WO2023245740A1 - 一种基于蚁群算法的第四方物流运输路径规划方法 - Google Patents
一种基于蚁群算法的第四方物流运输路径规划方法 Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
Definitions
- the invention relates to the field of fourth-party logistics transportation optimization, in particular to a fourth-party logistics transportation path planning method based on ant colony algorithm.
- the advantages of 4PL are obvious and have received widespread attention in the logistics field at home and abroad.
- the business process of 4PL can be divided into three different stages: customer entrustment, transportation and delivery.
- the transportation stage is the top priority.
- 4PL needs to design the transportation route, select the appropriate 3PL agent, and find a solution within a certain cost constraint budget and within the time expected by the customer. Therefore, the path and logistics time optimization problem is extremely important for 4PL.
- it requires additional comprehensive consideration of the supplier's transportation capacity, transportation cost and other factors. This makes the 4PL path problem larger and more difficult to solve. high. Therefore, the research on fourth-party logistics optimization has strong academic value and practical significance.
- Lu Fuqiang, Ren Liang and others used genetic algorithms and ant colony algorithms to solve 4PL optimization problems at the 13th International Conference on Automation Science and Engineering and the 26th China Control and Decision-making Conference respectively.
- the former algorithm is not effective when facing more complex models, and the latter algorithm has higher time complexity, which will consume more time to solve the problem.
- a fourth-party logistics transportation path planning method based on ant colony algorithm includes:
- the directed adjacency list gList includes N city nodes. Each two directed adjacency city nodes are connected by G transportation paths. Each transportation path represents the use of A corresponding transportation agent performs logistics transportation between two city nodes;
- the initialized ant individual k is located at the starting city node in the directed adjacency list gList.
- the pheromone ⁇ and Under the guidance of the heuristic information ⁇ the target transportation path is determined from the accessible paths of the current city node, and moves along the target transportation path to the next directed adjacent city node until individual ant k moves to the end city node.
- the pheromones on all transportation paths are globally updated, and the next round of iteration is performed until the iteration termination condition is reached, and the distance from the starting city node to the ending city node is obtained.
- the accessible path of any ant individual k at any city node i includes all transportation paths between city node i and all accessible city nodes except the transportation paths in the path taboo table edgeTabooList.
- Ant individual k is at the city node
- the accessible city node at i includes all city nodes in all directed adjacent city nodes of city node i except the city nodes in the node taboo list nodeTabooList;
- the node taboo list nodeTabooList of ant individual k at city node i contains
- the path taboo list edgeTabooList of ant individual k at city node i contains transportation paths that are connected to city node i and do not meet the carrying capacity constraints.
- the further technical solution is to initialize the transportation path between city node i and city node j corresponding to transportation agent g.
- the pheromone on C td is the transport path through Freud's algorithm Corresponding unit transportation time and the path length constructed by the transportation distance d ij between city node i and city node j; where, the transportation path Corresponding unit transportation time Indicates the transportation time required per unit transportation distance and per unit transportation volume when transportation agent g performs logistics transportation between city node i and city node j.
- the transportation path between city node i and city node j corresponds to the transportation agent g
- Heuristic information that is inversely proportional to transportation costs in is the transportation speed of transportation agent g
- d ij is the transportation path the transportation distance
- the further technical solution is that when individual ant k is located at city node i, for any directed adjacent city node j of city node i, if according to the transportation distance d ij between city node i and city node j and The minimum transportation cost c ij_min determines that the minimum transportation cost between city node i and city node j exceeds the rated maximum transportation cost C, then it is determined that city node j does not meet the transportation cost constraints and is included in the ant individual k in city node i In the node taboo list nodeTabooList;
- the minimum transportation cost c ij_min between city node i and city node j is the transportation cost per unit transportation distance and per unit carrying volume required by all transportation agents when performing logistics transportation between city node i and city node j. the minimum value.
- Its further technical solution is to determine the target transportation path from the accessible paths of the current city node, including:
- Indicates transportation path pheromones on Indicates transportation path heuristic information on,transportation paths Represents the transportation path between city node i and city node j corresponding to transportation agent g, ⁇ , ⁇ , q 0 are parameters, Indicates transportation path Contained in the set J k (i) composed of the accessible paths of ant individual k at city node i.
- t represents any transportation path in the set J k (i) of the accessible paths of individual ant k at city node i
- ⁇ t is the pheromone on transportation path t
- eta t represents the pheromone on transportation path t.
- the method also includes:
- the ant individual k does not have an accessible path at the current city node, and the city node where the ant individual k is currently located is not the end city node, then the ant individual k is controlled to return to the previous city node along the backtracking path, and the backtracking path is the ant individual k determines the target transportation path at the previous city node; adds the backtracking path to the path taboo list edgeTabooList of ant individual k at the previous city node and updates the accessible path of ant individual k at the previous city node accordingly. Redetermine the target transportation path of individual ant k at the previous city node.
- the transportation path between city node i and city node j corresponds to the transportation agent g
- the pheromone on is updated to ⁇ is a parameter, Indicates that the best ant individual so far is on the transportation path Pheromones released on the transport path included in the best transportation route to date, then If the transportation route If it is not included in the optimal transportation route so far, then
- speed best is the total transportation time of the best transportation path so far
- distance best is the total distance of the best transportation path so far
- cost best is the total cost of the best transportation path so far
- R k is the best transportation path so far.
- This application discloses a fourth-party logistics transportation path planning method based on the ant colony algorithm.
- This method uses the adjacency list method of a directed graph to save the information of the fourth-party logistics transportation network, and proposes a scenario-based coding method based on Based on the problem characteristics, heuristic information and pheromone calculation methods are designed to improve the quality of the solution from different angles.
- the ant colony algorithm can be used to obtain the transportation path under transportation cost constraints and carrying capacity constraints to achieve the shortest total transportation time for the entire logistics operation.
- the goal is to have lower solution difficulty and higher solution quality, which can take into account both solution quality and solution speed, and the path planning efficiency is higher.
- the node taboo table and the path taboo table are used to reduce the probability of infeasible solutions.
