CN114186368A - Cable laying path optimization method based on ant colony algorithm - Google Patents

Cable laying path optimization method based on ant colony algorithm Download PDF

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CN114186368A
CN114186368A CN202111385999.2A CN202111385999A CN114186368A CN 114186368 A CN114186368 A CN 114186368A CN 202111385999 A CN202111385999 A CN 202111385999A CN 114186368 A CN114186368 A CN 114186368A
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郭放
陈晨
樊庆玲
宋晓帆
白萍萍
王辉
钱翌明
张浩杰
王晓敏
韩云昊
米阳
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Economic and Technological Research Institute of State Grid Henan Electric Power Co Ltd
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Abstract

The invention relates to a cable laying path optimization method based on an ant colony algorithm, which comprises the following steps: step S1, carrying out network modeling on the laying path of the cable equipment, and determining node information corresponding to the equipment and the connection relation between nodes; and step S2, based on pheromone limitation and self-adaptive adjustment of pheromone volatilization factors, calculating by adopting an ant colony path optimization algorithm to obtain the shortest path between the corresponding nodes of any two devices and the length of the shortest path. Compared with the prior art, the method has the advantages of considering various constraints, being suitable for multi-endpoint laying and being shortest in laying path.

Description

Cable laying path optimization method based on ant colony algorithm
Technical Field
The invention relates to the field of cable laying, in particular to a cable laying path optimization method based on an ant colony algorithm.
Background
With the high-speed development of economy in China and the gradual modernization of more and more industries, electrical design parts in a plurality of projects are complex and tedious, and cable laying is a very important link. The traditional cable laying method determines the length of the cable through a design drawing and manual calculation, has large errors and often causes the waste of the cable. The modern technical level is improved, three-dimensional cable laying software is frequently generated, factors such as cable laying paths, optimization and layering are comprehensively considered, and a three-dimensional cable laying diagram is automatically generated. How to achieve the shortest cable laying length is the core of cable laying, and belongs to the problem of path optimization.
At the present stage, scholars apply various intelligent algorithms to cable laying and obtain certain effects. When the Dijkstra algorithm is used for solving the cable laying problem of the pumped storage power station, the influence of constraint conditions such as channel capacity limitation and turning quantity on cable laying is considered, and functions such as three-dimensional model management and three-dimensional data management are realized by cable laying software CAB. However, the Dijkstra algorithm is a single-endpoint algorithm, and only one initial position can appear during the operation of the algorithm, so that the cable laying speed cannot be increased. And the algorithm and the Floyd algorithm can only realize the laying of two ends of the cable without considering the laying condition of the multi-end cable.
Li Zhi et al establishes a multi-objective planning model for cable laying optimization based on various condition restrictions in combination with cable laying related standards in a cable laying optimization research based on a genetic algorithm and an improved Dijkstra algorithm, obtains a cable laying route by using the Dijkstra algorithm, and meets the requirements of constraint conditions by using a greedy laying algorithm.
The ant colony algorithm is used as an intelligent algorithm for optimizing the cable laying path, has the advantages of positive feedback, self-organization, strong robustness and the like, is similar to the cable laying layout in a transformer substation by using the ant colony tree-shaped search path in nature, and is more suitable for optimizing the cable laying path.
In the application of the ant colony optimization algorithm in cable laying, the optimization ant colony algorithm is proposed for cable laying, but the method does not consider the existence of various constraint conditions in the cable laying process.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an ant colony algorithm optimization-based cable laying method which considers various constraints, is suitable for multi-endpoint laying and has the shortest laying path.
The purpose of the invention can be realized by the following technical scheme:
the invention provides an ant colony algorithm-based cable laying path optimization method, which comprises the following steps:
step S1, carrying out network modeling on the cable laying path, and determining node information corresponding to the equipment and the connection relation between nodes;
and step S2, based on pheromone limitation and self-adaptive adjustment of pheromone volatilization factors, calculating by adopting an ant colony path optimization algorithm to obtain the shortest path between the corresponding nodes of any two devices and the length of the shortest path.
Preferably, the step S1 is specifically:
the three-dimensional cable is projected to a horizontal plane, each device and the intersection are equivalent to form a node, an edge between two nodes represents that a cable channel exists between the devices, and an edge weight represents the length of the cable channel.
Preferably, the cable channel comprises a bridge, a cable trench and a pipe.
