CN108492020B - Polluted vehicle scheduling method and system based on simulated annealing and branch cutting optimization - Google Patents

Polluted vehicle scheduling method and system based on simulated annealing and branch cutting optimization Download PDF

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CN108492020B
CN108492020B CN201810220197.8A CN201810220197A CN108492020B CN 108492020 B CN108492020 B CN 108492020B CN 201810220197 A CN201810220197 A CN 201810220197A CN 108492020 B CN108492020 B CN 108492020B
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李进
竹锦潇
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Zhejiang Gongshang University
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Abstract

The invention discloses a method and a system for dispatching polluted vehicles based on simulated annealing and branch cutting optimization, wherein the method comprises the following steps: establishing a transportation model according to the obtained distribution parameters, and establishing a carbon emission model according to the load parameters and the transportation model; optimizing and calculating a transportation model, a carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route; and finally, finishing the optimization of the polluted vehicle scheduling according to the distribution route information. According to the method, related models are established firstly, and then the integer solution is obtained more quickly by using the simulated annealing algorithm, so that the operation time of the integer solution is greatly reduced, and the calculation efficiency is improved; the simulated annealing algorithm is used for generating the optimal integer solution in the branch cutting algorithm and improving the optimal solution, the global optimizing capability of vehicle scheduling is improved, and the carbon dioxide emission of the vehicle can be reduced to the maximum extent by vehicle scheduling arrangement.

Description

Polluted vehicle scheduling method and system based on simulated annealing and branch cutting optimization
Technical Field
The invention relates to the technical field of engineering, in particular to a method and a system for dispatching polluted vehicles based on simulated annealing and branch cutting optimization, which are used for dispatching and planning vehicles for reducing automobile exhaust emission and environmental pollution in a logistics distribution system and a transportation system.
Background
Climate change and greenhouse effect problems have become one of the major global threats. Toxic gases such as carbon dioxide, carbon oxides and sulfides are among the largest contributors to these threats. Many companies are currently working to reduce the emissions of these gases from the environment. In recent decades, the problem of network distribution in low carbon supply chains has been one of the focuses of researchers. Low carbon supply chain management has received intense business and government attention in recent years. The supply chain is a network of suppliers, manufacturers, warehouses and distribution centers to maximize the benefits to customers. The most important part in a supply chain system is the transportation of material between different centres, such as supplier to manufacturer, manufacturer to warehouse and warehouse to distribution node.
Vehicle Scheduling Problem (VSP) is one of the important problems in many practical applications in the field of transportation. Carbon dioxide emissions are currently one of the major concerns of researchers. The Problem of Pollution Vehicle Scheduling (PVSP) is an extension of the Problem of Vehicle Scheduling. The problem plays a crucial role in protecting the environment and reducing the emission of harmful gases.
In logistics transportation technology, most enterprises ignore the emission of carbon dioxide and its impact on the environment. Recently, many companies and enterprises have begun to adopt different techniques for reducing carbon dioxide emissions. Distance is one of the main factors for reducing carbon dioxide, which is proportional to the distance traveled by the automobile. The vehicle scheduling problem is one of the main problems in the transportation and supply chain management system, and the vehicle scheduling problem is an integer programming problem in the combination optimization. The problem is to transport goods from the distribution centre warehouse to the distribution nodes with the aim of minimizing the total distance travelled. Minimization of carbon dioxide emissions will also be considered in the problem of polluted vehicle dispatch.
The Simulated Annealing Algorithm (Simulated Annealing Algorithm) is a random optimization Algorithm proposed by Metropolis et al in 1953, and is a probabilistic-based Algorithm simulating the solid Annealing principle, and can find the optimal solution in a large search space. The process is that starting from a certain higher initial temperature, along with the continuous decrease of the temperature, the global optimal solution of the objective function can be randomly searched in a solution space by combining the characteristic of probability jump. The simulated annealing algorithm can effectively avoid trapping in local minimum and finally tends to global optimum, and has strong local searching capability and short running time. Simulated annealing algorithms have been applied in many fields of engineering technology, including very large scale integrated circuit design, neural network computers, data mining and image processing. However, the simulated annealing algorithm has poor global search capability, is easily influenced by parameters, cannot ensure one-time convergence to an optimal value, and generally needs multiple attempts to obtain the optimal value.
The branch-cut algorithm is an algorithm that combines the branch-and-bound method with the cut-plane method. The method can solve the problem of pure 0-1 integer programming, and is applied to solving the problems of mixed 0-1 integer programming and mixed integer programming. The algorithm has been very commonly applied to large scale engineering problems with thousands of variables and other complex problems. The algorithm integrates the advantages of the branch-and-bound method and the secant plane method, can effectively and quickly find the optimal solution, and has high efficiency. However, the branch cutting algorithm cannot effectively solve all integer programming problems with large-scale variables, and the algorithm depends on a sparse coefficient matrix and has certain limitations.
In summary, PVSP is a current complex and difficult-to-solve vehicle scheduling problem, and with the increase of distribution nodes, the calculation amount of the existing algorithm increases exponentially, resulting in poor calculation effect and long consumed time. Therefore, there is a lack of a method and a system for dispatching a contaminated vehicle based on simulated annealing and branch cut optimization, which can reasonably arrange the route of the transportation vehicle, improve the efficiency of cargo delivery service of the transportation vehicle, and reduce carbon emission, thereby further reducing environmental pollution.