- the path backtracking method is used instead of initializing a new solution to repair the infeasible path.
- the ant colony algorithm is more efficient.
- Figure 1 is a schematic flowchart of a fourth-party logistics transportation path planning method in an embodiment.
- Figure 2 is a schematic diagram of a fourth-party logistics transportation network in an example.
- Figure 3 is a schematic flowchart of a fourth-party logistics transportation path planning method in another embodiment.
- Figure 4 is an algorithm convergence diagram between the method of this application and the other two algorithms in an experimental comparison example.
- This application discloses a fourth-party logistics transportation path planning method based on the ant colony algorithm. Please refer to the flow chart shown in Figure 1. The method includes the following steps:
- Step 1 Construct the directed adjacency list gList of the fourth-party logistics transportation network.
- This application uses a directed graph adjacency list to save the information of the fourth-party logistics transportation network.
- the directed adjacency list gList includes N city nodes, and each two directed adjacent city nodes are connected through G transportation paths. Each transportation route represents the use of a corresponding transportation agent for logistics transportation between two city nodes.
- Figure 2 shows a schematic diagram of a fourth-party logistics transportation network in an example.
- the corresponding directed adjacency list includes 7 city nodes, which respectively represent circles with values 1 to 7 in Figure 2.
- Each two Directly adjacent city nodes are connected by two transportation paths.
- city node 1 and city node 2 are connected by transportation path a 1,2 and transportation path b 1,2, and city node 1 and city node 4 are connected by transportation path a 1,2 and transportation path b 1,2 .
- the transport path a 1,4 is connected to the transport path b 1,4 , and so on.
- Figure 2 uses different subscripts to represent the transportation paths between different city nodes.
- Transportation path a between any two city nodes corresponds to transportation agent A
- transportation path b corresponds to transportation agent B.
- the transportation path a 1,2 between 2 means that transportation agent A is used to carry out logistics transportation between city node 1 and city node 2, and other meanings are similar.
- this application takes the transportation between two adjacent city nodes through the same number and the same type of transportation agents as an example. In the actual application process, if the number and type are different, the application can also be used. method.
- constraints of this model include transportation cost constraints and carrying capacity constraints, which are written as:
- d ij represents the transportation distance between city node i and city node j
- Q is the total load to be delivered of goods that need to be transported from the starting city node to the ending city node
- C is the rated maximum transportation cost that the user can bear.
- Q g is the maximum carrying capacity of transportation agent g.
- This application is based on the ant colony algorithm, combined with the information of the fourth-party logistics transportation network recorded in the directed adjacency list gList, and can solve the target model under the above constraints, thereby selecting the transportation path with the optimal transportation time.
- the specific method is as follows :
- Step 2 initialize the pheromones on all transport paths.
- C td is the transport path through Freud's algorithm Corresponding unit transportation time and the path length constructed by the transportation distance d ij between city node i and city node j.
- transport path Corresponding unit transportation time Indicates the transportation time required per unit transportation distance and per unit transportation volume when transportation agent g performs logistics transportation between city node i and city node j.
- Step 3 In each round of iteration, for any ant individual k, the initialized ant individual k is located at the starting city node in the directed adjacency list gList.
- the starting city node and the ending city node are both one of the directed adjacency list gList.
- City nodes are known city nodes.
- the target transportation path is determined from the accessible path of the city node where the ant individual k is currently located, and moves along the target transportation path to the next directed Adjacent city nodes, until the ant individual k moves to the end city node, the solution is completed.
- the pheromone ⁇ and the heuristic information eta are both related to the transportation distance, transportation speed and corresponding cost required by the transportation path, and the heuristic information eta is inversely proportional to the transportation cost required by the transportation path.
- transportation route Heuristic information that is inversely proportional to transportation costs is the transportation speed of transportation agent g, d ij is the transportation path the transportation distance, is the total cost of transportation agent g’s logistics transportation between city node i and city node j.
- the accessible path of any ant individual k at any city node i includes all transportation paths between city node i and all accessible city nodes except the transportation paths in the path taboo table edgeTabooList.
- the accessible city nodes of ant individual k at city node i include all city nodes in all directed adjacent city nodes of city node i except the city nodes in the node taboo table nodeTabooList. That is, the accessible path of ant individual k at city node i is the remaining transportation path after excluding the city nodes in nodeTabooList and the transportation paths in edgeTabooList among all transportation paths connected to city node i.
- the node taboo list nodeTabooList of ant individual k at city node i contains city nodes that are directed adjacent to city node i and do not meet the transportation cost constraints. Specifically: when individual ant k is located at city node i, for any directed adjacent city node j of city node i, if based on the transportation distance d ij between city node i and city node j and the minimum transportation cost c The minimum transportation cost determined by ij_min between city node i and city node j exceeds the rated maximum transportation cost C.
- city node j does not satisfy the transportation cost constraint and is included in the node taboo list nodeTabooList of ant individual k at city node i.
- the minimum transportation cost c ij_min between city node i and city node j is the minimum transportation cost per unit transportation distance and per unit carrying volume required by all transportation agents when performing logistics transportation between city node i and city node j. value, then when d ij ⁇ c ij_min ⁇ Q>C, it is determined that city node j does not meet the transportation cost constraints.
- the path taboo list edgeTabooList of individual ant k at city node i contains transportation paths that are connected to city node i and do not satisfy the carrying capacity constraints. Specifically: when individual ant k is located at city node i, for any transportation path between city node i and any directed adjacent city node j, if the maximum carrying capacity of the transportation agent corresponding to the transportation path is less than to be If the total delivery capacity Q is determined, it is determined that the transportation path does not meet the carrying capacity constraints and is included in the path taboo list edgeTabooList of the ant individual k at the city node i.
- the node taboo list nodeTabooList and the path taboo list edgeTabooList are determined according to the above method, and then the corresponding accessible path is determined. Please refer to the flow chart shown in Figure 3, and then Select a target transportation path to move to the next city node. Methods for determining the target transportation path include:
- the target transportation path is selected from the accessible paths through the roulette method.
- the transportation path with the highest corresponding probability among the accessible paths is selected as the target transportation path.