Preferably, the step S2 includes the following sub-steps:
step S21: initializing an ant colony path optimizing algorithm;
step S22, calculating the node transfer probability of ant colony path selection, and moving;
step S23, performing pheromone updating based on pheromone limitation and pheromone volatilization factor self-adaptive adjustment;
and S24, repeating the steps S22-S23, iteratively optimizing the ant colony path until the iteration times reach the maximum iteration times, and outputting the shortest path and the length of the shortest path.
Preferably, the step S1 is specifically: and initializing relevant parameters of the ant colony path optimization algorithm, wherein the relevant parameters comprise the ant colony number M, the maximum iteration number N, the pheromone enhancement coefficient Q, the pheromone influence factor alpha and the visibility influence factor beta.
Preferably, the node transition probability expression in step S22 is:
Figure BDA0003367050440000021
wherein the content of the first and second substances,
Figure BDA0003367050440000022
probability of selecting node j for ant k at node i
Figure BDA0003367050440000023
α is a pheromone influence factor, β is a visibility influence factor; tau isij(t)、τis(t) is a pheromone, the range of which is limited to a closed interval [ tau ]min,τmax]In which τ isminAnd τmaxRespectively representing a pheromone minimum value and a pheromone maximum value; etaij、ηis(t) is the visibility value, related to the distance between nodes; allowedkThe ant k is a set of nodes that have not been passed before the path to the target node.
Preferably, said visibility value ηijComprises the following steps:
Figure BDA0003367050440000031
wherein d isijIs the distance between node i and node j.
Preferably, in step S23, the pheromone updating expression is:
Figure BDA0003367050440000032
wherein rho is an pheromone volatilization factor, and the value range is between 0 and 1;
Figure BDA0003367050440000033
the sum of the left-over pheromones left between node i and node j in the iterative process of M ants.
Preferably, the pheromone volatilization factor ρ is adaptively adjusted by using a Gompertz growth function, and the expression is as follows:
Figure BDA0003367050440000034
wherein a, b and c are set constants; and x is the current iteration number.
Preferably, the legacy pheromone
Figure BDA0003367050440000035
The ant period model is adopted for calculation, and the expression is as follows:
Figure BDA0003367050440000036
wherein Q is a pheromone enhancement coefficient and is a set value; l iskThe length of all paths that the kth ant has traveled during the current iteration.
Compared with the prior art, the invention has the following advantages:
1) the method optimizes the ant colony algorithm from two aspects of pheromone limitation and pheromone volatilization factors, considers multiple constraints, overcomes the defects that the traditional ant colony algorithm is easy to fall into local optimum, has low convergence speed and the like, ensures the shortest cable laying path and greatly saves cable materials;
2) the Floyd algorithm can also be used for optimizing a cable laying path to obtain the shortest path, but the Floyd algorithm can only calculate the path lengths of two end points and has inherent limitations of the algorithm; compared with the Floyd algorithm, the ant colony algorithm adopted by the invention is more suitable for complex lines, and not only can cables between two end points be laid, but also multiple end points can be laid.
Drawings
FIG. 1 is a biological model of an ant colony algorithm;
FIG. 2 is a rack view of a cable;
FIG. 3 is a cross-sectional view of a cable;
FIG. 4 is a cable laying flow chart considering cable laying requirements during actual engineering construction;
FIG. 5 is a Gompertz function after coefficient assignment;
FIG. 6 is a flowchart of the ant colony algorithm based cabling method of the present invention;
fig. 7 is a schematic diagram of three-dimensional cable laying path network modeling in an embodiment.
FIG. 8 is a diagram showing the cable path optimization results of two devices in the embodiment;
FIG. 9 is a diagram showing the cable path optimization results of three devices in the embodiment;
fig. 10 is a diagram illustrating the cable path optimization results of four devices in the embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
The invention provides a cable laying path optimization method based on an ant colony algorithm, which starts from two aspects mainly for optimizing the cable laying path by adopting the ant colony algorithm,
1) pheromone definition: in the iterative process of the algorithm, ants can select several dominant paths, and pheromones on unselected paths gradually volatilize until completely disappear, so that the algorithm falls into a stagnation state. To this end, a maximum pheromone value and a minimum pheromone value are introduced, and the pheromone of the iterative process is limited to a range taumin≤τ≤τmaxIn addition, such a phenomenon can be suppressed.
2) Self-adaptive adjustment of pheromone volatilization factors: the pheromone volatilization factor has a value range between 0 and 1, and is a fixed value. If the value is too small, the volatilization speed of pheromones on a path which is not passed by ants in the iteration process is low, and pheromones still remain in the later stage of the algorithm, so that the convergence speed of the algorithm is influenced; if the pheromone volatilization factor is too large, the pheromone volatilization speed on some complex paths is high, the pheromone volatilization is easy to complete, and the algorithm is easy to fall into local optimum in the early stage.