Disclosure of Invention
The invention aims to provide a method and a system for dispatching polluted vehicles based on simulated annealing and branch cutting optimization, which can reasonably arrange the routes of transport vehicles, improve the efficiency of cargo delivery service of the transport vehicles and reduce carbon emission so as to further reduce environmental pollution.
The invention provides a polluted vehicle scheduling method based on simulated annealing and branch cutting optimization, which comprises the following steps of;
obtaining distribution parameters of each vehicle, and establishing a transportation model according to the distribution parameters;
acquiring load parameters of each vehicle, and establishing a carbon emission model according to the load parameters and a transportation model;
optimizing and calculating the transportation model, the carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route;
and finishing the optimization of the polluted vehicle scheduling according to the distribution route information.
As an implementation mode, the optimizing calculation of the transportation model, the carbon emission model and the preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route includes the following steps;
constructing initial feasible solutions of the transportation model, the carbon emission model and a capacity model preset by each vehicle by taking a branch cutting algorithm as a frame, and optimizing the initial feasible solutions by simulated annealing to obtain a route initial solution;
and evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree, and obtaining information of each distribution route according to an evaluation result.
As an implementable manner, the method comprises the following steps of evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree, and obtaining distribution route information according to an evaluation judgment result;
evaluating whether the objective function value of each route initial solution is an optimal value, and adding the optimum objective function value obtained through evaluation into a defined root node of a preset enumeration tree;
judging whether the enumeration tree meets a termination condition;
if the enumeration tree meets the termination condition, taking the initial solution of each route as the information of each distribution route;
if the enumeration tree does not meet the termination condition, solving the linear programming problem of each model by using a branch cutting algorithm, continuously updating to obtain an optimal solution, and obtaining all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
As an implementation manner, the obtaining of the delivery parameters of each vehicle and the building of the transportation model according to the delivery parameters includes the following steps;
obtaining distribution parameters of each vehicle, wherein the distribution parameters comprise starting parameters m of each vehicleabDistributed node parameters and distance parameters LabAccording to said enabling parameter mabNode parameter and distance parameter LabEstablishing a transportation model;
the transportation model is
Figure BDA0001599448700000031
Wherein Minimize represents the minimum total delivery distance; a represents the a-th distribution node, b represents the b-th distribution node, and s represents the total number of the distribution nodes; distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter mabShowing the operation of the vehicle from the a-th delivery node to the b-th delivery node when m ab1 denotes vehicle start-up, m ab0 means that the vehicle is not active.
As an implementation mode, the obtaining of the load parameters of each vehicle and the establishment of the carbon emission model according to the load parameters and the transportation model comprises the following steps;
acquiring load parameters of each vehicle, performing distance optimization on the transportation model, and establishing a carbon emission model according to a distance optimization result and the load parameters;
the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h represents the vehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load.
Correspondingly, the invention also provides a polluted vehicle dispatching system based on simulated annealing and branch cutting optimization, which comprises a first model building module, a second model building module, a route optimizing module and a vehicle dispatching module;
the first model building module is used for obtaining distribution parameters of each vehicle and building a transportation model according to the distribution parameters;
the second model establishing module is used for acquiring the load parameters of each vehicle and establishing a carbon emission model according to the load parameters and the transportation model;
the route optimization module is used for carrying out optimization calculation on the transportation model, the carbon emission model and a preset capacity model of each vehicle by utilizing a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route;
and the vehicle scheduling module is used for finishing the optimization of the polluted vehicle scheduling according to the distribution route information.
As an implementation, the route optimization module includes a construction unit and an evaluation judgment unit;
the construction unit is used for constructing initial feasible solutions of the transportation model, the carbon emission model and a capacity model preset by each vehicle by taking a branch cutting algorithm as a frame, and optimizing the initial feasible solutions by simulated annealing to obtain a route initial solution;
and the evaluation judging unit is used for evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree and obtaining information of each distribution route according to an evaluation result.
As one possible embodiment, the evaluation judging unit includes an evaluation subunit, a judging subunit, a first processing subunit, and a second processing subunit;
the evaluation subunit is configured to evaluate whether an objective function value of each route initial solution is an optimal value, and add the evaluated optimal objective function value to a root node defined by a preset enumeration tree;
the judging subunit is configured to judge whether the enumeration tree satisfies a termination condition;
the first processing subunit is configured to, if the enumeration tree satisfies a termination condition, use an initial solution of each route as information of each distribution route;
the second processing subunit is configured to, if the enumeration tree does not meet the termination condition, solve the linear programming problem of each model by using a branch cutting algorithm and continuously update the linear programming problem to obtain an optimal solution, and obtain all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
As an implementable manner, the first model building module comprises a transportation model building unit;
the transportation model establishing unit is used for obtaining distribution parameters of each vehicle, and the distribution parameters comprise starting parameters m of each vehicleabDistributed node parameters and distance parameters LabAccording to said enabling parameter mabNode parameter and distance parameter LabEstablishing a transportation model;
the transportation model is
Figure BDA0001599448700000051
Wherein Minimize represents the minimum total delivery distance; a represents the a-th distribution node, b represents the b-th distribution node, and s represents the total number of the distribution nodes; distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter mabShowing the operation of the vehicle from the a-th delivery node to the b-th delivery node when m ab1 denotes vehicle start-up, m ab0 means that the vehicle is not active.
