

关键词： sweep algorithm optimization three-point boundary conditions

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Optimal Distribution Route Planning based on Collaboration of Dijkstra and sweep algorithm 10

Optimal Distribution Route Planning based on Collaboration o...

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10th Annual International Conference on Information Technology and Electrical Engineering (ICITEE)

作者： Zulfiqar, La Ode Mohamad Isnanto, R. Rizal Nurhayati, Oky Dwi Univ Diponegoro Informat Syst Semarang Indonesia Univ Diponegoro Comp Engn Semarang Indonesia

ISBN: (纸本)9781538647394

More than half of company's logistic budget is spent for the transportation matter. Hence, applying the efficient way to distribute things is exactly needed for the transportation system in order to gain better profit. The combination of Dijkstra algorithm and sweep algorithm is a novel method that able to resolve optimal distribution route planning. As we gain from our research that by utilizing this method we achieve the reduction of both distance travel and trip's time. We are gaining better solution for 9.3% in distance travel and successful cutting time travel for 500% from the original trip's time.

关键词： route optimization distribution Dijkstra algorithm sweep algorithm

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A Hybrid Two-stage sweep algorithm for Capacitated Vehicle Routing Problem

A Hybrid Two-stage Sweep Algorithm for Capacitated Vehicle R...

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International Conference on Control, Automation and Robotics ICCAR

作者： Chen, Meng-Hui Chiu, Ching-Ying Chang, Pei-Chann Annadurai, Sivachandra Prabhu Yuan Ze Univ Dept Informat Management Taoyuan Taiwan

ISBN: (纸本)9781467375238

Capacitated Vehicle Routing Problem (CVRP) is a variant of Vehicle Routing Problem (VRP), where CVRP is only considered the capacity restrictions, and the object is to minimize the cost of the vehicles serve all customers. In this study, we proposed an approach which is hybrid two-phase sweep algorithm (SA) and greedy search for solving CVRP. At the first stage of SA, all customers are clustered by SA and define each cluster as a block. The second stage is to reconstruct each neighbour clusters based on the first stage. Then the greedy search is applied to minimize the cost of each vehicle. Finally, the computational result on standard instances show the proposed approach is effective.

关键词： capacitated vehicle routing problem sweep algorithm greedy search

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sweep algorithm and Mixed Integer Linear Program for Vehicle Routing Problem with Time Windows

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JOURNAL OF ADVANCED MANUFACTURING SYSTEMS 2018年第4期17卷 505-513页

作者： Savitri, H. Kurniawati, D. A. Univ Islam Negeri Sunan Kalijaga Fac Sci & Technol Ind Engn Dept Jalan Marsda Adisutjipto Yogyakarta 55281 Indonesia

CV. Jogja Transport is a company that distribute cakes "Sari Roti" in Yogyakarta, Indonesia. It has responsibility to distribute the cakes for every customer during the customers' time windows. The distribution problem of CV. Jogja Transport belongs to Vehicle Routing Problem with Time Window (VRPTW). This paper tries to solve the problem of CV. Jogja Transport by proposing "cluster first route second" algorithm of simple heuristic method. Then the algorithm is combined with sweep algorithm for clustering the customers and Mixed Integer Linear Programming (MILP) to select the best route so that it can minimize the distance of each cluster. The result indicate that implementation of sweep algorithm and MILP can reduce the distances and the fuel up to 10.95% and the travel distance up to 2.60%.

关键词： Optimization vehicle routing problem time windows sweep algorithm mixed integer linear programming cluster first route second distribution

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A sweep-HEURISTIC algorithm FOR CARBON EMISSIONS MODEL OF PICKING UP AND DELIVERING CUSTOMERS TO AIRPORT

A SWEEP-HEURISTIC ALGORITHM FOR CARBON EMISSIONS MODEL OF PI...

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17th International Conference of Hong-Kong-Society-for-Transportation-Studies (HKSTS)

作者： Yang, Peiying Yu, Yang Tang, Jiafu Liu, Bingxing Northeastern Univ Dept Syst Engn Coll Informat Sci & Engn Key Lab Integrated Automat Proc Ind Shenyang Peoples R China

ISBN: (纸本)9789881581419

Under the low carbon policy, how to reduce carbon emissions is a new significant objective in picking up and delivering customers to airport. The paper formulates the carbon emissions model of picking up and delivering customers to airport under the framework of Vehicle Allocation and Scheduling Problem. And then we propose a sweep-heuristic algorithm considering the partition of time and district to solve the carbon emissions model. We use five actual instances with the different satisfaction levels to illustrate application of the proposed algorithm. The useful conclusions and references for the airport shuttle service configuration and service degree setting are also obtained.