- t represents any transportation path in the set J k (i) of the accessible paths of individual ant k at city node i
- ⁇ t is the pheromone on transportation path t
- eta t represents the pheromone on transportation path t.
- edgeTabooList Add the backtracking path to the path taboo list edgeTabooList of ant individual k at the previous city node and update the accessible path of ant individual k at the previous city node accordingly, and re-determine the target transportation of ant individual k at the previous city node. path, and then move from the previous city node to the redetermined city node.
- Part of the function of edgeTabooList is to ensure that individual ants can avoid paths that do not meet the maximum transportation volume constraints that the transporter can bear, thereby improving the efficiency of the algorithm.
- the other part of the function is to record failed path information.
- Step 4 After all m individual ants have completed the construction of the solution and completed one iteration, globally update the pheromones on all transportation paths, and perform the next round of iteration until the iteration termination condition is reached, and obtain the path from the starting city node to the ending point.
- the transportation path between city node i and city node j corresponds to the transportation agent g.
- the pheromone on is updated to ⁇ is a parameter, Indicates that the best ant individual so far is on the transportation path Pheromones released on the transport path included in the best transportation route to date, then If the transportation route If it is not included in the optimal transportation route so far, then That is, the global pheromone is updated only on the edge of the best path so far.
- the best ant individual so far is on the transportation path
- the pheromones released are:
- speed best is the total transportation time of the best transportation path so far
- distance best is the total distance of the best transportation path so far
- cost best is the total cost of the best transportation path so far
- R k is the best transportation path so far.
- Algorithm 1 is used as the method provided by this application (IACO).
- Algorithm 2 is the fuzzy particle swarm optimization algorithm (CFPSO) that introduces the convergence factor and membership function in the article "Fuzzy Particle Swarm Optimization Algorithm for Fourth-Party Logistics Transportation Time Optimization” published in the Journal of Intelligent Systems in 2021.
- Algorithm 3 is the classic genetic algorithm (GA).
- Agent 1 The distance between city nodes in Calculation Example 1 is shown in the table below, and the transportation agents between each two adjacent city nodes are Agent 1 and Agent 2 respectively.
- the transportation cost of Agent 1 is 0.16RMB/ton, transportation speed is 80km/h.
- Agent 2's transportation cost is 0.08RMB/ton and the transportation speed is 40km/h.
- Agent 1 The distance between city nodes in Calculation Example 2 is shown in the table below, and the transportation agents between each two adjacent city nodes are Agent 1, Agent 2 and Agent 3 respectively.