As an implementable manner, the second model building module comprises a carbon emission model building unit;
the carbon emission model establishing unit is used for acquiring the load parameters of each vehicle, performing distance optimization on the transportation model, and establishing a carbon emission model according to the distance optimization result and the load parameters;
the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h represents the vehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load.
Compared with the prior art, the technical scheme has the following advantages:
the invention provides a method and a system for dispatching polluted vehicles based on simulated annealing and branch cutting optimization, wherein the method comprises the following steps: establishing a transportation model according to the obtained distribution parameters, and establishing a carbon emission model according to the obtained load parameters and the transportation model; optimizing and calculating a transportation model, a carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route; and finally, finishing the optimization of the polluted vehicle scheduling according to the distribution route information. According to the method, each relevant model is established according to relevant parameters, and then the integer solution of the transportation model, the carbon emission model and the capacity model is obtained more quickly by using a simulated annealing algorithm, so that the operation time of the integer solution is greatly reduced, and the calculation efficiency is improved; the simulated annealing algorithm is used for generating the optimal integer solution in the branch cutting algorithm and improving the optimal solution, the global optimization capability of vehicle scheduling is improved, the route planning time among distribution nodes is shortened, the optimization of polluted vehicle scheduling is completed by each distribution route information obtained after branch cutting, the carbon dioxide emission of vehicles can be reduced to the maximum extent by vehicle scheduling arrangement, the logistics transportation cost is greatly reduced, and the method has important practical significance.
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FIG. 1 is a schematic flow chart of a method for dispatching a contaminated vehicle based on simulated annealing and branch cut optimization according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating an optimization procedure using simulated annealing and branch cutting according to one embodiment of the present invention;
FIG. 3a is a schematic diagram illustrating a merging operation according to an embodiment of the present invention;
FIG. 3b is a diagram illustrating a merging operation according to a first embodiment of the present invention;
FIG. 4a is a diagram illustrating a switching operation according to a first embodiment of the present invention;
FIG. 4b is a diagram illustrating a swap operation according to an embodiment of the present invention;
FIG. 5a is a schematic view of a refueling station according to a first embodiment of the present invention before insertion;
FIG. 5b is a schematic view of the fueling station after an insertion operation in accordance with one embodiment of the present invention;
FIG. 6a is a schematic view of an oil filling station before a separation operation according to a first embodiment of the present invention;
FIG. 6b is a schematic view of the refueling station after a separation operation according to the first embodiment of the present invention;
FIG. 7 is a schematic structural diagram of a contaminated vehicle dispatching system based on simulated annealing and branch cut optimization according to a second embodiment of the present invention;
FIG. 8 is a schematic diagram of the structure of the route optimization module of FIG. 7;
fig. 9 is a schematic structural diagram of the evaluation judgment unit in fig. 8.
In the figure: 100. a first model building module; 110. a transportation model establishing unit; 200. a second model building module; 210. A carbon emission model establishing unit; 300. a route optimization module; 310. a construction unit; 320. an evaluation judging unit; 321. An evaluation subunit; 322. a judgment subunit; 323. a first processing subunit; 324. a second processing subunit; 400. and a vehicle dispatching module.
Detailed Description
The above and further features and advantages of the present invention will be apparent from the following, complete description of the invention, taken in conjunction with the accompanying drawings, wherein the described embodiments are merely some, but not all embodiments of the invention.
The problem of polluted vehicle dispatch is one of the standard vehicle dispatch problems. This problem has two goals: the first objective is to find the minimum driving distance and the second objective is to find the minimum emission of carbon dioxide. The PVSP scheme determines a group of delivery routes, can meet the requirements of the distribution center, and simultaneously obtains the lowest transportation travel cost from the distribution center to each distribution node. Generally, the total minimum cost is equivalent to the total route traveled by all vehicles. Assuming that the enterprise has a sufficient number of vehicles, each delivery node is allowed to use only one vehicle for delivery. All vehicles have a maximum capacity limit and they transport goods from the distribution center to the distribution node and then back to the distribution center.
In order to achieve the purpose, the invention adopts the following technical scheme: first, a carbon emission model of a vehicle based on distance and load is introduced, i.e., the amount of vehicle emissions is proportional to its distance traveled and load capacity. And associated transportation and capacity models. Then, a hybrid intelligent method based on simulated annealing and branch cutting is provided for calculating the minimum driving distance and the minimum carbon emission. The method comprises the following specific steps.
Referring to fig. 1, a method for dispatching a contaminated vehicle based on simulated annealing and branch cutting optimization according to an embodiment of the present invention includes the following steps;
s100, obtaining distribution parameters of each vehicle, and establishing a transportation model according to the distribution parameters;
s200, acquiring load parameters of each vehicle, and establishing a carbon emission model according to the load parameters and the transportation model;
s300, optimizing and calculating a transportation model, a carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route;
and S400, finishing the optimization of the polluted vehicle scheduling according to the distribution route information.