For this purpose, Gompertz growth function is introduced to adaptively adjust the volatilization factor, as shown in fig. 5. The Gompertz model is an increasing function, and the Gompertz model starts to increase quickly, reaches a certain critical value, becomes slow, and finally approaches a certain maximum value, but never reaches the maximum value.
The formula for the Gompertz growth function is:
Figure BDA0003367050440000041
the Gompertz growth function is adaptively adjusted to increase the volatility factor as the number of iterations increases. In the early stage of the algorithm, the volatilization factor is small, the guiding capability to the algorithm is weak, the global search is facilitated, and the accuracy of the algorithm is improved. As the iteration times are increased, the volatilization factor is increased, and the convergence speed of the algorithm is increased. The values of alpha, beta and gamma can be flexibly selected, and the plasticity and the flexibility of the algorithm are improved.
The method of the present invention is introduced in detail by combining the optimization angle of the ant colony algorithm, and specifically comprises the following steps:
step S1, carrying out network modeling on the laying path of the cable equipment, and determining the node information corresponding to the equipment and the connection relation between the nodes, wherein the process specifically comprises the following steps:
projecting the three-dimensional cable to a horizontal plane, constructing a weighted graph, enabling each device and a cross to be equivalent to a node, enabling an edge between two points to represent existence of the devices, and enabling the edge weight to represent the length of a cable channel; the cable channel comprises a bridge, a cable trench and a pipeline;
step S2, based on pheromone restriction and adaptive adjustment of pheromone volatilization factors, calculating by using an ant colony optimization algorithm to obtain a shortest path and a length of the shortest path between corresponding nodes of any two devices, specifically including the following substeps:
step S21: and initializing relevant parameters of the ant colony path optimization algorithm, wherein the relevant parameters comprise the ant colony number M, the maximum iteration number N, the pheromone enhancement coefficient Q, the pheromone influence factor alpha and the visibility influence factor beta.
Step S22, calculating the node transfer probability of ant colony path selection, and moving;
Figure BDA0003367050440000051
wherein the content of the first and second substances,
Figure BDA0003367050440000052
probability of selecting node j for ant k at node i
Figure BDA0003367050440000053
α is a pheromone influence factor, β is a visibility influence factor; tau isij(t)、τis(t) is a pheromone, the range of which is limited to a closed interval [ tau ]min,τmax]In which τ isminAnd τmaxRespectively representing a pheromone minimum value and a pheromone maximum value; etaij、ηis(t) is visibility value, which is inversely proportional to the distance between nodes, and is expressed as
Figure BDA0003367050440000054
Wherein d isijIs the distance between node i and node j; allowedkThe ant k is a set of nodes which have not passed through before reaching the target node path;
step S23, performing pheromone updating based on pheromone limitation and self-adaptive adjustment of pheromone volatilization factors; the pheromone updating expression is as follows:
Figure BDA0003367050440000055
wherein rho is an pheromone volatilization factor, and the value range is between 0 and 1;
Figure BDA0003367050440000056
selecting a periant model for the sum of the left-over pheromones left between the node i and the node j in the M ant iteration processes;
the pheromone volatilization factor rho is adaptively adjusted by adopting a Gompertz growth function, and the expression is as follows:
Figure BDA0003367050440000061
wherein a, b and c are set constants; and x is the current iteration number.
The legacy pheromone
Figure BDA0003367050440000062
The ant period model is adopted for calculation, and the expression is as follows:
Figure BDA0003367050440000063
wherein Q is a pheromone enhancement coefficient and is a set value; l iskThe length of all paths that the kth ant has traveled during the current iteration.
And S24, repeating the steps S22-S23, iteratively optimizing the ant colony path until the iteration times reach the maximum iteration times, and outputting the shortest path and the length of the shortest path.
In the mathematical model of the ant colony algorithm, the following assumptions are made:
1) all ants have the same moving speed;
2) all ants release equal amounts of pheromone on the path traveled.
Example 1
The embodiment utilizes the substation cable laying path diagram to verify the effectiveness of the invention.
The Floyd algorithm can also be used for optimizing a cable laying path to obtain the shortest path, but the Floyd algorithm can only calculate the path lengths of two end points and has inherent limitations of the algorithm. Compared with the Floyd algorithm, the ant colony algorithm adopted by the invention is more suitable for complex lines, and not only can cables between two end points be laid, but also multiple end points can be laid. The biological model of the ant colony algorithm is shown in fig. 1.