- Agent 1 The transportation cost is 0.16RMB/ton and the transportation speed is 80km/h.
- Agent 2's transportation cost is 0.08RMB/ton and the transportation speed is 40km/h.
- Agent 3's transportation cost is 1.5RMB/ton and the transportation speed is 750km/h.
- Agent 1 The transportation cost is 0.16RMB/ton and the transportation speed is 80km/h.
- Agent 2's transportation cost is 0.08RMB/ton and the transportation speed is 40km/h.
- Agent 3's transportation cost is 1.5RMB/ton and the transportation speed is 750km/h.
- the transportation networks of the above three examples have 6, 12 and 18 city nodes respectively.
- the starting point city node and the end city node in each example are the first city node and the last city node in the example respectively.
- the parameters of Algorithms 1, 2, and 3 are set through the control variable method. The specific parameters are as follows.
- w 1 , w 2 , and w 3 are all penalty term coefficients. Since IACO adopts a repair strategy, the solutions in the population are all feasible solutions.
- the three algorithms are all deployed in the same experimental environment, and different problem sizes and cost constraints are run as an independent problem twenty times. The experimental results of the three algorithms are compared as follows:
- the iteration number of the three algorithms is set to 500 generations.
- the algorithm convergence diagram is shown in Figure 4. 4 It can be seen that the three algorithms can converge well with iteration.
- the method of this application converges faster than other comparison algorithms and the curve converges smoothly, indicating that it has strong algorithm convergence ability and stability.
- the curve of the method of this application is below the curve of other algorithms, indicating that the quality of its solution is more stable than other algorithms.
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Abstract
一种基于蚁群算法的第四方物流运输路径规划方法，涉及第四方物流运输优化领域，该方法采用有向图的邻接表方式保存第四方物流运输网络的信息，并提出一种情景式编码方法，基于问题特征设计了启发式信息和信息素的计算方式，并结合节点禁忌表和路径禁忌表来确定可访问路径，利用蚁群算法可以在运输成分约束和运载量约束下得到运输路径，以实现物流作业整体的总运输时间最短的目标，求解难度较低且解的质量较高。
Description
本发明涉及第四方物流运输优化领域，尤其是一种基于蚁群算法的第四方物流运输路径规划方法。
随着信息技术的发展，物流体系逐渐完善，人们享受着足不出户便利购物体验。在这种大背景下，各类商家为了进一步降低成本提高效率，将物流业务转交给第三方物流(third party logistics，简称3PL)公司。但由于物流市场的不断拓展和疫情冲击下电商平台订单膨胀式的增加，3PL逐渐展现出在服务种类、资源协调、信息化程度等方面的短缺。第四方物流(fourth party logistics，简称4PL)为了弥补这些不足应运而生，它开创一种崭新的物流模式，通过整合3PL的物流资源，使用新的信息技术来构建一套完整的供应链解决方案。4PL在商家和第三方物流公司之间起到了至关重要的作用，对于商家可以专注与自身的核心业务，第三方物流公司则可以进一步提升物流效率。
4PL的优势是显而易见的，得到了国内外物流领域的广泛关注。4PL的业务流程可分为三个不同的阶段：客户委托、运输、交付。其中运输阶段是重中之重，4PL需要在接到委托任务后，设计运输路线，选择合适的3PL代理商，在一定的成本约束预算下和客户期望时间内找到解决方案。所以路径与物流时间优化问题对于4PL而言是极为重要的，相比于传统的3PL需要额外综合考量供应商的运输能力、运输成本等因素，这使得4PL路径问题求解空间更大，求解难度更高。所以对第四方物流优化的研究具有很强的学术价值和现实意义。
进化计算和运筹学方法是求解4PL相关优化问题的常用解决方法。卢福强和任亮等人分别在第十三届自动化科学与工程国际会议和第二十六届中国控制与决策会议上采用遗传算法和蚁群算法求解4PL优化问题。但是，前者在面对较为复杂的模型下算法效果欠佳，后者算法时间复杂度较高，从而会消耗较多的时间求解问题。
发明内容
本发明人针对上述问题及技术需求，提出了一种基于蚁群算法的第四方物 流运输路径规划方法，本发明的技术方案如下：
一种基于蚁群算法的第四方物流运输路径规划方法，该方法包括：
构建第四方物流运输网络的有向邻接表gList，有向邻接表gList中包括N个城市节点，每两个有向邻接的城市节点之间通过G条运输路径相连，每条运输路径表示使用对应的一个运输代理商在两个城市节点之间进行物流运输；