It should be noted that the relevant parameters for establishing the model may be directly obtained from the local database, or may be obtained from the cloud server by using big data. The relevant parameters refer to distribution parameters, load parameters and preset capacity models. Distribution parameters include, but are not limited to, an activation parameter m for each vehicleabDistributed node parameters and distance parameters LabAccording to the enabling parameter mabNode parameter and distanceDistance parameter LabEstablishing a transportation model; assuming that the enterprise has a sufficient number of vehicles, each distribution node allows only one vehicle to be used for distribution, and the total travel distance of the vehicles, i.e. the sum of the total distances of all the starting vehicles, is calculated. The transportation model is the minimum value for calculating the total distance. In other embodiments, it is also considered that the enterprise does not have enough vehicles, and in this embodiment, the number of vehicles is not limited.
Then the transportation model is established as
Figure BDA0001599448700000071
Wherein Minimize represents the minimum total delivery distance; a represents the a-th distribution node, b represents the b-th distribution node, and s represents the total number of the distribution nodes; distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter xijShowing the operation of the vehicle from the a-th delivery node to the b-th delivery node when m ab1 denotes vehicle start-up, m ab0 means that the vehicle is not active.
The preset capacity model of each vehicle is a constraint condition, namely the capacity of the vehicles passing through all the distribution nodes is required to be not more than C, and the capacity model is
Figure BDA0001599448700000072
Wherein, caIndicating the demand of the a-th distribution node, nakThis shows a case where the kth vehicle is used at the a-th distribution node. q represents the maximum number of vehicles, that is, the 1 st vehicle when k is 1, and the q-th vehicle when k is q. C represents the maximum capacity of the passing vehicle. n isak1 denotes that the kth vehicle is used at the a-th distribution node, and n ak0 means that the kth vehicle is not used at the a-th distribution node.
In this embodiment, the carbon emission model is established based on the load parameters and the transportation model, and the specific steps may include: acquiring the load parameters of each vehicle, optimizing the distance of the transportation model, and optimizing the distance and the load parameters according to the distance optimization resultEstablishing a carbon emission model; the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h represents the vehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load. In other embodiments, the carbon emission model may be established directly from the relevant parameters without first correlating the data in the carbon emission model. However, the scheme still needs to calculate the data relationship between the average distance traveled by the vehicle in the carbon emission model and the transportation distance and the vehicle in the transportation model, so that the calculation efficiency is reduced, and the complexity is increased.
The problems that the calculation effect is poor and the time consumption is long due to the fact that the calculation amount is exponentially increased along with the increase of the distribution nodes in the traditional algorithm are solved. And carrying out optimization calculation on the transportation model, the carbon emission model and the preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route. The integer solutions of the transportation model, the carbon emission model and the capacity model are obtained more quickly by utilizing the simulated annealing algorithm, and then the simulated annealing algorithm is used for generating the optimal integer solution in the branch cutting algorithm and improving the optimal solution, so that the aim of quickly optimizing the dispatching of the polluted vehicle is fulfilled. And each piece of distribution route information comprises at least one distribution route. Each delivery route here refers to route information from the delivery center to the delivery node (delivery node), from the delivery node to the delivery node, and from the delivery node to the delivery center. And each vehicle is scheduled according to each corresponding delivery route information, so that the optimization of the polluted vehicle scheduling can be completed. Meanwhile, the technical scheme of the invention can also be applied to the technical fields of railway logistics scheduling, robot scheduling, artificial intelligence and the like.
The invention provides a method and a system for dispatching polluted vehicles based on simulated annealing and branch cutting optimization, wherein the method comprises the following steps: establishing a transportation model according to the obtained distribution parameters, and establishing a carbon emission model according to the obtained load parameters and the transportation model; optimizing and calculating a transportation model, a carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route; and finally, finishing the optimization of the polluted vehicle scheduling according to the distribution route information. According to the method, each relevant model is established according to relevant parameters, and then the integer solution of the transportation model, the carbon emission model and the capacity model is obtained more quickly by using a simulated annealing algorithm, so that the operation time of the integer solution is greatly reduced, and the calculation efficiency is improved; the simulated annealing algorithm is used for generating the optimal integer solution in the branch cutting algorithm and improving the optimal solution, the global optimization capability of vehicle scheduling is improved, the route planning time among distribution nodes is shortened, the optimization of polluted vehicle scheduling is completed by each distribution route information obtained after branch cutting, the carbon dioxide emission of vehicles can be reduced to the maximum extent by vehicle scheduling arrangement, the logistics transportation cost is greatly reduced, and the method has important practical significance.
Further, step S300 includes the following steps;
s310, constructing initial feasible solutions of a transportation model, a carbon emission model and a capacity model preset by each vehicle by taking a branch cutting algorithm as a frame, and optimizing the initial feasible solutions by simulated annealing to obtain a route initial solution;
and S320, evaluating and judging the objective function value of the initial solution of each route according to a preset initial enumeration tree, and obtaining information of each distribution route according to an evaluation result.