关键词： Vehicle Allocation and Scheduling Problem Picking up and Delivering Customers to Airport Service sweep algorithm Carbon emissions

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Distance based sweep Nearest algorithm to Solve Capacitated Vehicle Routing Problem

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INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS 2019年第10期10卷 259-264页

作者： Peya, Zahrul Jannat Akhand, M. A. H. Sultana, Tanzima Rahman, M. M. Hafizur Khulna Univ Engn & Technol Dept Comp Sci & Engn Khulna 9203 Bangladesh King Faisal Univ Coll Comp Sci & Informat Technol Dept Commun & Networks Al Hufuf Al Hasa Saudi Arabia

The Capacitated Vehicle Routing Problem (CVRP) is an optimization problem owing to find minimal travel distances to serve customers with homogeneous fleet of vehicles. Clustering customers and then assign individual vehicles is a widely-studied way, called cluster first and route second (CFRS) method, for solving CVRP. Cluster formation is important between two phases of CFRS for better CVRP solution. sweep (SW) clustering is the pioneer one in CFRS method which solely depends on customers' polar angle: sort the customers according to polar angle;and a cluster starts with customer having smallest polar angle and completes it considering others according to polar angle. On the other hand, sweep Nearest (SN) algorithm, an extension of sweep, also considers smallest polar angle customer to initialize a cluster but inserts other customer(s) based on the nearest neighbor approach. This study investigates a different way of clustering based on nearest neighbor approach. The proposed Distance based sweep Nearest (DSN) method starts clustering from the farthest customer point and continues for a cluster based on nearest neighbor concept. The proposed method does not rely on polar angle of the customers like SW and SN. To identify the effectiveness of the proposed approach, SW, SN and DSN have been implemented in this study for solving benchmark CVRPs. For route optimization of individual vehicles, Genetic algorithm, Ant Colony Optimization and Particle Swarm Optimization are considered for clusters formation with SW, SN and DSN. The experimental results identified that proposed DSN outperformed SN and SW in most of the cases and DSN with PSO was the best suited method for CVRP.

关键词： Capacitated vehicle routing problem sweep algorithm sweep nearest algorithm genetic algorithm ant colony optimization particle swarm optimization

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sweep algorithms for the Vehicle Routing Problem with TimeWindows 5th

Sweep Algorithms for the Vehicle Routing Problem with TimeWi...

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4th International Conference on Optimization and Learning (OLA)

作者： Armbrust, Philipp Maier, Kerstin Truden, Christian Univ Klagenfurt Dept Math A-9020 Klagenfurt Austria Lakeside Labs Gmbh A-9020 Klagenfurt Austria

ISBN: (纸本)9783031220388;9783031220395

Attended home delivery services like online grocery shopping services require the attendance of the customers during the delivery. Therefore, the Vehicle Routing Problem with TimeWindows occurs, which aims to find an optimal schedule for a fleet of vehicles to deliver goods to customers. In this work, we propose three sweep algorithms, which account for the family of cluster-first, route-second methods, to solve the Vehicle Routing Problem with Time Windows. In the first step, the customers are split into subsets such that each set contains as many as possible customers that can be served within one tour, e.g., supplied with one vehicle. The second step computes optimal tours for all assigned clusters. In our application, the time windows follow no special structure, and hence, may overlap or include each other. Further, time windows of different lengths occur. This gives additional freedom to the company during the planning process, and hence, allows to offer discounted delivery rates to customers who tolerate longer delivery time windows. Our sweep algorithms differ in the clustering step. We suggest a variant based on the standard sweep algorithm and two variants focusing on time window length and capacity of vehicles. In the routing step, a Mixed-Integer Linear Program is utilized to obtain the optimal solution for each cluster. The paper is concluded by a computational study that compares the performance of the three variants. It shows that our approach can handle 1000 customers within a reasonable amount of time.

关键词： Vehicle routing Time windows sweep algorithm Attended home delivery Transportation Logistics

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