初始化所有运输路径上的信息素，在每一轮迭代中，对于任意蚂蚁个体k，初始化蚂蚁个体k位于有向邻接表gList中的起点城市节点处，根据有向邻接表gList在信息素τ以及启发式信息η的引导下、从当前所在的城市节点的可访问路径中确定目标运输路径，并沿着目标运输路径移动至下一个有向邻接的城市节点，直至蚂蚁个体k移动到达终点城市节点时完成解的构建，其中信息素τ和启发式信息η均与运输路径所需的运输花费相关且启发式信息η与运输路径所需的运输花费成反比；
在所有m个蚂蚁个体都完成解的构建而完成一轮迭代后，全局更新所有运输路径上的信息素，并执行下一轮迭代直至达到迭代终止条件，得到从起点城市节点至终点城市节点的总运输时间最短的运输路径；
其中，任意蚂蚁个体k在任意城市节点i处的可访问路径包括城市节点i与所有可访问城市节点之间除路径禁忌表edgeTabooList中的运输路径之外的所有运输路径，蚂蚁个体k在城市节点i处的可访问城市节点包括城市节点i的所有有向邻接的城市节点中除节点禁忌表nodeTabooList中的城市节点之外的所有城市节点；蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList包含与城市节点i有向邻接且不满足运输成本约束条件的城市节点，蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList包含与城市节点i相连且不满足运载量约束条件的运输路径。
其进一步的技术方案为，初始化城市节点i与城市节点j之间对应于运输代理商g的运输路径
上的信息素为
C
td是由弗洛伊德算法通过运输路径
对应的单位运输时间
和城市节点i与城市节点j之间的运输距离d
ij构造的路径长度；其中，运输路径
对应的单位运输时间
表示运输代理商g在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输时间。
其进一步的技术方案为，城市节点i与城市节点j之间对应于运输代理商g 的运输路径
上与运输花费成反比的启发式信息
其中，
为运输代理商g的运输速度，d
ij为运输路径
的运输距离，
是运输代理商g在城市节点i与城市节点j之间进行物流运输时的总花费。
其进一步的技术方案为，当蚂蚁个体k位于城市节点i处时，对于城市节点i的任意一个有向邻接的城市节点j，若根据城市节点i与城市节点j之间的运输距离d
ij以及最低运输成本c
ij_min确定得到的城市节点i与城市节点j之间的最低运输成本超过额定最大运输成本C，则确定城市节点j不满足运输成本约束条件、且包含在蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList中；
其中，城市节点i与城市节点j之间的最低运输成本c
ij_min是所有运输代理商在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输成本的最小值。
其进一步的技术方案为，当蚂蚁个体k位于城市节点i处时，对于城市节点i与任意一个有向邻接的城市节点j之间的任意一条运输路径，若运输路径对应的运输代理商的最大运载量小于待配送总运载量Q，则确定运输路径不满足运载量约束条件、且包含在蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList中。
其进一步的技术方案为，从当前所在的城市节点的可访问路径中确定目标运输路径，包括：
生成一个随机数q∈[0,1]，若q≤q
0则按照
的公式、选择可访问路径中使得
最大的运输路径作为目标运输路径，否则通过轮盘赌的方法从可访问路径中选择得到目标运输路径；
其中，
表示运输路径
上的信息素，
表示运输路径
上的启发式信息，运输路径
表示城市节点i与城市节点j之间对应于运输代理商g的运输路径，α、β、q
0为参数，
表示运输路径
包含在蚂蚁个体k在城市节点i处的可访问路径构成的集合J
k(i)中。
其进一步的技术方案为，通过轮盘赌的方法从可访问路径中选择得到目标运输路径，包括：
从可访问路径中选择对应概率最大的运输路径作为目标运输路径，任意的运输路径
对应的概率
为：
其中，t表示蚂蚁个体k在城市节点i处的可访问路径构成的集合J
k(i)中的任意一个运输路径，τ
t是运输路径t上的信息素，η
t表示运输路径t上的启发式信息。
其进一步的技术方案为，在任意一轮迭代中对于任意一个蚂蚁个体k，方法还包括：
若蚂蚁个体k在当前的城市节点处不存在可访问路径，且蚂蚁个体k当前所在的城市节点不是终点城市节点，则控制蚂蚁个体k沿着回溯路径返回至上一个城市节点，回溯路径是蚂蚁个体k在上一个城市节点处确定得到的目标运输路径；将回溯路径添加到蚂蚁个体k在上一个城市节点处的路径禁忌表edgeTabooList中并对应更新蚂蚁个体k在上一个城市节点的可访问路径，重新确定蚂蚁个体k在上一个城市节点处的目标运输路径。
其进一步的技术方案为，全局更新所有运输路径上的信息素，包括：
将城市节点i与城市节点j之间对应于运输代理商g的运输路径
上的信息素更新为
ρ是参数，
表示至今最优的蚂蚁个体在运输路径
上释放的信息素，若运输路径
包含在至今最优的运输路径中则
若运输路径
不包含在至今最优的运输路径中则
其进一步的技术方案为，至今最优的蚂蚁个体在运输路径
上释放的信息素为：
其中，speed
best为至今最优的运输路径的总的运输时间，distance
best为至今最优的运输路径的总距离，cost
best为至今最优的运输路径的总花费，R
k为至今最优的运输路径。
本发明的有益技术效果是：
本申请公开了一种基于蚁群算法的第四方物流运输路径规划方法，该方法采用有向图的邻接表方式保存第四方物流运输网络的信息，并提出一种情景式编码方法，基于问题特征设计了启发式信息和信息素计算方式，从不同角度提高解的质量，利用蚁群算法可以在运输成本约束和运载量约束下得到运输路径， 以实现物流作业整体的总运输时间最短的目标，求解难度较低且解的质量较高，可以兼顾求解质量和求解速度，路径规划效率较高。
在蚁群算法应用过程中，使用节点禁忌表和路径禁忌表来减少不可行解产生的概率，另外使用了路径回溯的方法代替初始化新解来修复不可行路径，蚁群算法效率较高。
图1是一个实施例中的第四方物流运输路径规划方法的流程示意图。
图2是一个实例中的第四方物流运输网络的示意图。
图3是另一个实施例中的第四方物流运输路径规划方法的流程示意图。
图4是一个实验对比例中本申请的方法与其他两种算法的算法收敛图。
下面结合附图对本发明的具体实施方式做进一步说明。
本申请公开了一种基于蚁群算法的第四方物流运输路径规划方法，请参加图1所示的流程图，该方法包括如下步骤：
步骤1，构建第四方物流运输网络的有向邻接表gList。本申请采用有向图的邻接表方式保存第四方物流运输网络的信息，有向邻接表gList中包括N个城市节点，每两个有向邻接的城市节点之间通过G条运输路径相连，每条运输路径表示使用对应的一个运输代理商在两个城市节点之间进行物流运输。
比如如图2示出了一个实例中的第四方物流运输网络的示意图，则对应的有向邻接表中包括7个城市节点，分别表示图2中的数值1～7的圆圈，每两个有向邻接的城市节点之间通过2条运输路径相连，比如城市节点1与城市节点2之间通过运输路径a
1,2和运输路径b
1,2相连，城市节点1与城市节点4之间通过运输路径a
1,4和运输路径b
1,4相连，以此类推。图2以不同的下标表示不同城市节点之间的运输路径，任意两个城市节点之间的运输路径a对应运输代理商A、运输路径b对应运输代理商B，则城市节点1与城市节点2之间的运输路径a
1,2表示使用运输代理商A在城市节点1与城市节点2之间进行物流运输，其他含义也是类似的。