When constructing the initial feasible solution of the routes of the transportation model, the carbon emission model and the preset capacity model of each vehicle by using the branch cutting algorithm as a framework, firstly, a simple route is established from the distribution center for each distribution node. Then, all routes in the solution (T)1,T2) The cost savings obtained when they are merged are checked and the merging is achieved by merging the pair of delivery nodes that provide the greatest cost savings. I.e. the merging of a pair of delivery nodes with the maximum saved route cost, i.e. the initial feasible solution is also optimized by the merging. Of course, in certain specific cases, unsatisfied conditions may occurAnd conditional solutions, then the initial feasible solution is redistributed to establish a simple route start calculation, i.e. the initial feasible solution is the data set of the route. And optimizing the initial feasible solution by using a simulated annealing algorithm, wherein the optimization process adopts a random search technology, and specifically adopts a neighborhood search mode to carry out combination, exchange, gas station insertion, gas station separation and the like. Therefore, the operation time for changing the initial solution of the route into the integer solution is greatly reduced, and the calculation efficiency is improved.
The preset initial enumeration tree is a cyclic process of evaluating and judging the objective function value of each route initial solution, and it can be understood that each piece of final distribution route information can be obtained only after the termination condition is met. The termination condition here refers to whether the enumeration tree is an empty set, i.e., the enumeration tree
Figure BDA0001599448700000091
Or other termination conditions. Other termination conditions are, for example, arithmetic errors, infinite loops, etc. Thereby ensuring the efficiency of the calculation.
Further, step S320 includes the following steps;
s321, evaluating whether the objective function value of each route initial solution is an optimal value, and adding the optimal objective function value obtained through evaluation into a defined root node of a preset enumeration tree;
s322, judging whether the enumeration tree meets a termination condition;
s323, if the enumeration tree meets the termination condition, taking the initial solution of each route as the information of each distribution route;
s324, if the enumeration tree does not meet the termination condition, solving the linear programming problem of each model by using a branch cutting algorithm, continuously updating to obtain an optimal solution, and obtaining all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
The evaluation process is actually an evaluation process of whether the objective function value of each route initial solution is an optimal value. Specifically, it can be understood that if an optimal value exists, the optimal objective function value obtained through evaluation is added to the root node defined by the preset enumeration tree, that is, if the root node does not meet the termination condition, the initial solution of the new route is obtained through continuous updating. And simultaneously, deleting the corresponding node in the enumeration tree. And if the route initial solution does not obtain the optimal value after evaluation, the terminal condition is met, and each route initial solution is used as each distribution route information.
The method and the device construct effective inequalities for the integer solutions, acquire effective constraints by utilizing greedy constructive heuristic separation inequalities, enable the branch cutting algorithm to update the separated high-quality integers, effectively reduce the influence of the branch cutting algorithm on the separation of the potential fractional solutions containing the optimal integer solutions, and improve the efficiency of the algorithm.
As shown in fig. 2, the following describes the optimization steps using simulated annealing and branch cutting in detail, and may specifically include the following steps.
And 2.1, constructing an initial feasible solution.
First, a simple route is established from the distribution center for each distribution node. Then, all routes in the solution (T)1,T2) The cost savings obtained when they are merged are checked and the merging is achieved by merging the pair of nodes that provide the greatest cost savings. I.e., the condition for merging with the greatest cost savings, to construct an initial feasible solution.
And 2.2, judging whether the combination meeting the conditions exists or not, if so, returning to the step 2.1 to execute again, and if not, continuing the next step.
And 2.3, obtaining an initial solution of the branch cutting algorithm.
At initial feasible solution R'0After generation, obtaining an initial solution R of a branch cutting algorithm through a simulated annealing algorithm0. The simulated annealing algorithm is a random search technique and utilizes simulated annealingThe fire algorithm carries out the processes of merging, exchanging, gas station inserting and gas station separating of neighborhood search operators.
Merging operation As shown in FIGS. 3a and 3b, two routes (T) are randomly selected1,T2)，T2(0-4-2-0) by T1(0-6-3-5-1-0) and selecting the best feasible location, and routing the route T1(0-6-3-5-1-0) and T2(0-4-2-0) are combined into a new route (0-6-3-5-4-2-1-0). Switching operation as shown in fig. 4a and 4b, two randomly selected distribution nodes are switched on the same route or on two different routes, that is, the distribution nodes 1 and 8 are switched, and the switched routes are (0-5-3-7-4-8-0) and (0-1-6-2-0) with reference to fig. 4 b. Gasoline station insertion operation as shown in fig. 5a and 5b, two random delivery nodes are consecutively selected, and a gasoline station is joined on the route if there is no gasoline station passing between them. The gas station 3 is closest to the delivery node 6 and the delivery node 2, and the gas station 3 is interposed between the delivery node 6 and the delivery node 2. The next iteration after the insertion becomes a new path (0-1-6-3-2-5-7-4-0) by merging the paths (0-1-6-3-2-0) and (0-5-7-4-0). Gas station separation operation as shown in fig. 6a and 6b, a randomly selected gas station is deleted if possible, the gas stations 3 between the delivery node 2 and the delivery node 9 are deleted, and a new route is added to these delivery nodes.
And 2.4, constructing an initial enumeration tree.
To construct an initial enumeration tree, first, all initial solutions need to be obtained, and objective function values f of the initial solutions are evaluated (S)0) The optimal value and the optimal target value are defined as follows: rb←R0,f(Rb)←f(R0)。
Wherein R isbThe optimal value in all initial solutions at present, f (R), is represented in the formulab) An objective function value representing the optimum value. Defining nodes of an enumeration tree, assigning a value of f (R)b) And added to the root node of the enumeration tree Θ as the current node d.
