VRP相关知识整理

一、扩展问题分类：

★ the capacitated vehicle routing problem (CVRP) , 即classical VRP

★ the vehicle routing problem with time windows (VRPTW) , 带时间窗
    - VRPHTW 硬时间窗   ｜   VRPSTW 软时间窗   ｜   VRPTD（VRP with Time Deadlines）带顾客最迟服务时间

★ (VRPSD) the Vehicle Routing Problem with Split Deliveries，分割配送

- the Vehicle Routing Problem with Split Demands，需求分割 [二者实质相同]

★ the Multiple Depot Vehicle Routing Problem (MDVRP) , 多车场

★ the Period Vehicle Routing Problem (PVRP) , 周期车辆路径问题

★ the site-dependent vehicle routing problem (SDVRP) ，

★ the open vehicle routing problem (OVRP) ，开放式

★ the Vehicle Routing Problem with Backhauls（VRPB）, 带回程

★ the Vehicle Routing Problem with Pickup and Delivery（VRPPD）, 带取送货

- with Simultaneous Distribution and Collection

★ the Vehicle Routing Problem with Multiple Trips（VRPMT）, 多车程

★ the fleet size and mix vehicle-routing problem (FSMVRP) , 异型车辆

-  vehicle routing problem with heterogeneous fleet (VRPHE)  [貌似这两个是同一类型]

★ the Vehicle Routing Problem with Truck and Trailer（VRPTT）, 带拖车

★ vehicle routing problem with multiple uses of vehicles (VRPM) , 车辆复用

★ Stochastic VRP（SVRP） 随机车辆路径问题：

- 随机顾客   ｜   随机需求   ｜   随机时间

★ Fuzzy Vehicle Routing Problem（FVRP）, 模糊车辆路径问题

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二、算法分类：

★ exact algoritms :  direct tree search , 直接树搜索   |   dynamic programming , 动态规划   |   integer linear programming , 整数线性规划

★ Classical Heuristics :

Saving Heuristic , 节约算法 (Clarke & Wright)   Matching Algorithm
Sweep Algorithm , 扫描算法 (Gillet & Miller)
Two-phase Process , 两阶段算法 (Christofides Fisher Jaikumar)

① route construction heuristics ,  路径构造算法

- Savings Heuristic Parallel  |  Sequential  |  Enhancement

- Insertion Heuristic

② route improvement heuristics , 路径改进算法 Thompson & Psaraftis

- 2-change  |  3-change  |  1-Relocate  |  2-Relocate  |  Swap  |  GENI  |  b-cyclic k-transfer

③ composite heuristics （包括上面两类）

- Greedy Randomized Adaptive Search Procedure (GRASP) ,贪婪随机自适应搜索过程

Column Generation Algorithm
adaptive memory algorithms
Ejection Chain Algorithms

set covering based algorithms

Sequential Insertion Heuristic

• Hvattum, L.M., A. Løkketangen and G. Laporte. “A Branch-and-Prune heuristic for Stochastic and Dynamic Vehicle Routing Problems”.
• Hvattum, L.M., A. Løkketangen and G. Laporte. “Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario based Hedging Heuristic”. Forthcoming in Transportation Science.

★ Metaheuristics (Modern Heuristic) :

Simulated Annealing 模拟退火

Tabu Search 禁忌搜索

Genetic Algoritm 遗传算法    |    Genetic Programming 遗传规划
Genetic Network Programming 遗传网络规划

Memetic Algorithm : hybrid genetic algorithms are often referred as memetic algorithms.
Parallel Genetic Algorithms    |   Genetic Local Search

Ant Algorithms :    ACO
ACS, Ant Colony System 蚁群算法

PSO，Particle Swarm Optimization 粒子群优化算法

DE，Differential Evolution 差分进化算法
Evolutionary Programming 进化规划

★ Local Search : 属于启发式算法

variable neighborhood search (VNS) ,变邻域搜索 另：变邻域下降搜索(VND, Descent)
Evolutionary local search (ELS) ,进化局部搜索
Iterated Local Search (ILS) ,迭代局部搜索 
Iterative Improvement，迭代改进
Large Neighborhood Search (LNS) ,大邻域搜索    |    adaptive large neighborhood search (ALNS) 
Guided Local Search (GLS) ,引导局部搜索
Cyclic Transfer Algorithms

★ 邻域操作方法：
2-opt    |    2-opt*    |    Or-opt
The CROSS exchange

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三、obtained books：

图书章节：(in VRP->books\)
1. Carlos Cotta.Evolutionary Computation in Combinatorial Optimization.Springer.2007.pdf  
（P106）Accelerating Local Search in a Memetic Algorithm for the Capacitated Vehicle Routing Problem  
（P131） A New Metaheuristic for the Vehicle Routing Problem with Split Demands    
（P152） Edge Assembly Crossover for the Capacitated Vehicle Routing Problem   
（P176） A Population-Based Local Search for Solving a Bi-objective Vehicle Routing Problem

2. Christofides (ed.). Combinatorial optimization (Wiley, 1978)(L)(T)(212s).djvu

(P159)   The Vehicle Routing Problems

3. Springer.Combinatorial.Optimization.and.Applications.Second.International.Conference.COCOA.2008.Sep.2008.pdf

(P296) An Improved Approximation Algorithm for the Capacitated Multicast Tree Routing Problem

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四、resources on the Internet：

1. The VRP Web很详尽的网站

2. Solomon's benchmark 数据集：56个数据集R1、R2、C1、C2、RC1和RC2是VRPTW问题数值实验的经典数据集。
R1包含客户点随机分布的12个问题。C1有9个问题，其中的客户点聚类到确定的区域。RC1包含8个问题，它们的客户点混合了聚类和随机分布。

3. Network and Emerging Optimization

4. OR-Library of J. E. Beasley：各种优化问题的数据集。

5. J. E. Beasly 的 publications

Google Code上的项目：

1. vrp-uts-insa2008-5info （Solving the VRP problem with a unified tabu search in JAVA. That project is a last year study project at INSA Toulouse. ）

2. VRPSolver （a wizard-like application which solves a basic VRP using the Savings Heuristic Method invented by Clarke and Wright in 1964. ）

3. Swan-VRP

4. EVITA-VRP （Project to unify the EVITA(Evolutionary inventory and transportation algorithm) code for VRP book chapter. ）

5. vrpft （Vehicle Routing Problem with Full Truckloads. ）

程序员联合开发网上的程序：

1. 基于遗传算法的车辆路径优化的 C# 程序

2. 用C++编写的vrp问题的源码

3. 一个求解车辆路径问题的粒子群算法的源码，用C++编写

4. 蚁群算法解决车辆最优路径问题

5. PSO，通过迭代搜索更新产生更优良的下一代解