需要说明的是，本申请以每两个有向邻接的城市节点之间通过相同数量、相同类型的运输代理商进行运输为例，实际应用过程中若数量和类型存在不同也可以沿用本申请的方法。
请参加图2所示的第四方物流运输网络的结构，当需要从一个起点城市节 点向一个终点城市节点进行物流运输时，有多种路径选择，如图2中，当需要从城市节点1向城市节点5进行物流运输时，可以从城市节点1途径城市节点2到达城市节点5，或者从城市节点1途径城市节点4到达城市节点5，而在每两个城市节点之间也可以选用不同的运输代理商进行运输，比如可以通过运输路径a
1,2和运输路径a
2,5到达城市节点5，也可以通过运输路径b
1,4和运输路径a
4,5到达城市节点5，其他还有更多种可选的运输路径，当第四方物流运输网络更为复杂时，可选的运输路径更多。
在众多可选的运输路径中，需要考虑在一定的运输成本下选择最佳路径和适合的运输代理商，进而实现物流作业整体的总运输时间最短的目标，此模型优化目标定义为：
其中，
表示运输代理商g在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输时间。
表示利用运输代理商g在城市节点i与城市节点j之间进行物流运输的运输路径，当选用运输代理商g进行运输时，
取1，否则
取0。
此模型的约束条件包括运输成本约束条件和运载量约束条件，写为：
Q≤Q
g,g∈{1,2,…,G}
其中，d
ij表示城市节点i与城市节点j之间的运输距离，Q为需要从起点城市节点向终点城市节点运输的货物的待配送总运载量，
表示利用运输代理商g在城市节点i与城市节点j之间进行物流运输的每单位运输距离以及每单位运载量所需的运输成本。C是用户能够承担的额定最大运输成本。Q
g为运输代理商g的最大运载量。
本申请基于蚁群算法，结合有向邻接表gList所记载的第四方物流运输网络 的信息，可以在上述约束条件下求解得到目标模型，从而选择出运输时间最优的运输路径，具体做法如下：
步骤2，初始化所有运输路径上的信息素。
在一个实施例中，对于任意一个城市节点i与城市节点j之间对应于运输代理商g的运输路径
上的信息素，将其初始化为
其中，m是蚁群算法中所有蚂蚁个体的总个数。C
td是由弗洛伊德算法通过运输路径
对应的单位运输时间
和城市节点i与城市节点j之间的运输距离d
ij构造的路径长度。运输路径
对应的单位运输时间
表示运输代理商g在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输时间。
步骤3，在每一轮迭代中，对于任意蚂蚁个体k，初始化蚂蚁个体k位于有向邻接表gList中的起点城市节点处，起点城市节点和终点城市节点都是有向邻接表gList中的一个城市节点，是已知的城市节点。
根据有向邻接表gList在信息素τ以及启发式信息η的引导下、从蚂蚁个体k当前所在的城市节点的可访问路径中确定目标运输路径，并沿着目标运输路径移动至下一个有向邻接的城市节点，直至蚂蚁个体k移动到达终点城市节点时完成解的构建。
其中，信息素τ和启发式信息η均与运输路径所需的运输距离、运输速度和相应花费相关且启发式信息η与运输路径所需的运输花费成反比。具体的，运输路径
上与运输花费成反比的启发式信息
为运输代理商g的运输速度，d
ij为运输路径
的运输距离，
是运输代理商g在城市节点i与城市节点j之间进行物流运输时的总花费。
任意蚂蚁个体k在任意城市节点i处的可访问路径包括城市节点i与所有可访问城市节点之间除路径禁忌表edgeTabooList中的运输路径之外的所有运输路径。而蚂蚁个体k在城市节点i处的可访问城市节点包括城市节点i的所有有向邻接的城市节点中除节点禁忌表nodeTabooList中的城市节点之外的所有城市节点。也即，蚂蚁个体k在城市节点i处的可访问路径是城市节点i连接的所有运输路径中排除掉nodeTabooList中的城市节点以及排除掉edgeTabooList中的运输路径后剩余的运输路径。
蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList包含与城市节点i有 向邻接且不满足运输成本约束条件的城市节点。具体的：当蚂蚁个体k位于城市节点i处时，对于城市节点i的任意一个有向邻接的城市节点j，若根据城市节点i与城市节点j之间的运输距离d
ij以及最低运输成本c
ij_min确定得到的城市节点i与城市节点j之间的最低运输成本超过额定最大运输成本C。则确定城市节点j不满足运输成本约束条件、且包含在蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList中。城市节点i与城市节点j之间的最低运输成本c
ij_min是所有运输代理商在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输成本的最小值，则当d
ij×c
ij_min×Q>C时，确定城市节点j不满足运输成本约束条件。
蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList包含与城市节点i相连且不满足运载量约束条件的运输路径。具体的：当蚂蚁个体k位于城市节点i处时，对于城市节点i与任意一个有向邻接的城市节点j之间的任意一条运输路径，若运输路径对应的运输代理商的最大运载量小于待配送总运载量Q，则确定运输路径不满足运载量约束条件、且包含在蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList中。
比如，基于图2所示的第四方物流运输网络，当蚂蚁个体k在任意城市节点1处时，假设其节点禁忌表nodeTabooList中包括城市节点3，路径禁忌表edgeTabooList中包括运输路径b
1,4。则此时，城市节点i的所有有向邻接的城市节点包括城市节点2、城市节点3和城市节点4，排除掉节点禁忌表nodeTabooList中的城市节点3后，确定此时所有可访问城市节点包括城市节点2和城市节点4。城市节点1与城市节点2和城市节点4之间的所有运输路径包括a
1,2、b
1,2、a
1,4、b
1,4，排除掉edgeTabooList中包含的b
1,4，就能确定此时蚂蚁个体k在城市节点1处的可访问路径包括a
1,2、b
1,2、a
1,4。
在蚂蚁个体k位于每个城市节点i处时，都按照上述方法确定此时的节点禁忌表nodeTabooList和路径禁忌表edgeTabooList，继而确定相应的可访问路径，请参考图3所示的流程图，然后从中选取目标运输路径以移动到下一个城市节点，确定目标运输路径的方法包括：
生成一个随机数q∈[0,1]，若q≤q
0则按照
的公式、选择可访问路径中使得
最大的运输路径作为目标运输路径，
表示运输路径
上的信息素，
表示运输路径
上的启发式信息，运输路径
表示 城市节点i与城市节点j之间对应于运输代理商g的运输路径，α、β、q
0为参数，
表示运输路径
包含在蚂蚁个体k在城市节点i处的可访问路径构成的集合J
k(i)中。
若q>q
0，则通过轮盘赌的方法从可访问路径中选择得到目标运输路径。在通过轮盘赌的方法从可访问路径中选择得到目标运输路径时，可访问路径中选择对应概率最大的运输路径作为目标运输路径，任意的运输路径
对应的概率
为：
其中，t表示蚂蚁个体k在城市节点i处的可访问路径构成的集合J
k(i)中的任意一个运输路径，τ
t是运输路径t上的信息素，η
t表示运输路径t上的启发式信息。