Step 2.5, judging whether an enumeration tree exists or not
Figure BDA00015994487000001115
Or the end condition is satisfied, if the end condition exists, R is returnedbThe algorithm stops; otherwise, take a node d out of the enumeration tree.
And 2.6, solving the linear programming problem, and updating to obtain a new optimal solution.
Solving the corresponding linear programming problem to obtain an optimal solution
Figure BDA0001599448700000111
This optimal solution is likely to be a fraction. Judgment of
Figure BDA0001599448700000112
If the conditions are met, deleting the current node from the enumeration tree if the conditions are not met, and skipping to the step 2.5; determine if there is
Figure BDA0001599448700000113
If yes, deleting the current node from the enumeration tree, and skipping to the step 2.5; judgment of
Figure BDA0001599448700000114
If the number is an integer, judging whether the integer exists or not again if the integer exists
Figure BDA0001599448700000115
If yes, the following operations are executed:
Figure BDA0001599448700000116
the formula represents the optimal solution to be updated, and the next step is continuously executed; otherwise, the current node is deleted from the enumeration tree and the process jumps to step 2.5. If the two are not the same, the next step is continuously executed.
And 2.7, obtaining high-quality integer solution from the fractional solution.
Observing that the optimal fractional solution may contain some information about the optimal integer solution, it is likely through the use of heuristic or exact solution processesA high quality integer solution is obtained. Is provided with
Figure BDA0001599448700000117
And
Figure BDA0001599448700000118
is the optimal solution for any node in the enumeration tree. First, the route T is selected to have the maximum
Figure BDA0001599448700000119
(or
Figure BDA00015994487000001110
) Distribution node a of*Initially, a new delivery node b is then continuously added to the route T*To the maximum
Figure BDA00015994487000001111
(or
Figure BDA00015994487000001112
) The route to the last delivery node, provided that an addition is possible, is repeated until all delivery nodes have been assigned a route. Produce a feasible solution R'tThereafter, an improved solution can be obtained by step 2.4
Figure BDA00015994487000001113
To reduce the computational time spent on this process, the simulated annealing algorithm is applied to all nodes within ten levels of depth and all nodes at every tenth depth level in the enumeration tree.
And 2.8, determining an effective inequality.
In the branch cut algorithm of the present invention, since there is only one constraint, there is an inequality directly applied to the algorithm model at the beginning of the algorithm, which is defined as follows:
Figure BDA00015994487000001114
wherein, UK＝{u1,u2,...,ukDenotes a delivery node. SF＝{uK+1,uK+2,...,uK+SDenotes a petrol station. S (U)K) Indicating the lowest number of vehicles. m isabRepresenting a binary variable equal to 1 if the vehicle goes directly from node a to node b, and 0 otherwise. n isabkRepresenting a binary variable equal to 1 if the vehicle passes from node a to node b through the fueling station F, and 0 otherwise.
Thus, a process of acquiring the constraint is required. To this end, a greedy, constructive heuristic is introduced to separate the inequalities. In each iteration of the process, a delivery node is randomly selected as a seed node, and the delivery node set X is initialized with the seed. Then, a new delivery node x is selected*X is through X*Expanded, namely X ← XYx*. The relaxation values are defined as follows:
Figure BDA0001599448700000121
Figure BDA0001599448700000122
Figure 4
where x represents the number of available vehicles. HmaxIndicating the duration of a work day. value and value' represent two slack values, respectively.
Figure BDA0001599448700000124
Time estimates of the total route using the non-sequential information of the first and second nearest nodes in the range of XYx are shown. U represents a set of all nodes, i.e., U ═ 0"YUKYSFAnd "0" indicates a distribution center.
Figure 2
Representing only paths from node aAnd passing the time of the node b and returning to the distribution center.
Figure 5
Indicating the time from the distribution center to the a node after the b node.
Figure 3
Indicating the time from node a, through the gas station f and b nodes, and back to the distribution center.
Figure 6
Indicating the time from the center of delivery to node a through the gas stations f and b in order. The process of obtaining the minimum constraint slack is as follows:
Figure BDA0001599448700000129
wherein, argmin { value }x} and argmin { valuexRespectively indicate that the relaxation value function value is caused to bexAnd valuexThe set of all arguments x for which the minimum value is taken.
And 2.9, checking constraint validity.
When selecting the distribution node x*The validity of the current constraint is checked. If a violation occurs with set X, it is added to the cut pool. This process is repeated until all violating cuts are found. These cuts were applied to the LP model and re-optimized.
Step 2.10, create a new node.
A non-integer decision variable is selected according to the branching rule, a new node is created and added to the enumeration tree Θ, and the process goes to step 2.5.
Therefore, the optimization efficiency of the polluted vehicle dispatching is improved, the carbon dioxide emission of the vehicles can be reduced to the maximum extent by the vehicle dispatching arrangement, and the logistics transportation cost is greatly reduced.
Based on the same inventive concept, the embodiment of the invention also provides a polluted vehicle dispatching system based on simulated annealing and branch cutting optimization, and the implementation of the system can be realized by referring to the process of the method, and the repetition part is not described in detail.
Fig. 7 is a schematic structural diagram of a contaminated vehicle dispatching system based on simulated annealing and branch cutting optimization according to a second embodiment of the present invention, which includes a first model building module 100, a second model building module 200, a route optimizing module 300, and a vehicle dispatching module 400; the first model building module 100 is configured to obtain distribution parameters of each vehicle, and build a transportation model according to the distribution parameters; the second model establishing module 200 is used for acquiring load parameters of each vehicle and establishing a carbon emission model according to the load parameters and the transportation model; the route optimization module 300 is configured to perform optimization calculation on the transportation model, the carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route; the vehicle scheduling module 400 is used to accomplish optimization of contaminated vehicle scheduling according to the delivery route information.
According to the method, each relevant model is established according to relevant parameters, and then the integer solution of the transportation model, the carbon emission model and the capacity model is obtained more quickly by using a simulated annealing algorithm, so that the operation time of the integer solution is greatly reduced, and the calculation efficiency is improved; the simulated annealing algorithm is used for generating the optimal integer solution in the branch cutting algorithm and improving the optimal solution, the global optimization capability of vehicle scheduling is improved, the route planning time among distribution nodes is shortened, the optimization of polluted vehicle scheduling is completed by each distribution route information obtained after branch cutting, the carbon dioxide emission of vehicles can be reduced to the maximum extent by vehicle scheduling arrangement, the logistics transportation cost is greatly reduced, and the method has important practical significance.
As shown in fig. 8, the schematic diagram of the route optimization module 300 includes a construction unit 310 and an evaluation and judgment unit 320; the construction unit 310 is configured to construct an initial feasible solution of the transportation model, the carbon emission model and a capacity model preset by each vehicle by using a branch cutting algorithm as a frame, and optimize the initial feasible solution by simulated annealing to obtain a route initial solution; the evaluation and judgment unit 320 is configured to evaluate and judge the objective function value of each route initial solution according to a preset initial enumeration tree, and obtain information of each distribution route according to an evaluation result.
As shown in fig. 9, the evaluation determining unit 320 is a schematic structural diagram, and includes an evaluation subunit 321, a determining subunit 322, a first processing subunit 323, and a second processing subunit 324; the evaluation subunit 321 is configured to evaluate whether an objective function value of each route initial solution is an optimal value, and add the evaluated optimal objective function value to a root node defined by a preset enumeration tree; the judging subunit 322 is configured to judge whether the enumeration tree satisfies a termination condition; the first processing subunit 323 is configured to, if the enumeration tree satisfies the termination condition, use an initial solution of each route as information of each distribution route; the second processing subunit 324 is configured to, if the enumeration tree does not meet the termination condition, solve the linear programming problem of each model by using a branch cutting algorithm and continuously update the linear programming problem to obtain an optimal solution, and obtain all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
Further, to simplify the model parameters, the first model building module 100 comprises a transportation model building unit 110; a transportation model establishing unit 110 for obtaining distribution parameters of each vehicle, wherein the distribution parameters comprise an enabling parameter m of each vehicleabDistributed node parameters and distance parameters LabAccording to the enabling parameter mabNode parameter and distance parameter LabEstablishing a transportation model;
the transportation model is
Figure BDA0001599448700000141
Wherein Minimize represents the minimum total delivery distance; a denotes the a-th delivery node, b denotes the b-th delivery node, and s denotes the total number of delivery nodes(ii) a Distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter mabShowing the operation of the vehicle from the a-th delivery node to the b-th delivery node when m ab1 denotes vehicle start-up, m ab0 means that the vehicle is not active.
Further, in order to enhance the relevance between the two models and reduce the computation amount, the second model building module 200 includes a carbon emission model building unit 210; a carbon emission model establishing unit 210, configured to obtain load parameters of each vehicle, perform distance optimization on the transportation model, and establish a carbon emission model according to a distance optimization result and the load parameters;
the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h represents the vehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (6)

1. A polluted vehicle dispatching method based on simulated annealing and branch cutting optimization is characterized by comprising the following steps:
obtaining distribution parameters of each vehicle, and establishing a transportation model according to the distribution parameters;
acquiring load parameters of each vehicle, and establishing a carbon emission model according to the load parameters and a transportation model;
optimizing and calculating the transportation model, the carbon emission model and a preset capacity model of each vehicle by using a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route;
finishing the optimization of the polluted vehicle scheduling according to the distribution route information;
the method comprises the steps of carrying out optimization calculation on a transportation model, a carbon emission model and a preset capacity model of each vehicle by utilizing a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route, and specifically comprises the following steps;
constructing initial feasible solutions of the transportation model, the carbon emission model and a capacity model preset by each vehicle by taking a branch cutting algorithm as a frame, and optimizing the initial feasible solutions by simulated annealing to obtain a route initial solution;
evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree, and obtaining information of each distribution route according to an evaluation result;
the method comprises the following steps of evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree, and obtaining distribution route information according to an evaluation judgment result:
evaluating whether the objective function value of each route initial solution is an optimal value, and adding the optimum objective function value obtained through evaluation into a defined root node of a preset enumeration tree;
judging whether the enumeration tree meets a termination condition;
if the enumeration tree meets the termination condition, taking the initial solution of each route as the information of each distribution route;
if the enumeration tree does not meet the termination condition, solving the linear programming problem of each model by using a branch cutting algorithm, continuously updating to obtain an optimal solution, and obtaining all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
2. The method for dispatching the polluted vehicles based on simulated annealing and branch cutting optimization as claimed in claim 1, wherein the steps of obtaining the delivery parameters of each vehicle and establishing a transportation model according to the delivery parameters comprise the following steps:
obtaining distribution parameters of each vehicle, wherein the distribution parameters comprise starting parameters m of each vehicleabDistributed node parameters and distance parameters LabAccording to said enabling parameter mabNode parameter and distance parameter LabEstablishing a transportation model;
the transportation model is
Figure FDA0002780435410000021
Wherein Minimize represents the minimum total delivery distance; a represents the a-th distribution node, b represents the b-th distribution node, and s represents the total number of the distribution nodes; distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter mabShowing the operation of the vehicle from the a-th delivery node to the b-th delivery node when mab1 denotes vehicle start-up, mab0 means that the vehicle is not active.