请参考图3，在蚂蚁个体k逐步移动的过程中，若蚂蚁个体k在当前的城市节点处不存在可访问路径，且蚂蚁个体k当前所在的城市节点是终点城市节点，则表示已经完成了解的构建。若蚂蚁个体k在当前的城市节点处不存在可访问路径，且蚂蚁个体k当前所在的城市节点不是终点城市节点，则控制蚂蚁个体k沿着回溯路径返回至上一个城市节点，回溯路径是蚂蚁个体k在上一个城市节点处确定得到的目标运输路径。将回溯路径添加到蚂蚁个体k在上一个城市节点处的路径禁忌表edgeTabooList中并对应更新蚂蚁个体k在上一个城市节点的可访问路径，重新确定蚂蚁个体k在上一个城市节点处的目标运输路径，继而重新从上一个城市节点处移动至重新确定的城市节点处。edgeTabooList的一部分作用是保证蚂蚁个体能够避开不符合运输商能够承担的最大运输量约束的路径，提高算法的效率，另一部分作用是负责记录失败的路径信息，当蚂蚁个体所在的最后的一个城市节点不是期望的终点城市节点时，通过路径的回溯可以回到上一城市节点来修复不可行路径。
步骤4，在所有m个蚂蚁个体都完成解的构建而完成一轮迭代后，全局更新所有运输路径上的信息素，并执行下一轮迭代直至达到迭代终止条件，得到从起点城市节点至终点城市节点的总运输时间最短的运输路径。
具体的迭代过程为，在开始一轮迭代时，初始化k＝0，通过上述方法控制蚂蚁个体k移动到达终点城市节点时完成解的构建，并令k＝k+1，若满足k<m，则利用更新后的k对下一个蚂蚁个体进行解的构建。若不满足k<m，则确定完 成一轮迭代，并全局更新所有运输路径上的信息素执行下一轮迭代直至达到迭代终止条件。迭代终止条件可以预先设定，比如设定迭代的总轮数等等。
在全局更新所有运输路径上的信息素时，将城市节点i与城市节点j之间对应于运输代理商g的运输路径
上的信息素更新为
ρ是参数，
表示至今最优的蚂蚁个体在运输路径
上释放的信息素，若运输路径
包含在至今最优的运输路径中则
若运输路径
不包含在至今最优的运输路径中则
也即全局信息素的更新仅在至今最优的路径的边上进行更新。其中，至今最优的蚂蚁个体在运输路径
上释放的信息素为：
其中，speed
best为至今最优的运输路径的总的运输时间，distance
best为至今最优的运输路径的总距离，cost
best为至今最优的运输路径的总花费，R
k为至今最优的运输路径。
为了说明本申请方法的有效性，本申请设置如下实例进行实验数据对比：以算法一为本申请提供的方法(IACO)。算法二为2021年发表在智能系统学报中的《模糊粒子群优化算法的第四方物流运输时间优化》一文中的引入收敛因子和隶属度函数的模糊粒子群优化算法(CFPSO)。算法三为经典的遗传算法(GA)。
以算法二的论文提供的三个不同规模的算例为实验数据，分别利用算法一、二、三进行求解，这三个算例包含了不同的数据规模与成本约束，能够很好的验证求解算法的性能，三个算例的具体内容如下表所示：
(1)、算例一的城市节点间距离如下表所示，且每两个有向邻接的城市节点之间包括运输代理商分别为代理商1和代理商2，代理商1的运输成本为0.16RMB/吨、运输速度为80km/h。代理商2的运输成本为0.08RMB/吨、运输速度为40km/h。
| 城市 | 杭州 | 南京 | 上海 | 南通 | 泰州 | 淮安 |
| 杭州 | 0 | 330 | 195 | — | — | — |
| 南京 | 330 | 0 | 248 | 306 | — | 355 |
| 上海 | 195 | 248 | 0 | 103 | 217 | — |
| 南通 | — | 306 | 103 | 0 | 160 | 354 |
| 泰州 | — | — | 217 | 160 | 0 | 193 |
| 淮安 | — | 355 | — | 354 | 193 | 0 |
(2)算例二的城市节点间距离如下表所示，且每两个有向邻接的城市节点之间包括运输代理商分别为代理商1、代理商2和代理商3，代理商1的运输成本为0.16RMB/吨、运输速度为80km/h。代理商2的运输成本为0.08RMB/吨、运输速度为40km/h。代理商3的运输成本为1.5RMB/吨、运输速度为750km/h。
(3)算例三的城市节点间距离如下表所示，且每两个有向邻接的城市节点之间包括运输代理商分别为代理商1、代理商2和代理商3，代理商1的运输成本为0.16RMB/吨、运输速度为80km/h。代理商2的运输成本为0.08RMB/吨、运输速度为40km/h。代理商3的运输成本为1.5RMB/吨、运输速度为750km/h。
| 城市 | 杭州 | 南京 | 上海 | 南通 | 泰州 | 淮安 | 合肥 | 郑州 | 连云港 | 日照 |
| 杭州 | 0 | 330 | 195 | — | — | — | — | — | — | — |
| 南京 | 330 | 0 | 248 | 306 | — | 355 | 65 | 1673 | — | 761 |
| 上海 | 195 | 248 | 0 | 103 | 217 | — | — | — | — | — |
| 南通 | — | 306 | 103 | 0 | 160 | 354 | — | 1971 | 779 | 1064 |
| 泰州 | — | — | 217 | 160 | 0 | 193 | 306 | 1871 | — | 982 |
| 淮安 | — | 355 | — | 354 | 193 | 0 | 362 | 1788 | — | 939 |
| 合肥 | — | 65 | — | — | 306 | 362 | 0 | 1610 | 499 | — |
| 郑州 | — | 1673 | — | 1971 | 1871 | 1788 | 1610 | 0 | 1220 | 915 |
| 连云港 | — | — | — | 779 | — | — | 499 | 1220 | 0 | 397 |
| 日照 | — | 761 | — | 1064 | 982 | 939 | — | 915 | 397 | 0 |
| 蚌埠 | — | — | — | — | 428 | — | — | 1444 | — | 553 |
| 青岛 | — | 905 | — | — | — | — | — | 776 | 528 | 145 |
| 临沂 | — | — | — | — | — | — | 983 | — | — | — |
| 枣庄 | — | — | — | — | — | — | — | — | — | — |
| 济南 | — | 1553 | — | — | — | — | — | 257 | 1064 | 828 |
| 邢台 | — | — | — | — | — | — | — | — | — | — |
| 邯郸 | — | — | — | — | — | — | — | — | — | |
| 石家庄 | — | — | — | — | — | — | — | — | — | — |
以上三个算例的运输网络分别有6、12和18个城市节点，每个算例中的起点城市节点和终点城市节点分别是算例中第一个城市节点和最后一个城市节点。算法一、二、三的参数通过控制变量方法进行设置，具体的参数如下表。
CFPSO与GA适应度函数的构建都采用罚函数法，可表示为：
其中w
1、w
2、w
3都为惩罚项系数。由于IACO采用了修复策略，所以种群中的解都为可行解。三个算法都部署在同一实验环境下，且不同问题规模和成本约束都作为一个独立的问题运行二十次，三种算法的实验结果对比如下：