3. The method for dispatching pollution vehicles based on simulated annealing and branch cutting optimization as claimed in claim 1, wherein the steps of obtaining the load parameters of each vehicle and establishing a carbon emission model according to the load parameters and a transportation model comprise the following steps:
acquiring load parameters of each vehicle, performing distance optimization on the transportation model, and establishing a carbon emission model according to a distance optimization result and the load parameters;
the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h-representation vehicleVehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load.
4. A pollution vehicle dispatching system based on simulated annealing and branch cutting optimization is characterized by comprising a first model building module, a second model building module, a route optimization module and a vehicle dispatching module;
the first model building module is used for obtaining distribution parameters of each vehicle and building a transportation model according to the distribution parameters;
the second model establishing module is used for acquiring the load parameters of each vehicle and establishing a carbon emission model according to the load parameters and the transportation model;
the route optimization module is used for carrying out optimization calculation on the transportation model, the carbon emission model and a preset capacity model of each vehicle by utilizing a simulated annealing algorithm and a branch cutting algorithm to obtain information of each distribution route;
the vehicle scheduling module is used for finishing the optimization of the polluted vehicle scheduling according to the distribution route information;
the route optimization module comprises a construction unit and an evaluation judgment unit;
the construction unit is used for constructing initial feasible solutions of the transportation model, the carbon emission model and a capacity model preset by each vehicle by taking a branch cutting algorithm as a frame, and optimizing the initial feasible solutions by simulated annealing to obtain a route initial solution;
the evaluation judgment unit is used for evaluating and judging the objective function value of each route initial solution according to a preset initial enumeration tree and obtaining information of each distribution route according to an evaluation result;
the evaluation judging unit comprises an evaluation subunit, a judging subunit, a first processing subunit and a second processing subunit;
the evaluation subunit is configured to evaluate whether an objective function value of each route initial solution is an optimal value, and add the evaluated optimal objective function value to a root node defined by a preset enumeration tree;
the judging subunit is configured to judge whether the enumeration tree satisfies a termination condition;
the first processing subunit is configured to, if the enumeration tree satisfies a termination condition, use an initial solution of each route as information of each distribution route;
the second processing subunit is configured to, if the enumeration tree does not meet the termination condition, solve the linear programming problem of each model by using a branch cutting algorithm and continuously update the linear programming problem to obtain an optimal solution, and obtain all integer solutions from fractional solutions separated from the optimal solution by using a simulated annealing algorithm; constructing an effective inequality for the integer solution, and separating the inequality by utilizing a greedy constructivity heuristic method so as to obtain new constraint; and re-optimizing the transportation model according to the effective constraint, returning to each model to continuously update the optimal solution until no new solution is separated, and creating nodes according to the updated optimal solution to add into the enumeration tree.
5. The simulated annealing and branch cut optimization-based contaminated vehicle dispatching system of claim 4, wherein said first model building module comprises a transportation model building unit;
the transportation model establishing unit is used for obtaining distribution parameters of each vehicle, and the distribution parameters comprise starting parameters m of each vehicleabDistributed node parameters and distance parameters LabAccording to said enabling parameter mabNode parameter and distance parameter LabEstablishing a transportation model;
the transportation model is
Figure FDA0002780435410000031
Wherein Minimize represents the minimum total delivery distance; a represents the a-th distribution node, b represents the b-th distribution node, and s represents the total number of the distribution nodes; distance parameter LabRepresenting the distance from the a-th delivery node to the b-th delivery node; enabling parameter mabRepresents fromStarting up the vehicles from the a-th distribution node to the b-th distribution node when m isab1 denotes vehicle start-up, mab0 means that the vehicle is not active.
6. The simulated annealing and branch cut optimization-based pollutant vehicle dispatching system of claim 4, wherein the second model building module comprises a carbon emission model building unit;
the carbon emission model establishing unit is used for acquiring the load parameters of each vehicle, performing distance optimization on the transportation model, and establishing a carbon emission model according to the distance optimization result and the load parameters;
the carbon emission model is CO2-Emission＝H×Sv×Kf；
Wherein, CO2-EmissionRepresents the minimum carbon dioxide emission; h represents the vehicle load; svRepresents the average distance traveled by the vehicle; kfAnd represents the carbon dioxide emission coefficient per kilometer of the vehicle on average and per unit load.
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