(1)三种算法在算例一上的实验结果对比如下
(2)三种算法在算例二上的实验结果对比如下
(3)三种算法在算例三上的实验结果对比如下
实验结果表明，本申请的方法在不同的数据规模和成本约束下均能取得较对比算法更好的结果。随着数据规模越大时，求解难度也显著增加，但本申请方法取得的结果较小规模相比却领先其他算法越多，说明了本申请的方法有较强的处理大规模问题的能力。观察实验结果可以发现，本申请方法在各个问题规模和成本约束下的最小和平均运输时间差异很小说明本发明方法具有较强的稳定性。
为了进一步的分析本申请方法与其他对比算法的性能，基于算例3且成本约束为300000元问题下，三种算法的迭代次数都设置为500代的算法收敛图如图4所示，由图4可以看出三个算法随着迭代都可以很好的收敛。而本申请方法较其它对比算法收敛快且曲线收敛平稳，说明具有较强的算法收敛能力和稳定性。且本申请方法的曲线在其它算法曲线下方，说明其解的质量稳定高于其他算法。
以上所述的仅是本申请的优选实施方式，本发明不限于以上实施例。可以理解，本领域技术人员在不脱离本发明的精神和构思的前提下直接导出或联想到的其他改进和变化，均应认为包含在本发明的保护范围之内。
Claims (10)
- 一种基于蚁群算法的第四方物流运输路径规划方法，其特征在于，所述方法包括：构建第四方物流运输网络的有向邻接表gList，所述有向邻接表gList中包括N个城市节点，每两个有向邻接的城市节点之间通过G条运输路径相连，每条运输路径表示使用对应的一个运输代理商在两个城市节点之间进行物流运输；初始化所有运输路径上的信息素，在每一轮迭代中，对于任意蚂蚁个体k，初始化蚂蚁个体k位于所述有向邻接表gList中的起点城市节点处，根据所述有向邻接表gList在信息素τ以及启发式信息η的引导下、从当前所在的城市节点的可访问路径中确定目标运输路径，并沿着所述目标运输路径移动至下一个有向邻接的城市节点，直至蚂蚁个体k移动到达终点城市节点时完成解的构建，其中，信息素τ和启发式信息η均与运输路径所需的运输花费相关且启发式信息η与运输路径所需的运输花费成反比；在所有m个蚂蚁个体都完成解的构建而完成一轮迭代后，全局更新所有运输路径上的信息素，并执行下一轮迭代直至达到迭代终止条件，得到从所述起点城市节点至所述终点城市节点的总运输时间最短的运输路径；其中，任意蚂蚁个体k在任意城市节点i处的可访问路径包括城市节点i与所有可访问城市节点之间除路径禁忌表edgeTabooList中的运输路径之外的所有运输路径，蚂蚁个体k在城市节点i处的可访问城市节点包括城市节点i的所有有向邻接的城市节点中除节点禁忌表nodeTabooList中的城市节点之外的所有城市节点；蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList包含与城市节点i有向邻接且不满足运输成本约束条件的城市节点，蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList包含与城市节点i相连且不满足运载量约束条件的运输路径。
- 根据权利要求1所述的方法，其特征在于，初始化城市节点i与城市节点j之间对应于运输代理商g的运输路径上的信息素为
C td是由贪婪算法通过运输路径
对应的单位运输时间
和城市节点i与城市节点j之间的运输距离d ij构造的路径长度；其中，运输路径
对应的单位运输时间
表示运输代理商g在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输时间。
- 根据权利要求1所述的方法，其特征在于，城市节点i与城市节点j之间对应于运输代理商g的运输路径上与运输花费成反比的启发式信息
其中，
为运输代理商g的运输速度，d ij为运输路径
的运输距离，
是运输代理商g在城市节点i与城市节点j之间进行物流运输时的总花费。
- 根据权利要求1所述的方法，其特征在于，当蚂蚁个体k位于城市节点i处时，对于城市节点i的任意一个有向邻接的城市节点j，若根据城市节点i与城市节点j之间的运输距离d ij以及最低运输成本c ij_min确定得到的城市节点i与城市节点j之间的最低运输成本超过额定最大运输成本C，则确定城市节点j不满足运输成本约束条件、且包含在蚂蚁个体k在城市节点i处的节点禁忌表nodeTabooList中；其中，城市节点i与城市节点j之间的最低运输成本c ij_min是所有运输代理商在城市节点i与城市节点j之间进行物流运输时每单位运输距离以及每单位运载量所需的运输成本的最小值。
- 根据权利要求1所述的方法，其特征在于，当蚂蚁个体k位于城市节点i处时，对于城市节点i与任意一个有向邻接的城市节点j之间的任意一条运输路径，若所述运输路径对应的运输代理商的最大运载量小于待配送总运载量Q，则确定所述运输路径不满足运载量约束条件、且包含在蚂蚁个体k在城市节点i处的路径禁忌表edgeTabooList中。
- 根据权利要求1所述的方法，其特征在于，所述从当前所在的城市节点的可访问路径中确定目标运输路径，包括：生成一个随机数q∈[0,1]，若q≤q 0则按照的公式、选择可访问路径中使得
最大的运输路径作为所述目标运输路径，否则通过轮盘赌的方法从可访问路径中选择得到所述目标运输路径；
其中，表示运输路径
上的信息素，
表示运输路径
上的启发式信息，运输路径
表示城市节点i与城市节点j之间对应于运输代理商g的运输路径，α、β、q 0为参数，
表示运输路径
包含在蚂蚁个体k在城市节点i处的可访问路径构成的集合J k(i)中。
- 根据权利要求6所述的方法，其特征在于，所述通过轮盘赌的方法从可 访问路径中选择得到所述目标运输路径，包括：从可访问路径中选择对应概率最大的运输路径作为所述目标运输路径，任意的运输路径对应的概率
为：
其中，t表示蚂蚁个体k在城市节点i处的可访问路径构成的集合J k(i)中的任意一个运输路径，τ t是运输路径t上的信息素，η t表示运输路径t上的启发式信息。 - 根据权利要求1所述的方法，其特征在于，在任意一轮迭代中对于任意一个蚂蚁个体k，所述方法还包括：若蚂蚁个体k在当前的城市节点处不存在可访问路径，且蚂蚁个体k当前所在的城市节点不是所述终点城市节点，则控制蚂蚁个体k沿着回溯路径返回至上一个城市节点，所述回溯路径是蚂蚁个体k在上一个城市节点处确定得到的目标运输路径；将所述回溯路径添加到蚂蚁个体k在上一个城市节点处的路径禁忌表edgeTabooList中并对应更新蚂蚁个体k在上一个城市节点的可访问路径，重新确定蚂蚁个体k在上一个城市节点处的目标运输路径。
- 根据权利要求1所述的方法，其特征在于，所述全局更新所有运输路径上的信息素，包括：将城市节点i与城市节点j之间对应于运输代理商g的运输路径上的信息素更新为
ρ是参数，
表示至今最优的蚂蚁个体在运输路径
上释放的信息素，若运输路径
包含在至今最优的运输路径中则
若运输路径
不包含在至今最优的运输路径中则
- 根据权利要求9所述的方法，其特征在于，至今最优的蚂蚁个体在运输路径上释放的信息素为：
其中，speed best为至今最优的运输路径的总的运输时间，distance best为至今最优的运输路径的总距离，cost best为至今最优的运输路径的总花费，R k为至今最优的运输路径。
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