The transformer substation is provided with outdoor distribution devices, indoor screen cabinets and other equipment for information transmission through cables, and the equipment such as cable ditches, bridges, pipelines and the like is required to load the cables, so that the transformer substation is a three-dimensional diagram. Wherein the cable support is shown in figure 2 and the cable is shown in cross-section in figure 3. The cable laying process comprises the processes of compiling a cable inventory, checking the cable, testing the insulation resistance and the voltage resistance of the cable, laying the cable, fixing the cable, protecting a pipe orifice from water, hanging a cable plate and checking and accepting, and a flow chart is shown in figure 4.
The cable laying length is basically kept unchanged by projecting the cable laying length to a horizontal plane. The optimization design of cable laying is realized through an ant colony algorithm, a weighted graph needs to be constructed firstly, each device or intersection is equivalent to a point for analysis, an edge between two points represents a cable channel, the edge weight represents the length of the cable channel, the cable length required by the connection position of the devices is ignored, and finally the device is abstracted as shown in fig. 7. Wherein equipment 1 represents the main controller of the main controller, equipment 8 represents the main control room equipment, and 9 represents the main transformer breaker terminal box.
The parameters taken in the algorithm are: the pheromone influence factor alpha is taken as 1, the visibility influence factor beta is taken as 5, the total number M of ants is taken as 50, the iteration number N is taken as 100, the pheromone intensity Q is taken as 1, and the maximum value rho of the volatilization coefficient is taken as 1maxTake 0.6.
In the path optimizing process, the ant colony algorithm searches paths node by node, and when facing multiple nodes, the next path is selected by a roulette method in cooperation with transition probability.
Cabling between the device 3 and the device 7 is performed as shown in fig. 8. In the first iteration process, ants on the node d have two paths to be selected, the ants calculate the transition probability by using the pheromone influence factors, the visibility values and other parameters to select the next path, and the next ants select the node e or the node c by using the same method. Ants arriving at node c will also have paths cb or cf to choose from until reaching the final node device 7. At the end of the first iteration, 3 paths will appear: the lengths of the equipment 3-d-e-h-i-j-k-l-equipment 7, the equipment 3-d-c-f-g-k-l-equipment 7 and the equipment 3-d-c-b-n-k-l-equipment 7 are inconsistent, and the residual pheromones on each path are inconsistent. In the second and subsequent iteration processes, the pheromone is continuously subjected to iteration change along with different paths passed by ants, and finally the iteration converges on the path equipment 3-d-c-f-g-k-L-equipment 7, wherein the length of the path is LkAnd (7) checking to meet the requirement of the shortest path. Optionally selecting other two points, and keeping fullAnd (4) a foot path optimization principle is adopted, and the initial requirements of cable laying are met.
Example 2
Cabling is performed between the three vertices of the device 1, the device 3 and the device 7 as shown in fig. 9. The rest is the same as in example 1.
After the first iteration process is finished, three laying paths are formed in total: 7-l-k-g-f-c- (d-device 3) - (b-a-device 1), 7-l-k-j-i-h-e-d- (device 3) - (c-b-a-device 1), 7-l-k-n-b- (a-device 1) - (c-d-device 3), the lengths are not uniform, and the pheromones remaining on each path are not uniform. In the second and subsequent iteration processes, the pheromone is continuously subjected to iteration change along with different paths passed by ants, and finally the iteration converges on path equipment 7-L-k-g-f-c- (d-equipment 3) - (b-a-equipment 1) and path length Lk167, it is verified that the shortest path laying requirement is met.
Example 3
Cabling is performed between the four vertices of device 1, device 3, device 7 and device 9 as shown in fig. 10. The rest is the same as in example 1.
Similarly, after the first iteration process is finished, four laying paths appear in total: device 7-l-k-n-b- (a-device 1) -c-d- (device 3) - (e-h-i-j-device 9), device 7-l-k-n-b- (a-device 1) -c- (d-device 3) - (f-g-k-j-device 9), device 7-l-k-j- (device 9) -i-h-e-d- (device 3) - (c-b-a-device 1), device 7-l-k- (j-device 9) -g-f-c- (d-device 3) - (b-a-device 1), the lengths are not uniform and the pheromones remaining on each path are not uniform. In the second and subsequent iteration processes, the pheromone is continuously subjected to iteration change along with different paths passed by ants, and finally the iteration converges on path equipment 7-L-k- (j-equipment 9) -g-f-c- (d-equipment 3) - (b-a-equipment 1) and path length LkAnd (222) according with the shortest path laying requirement after verification.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A cable laying path optimization method based on an ant colony algorithm is characterized by comprising the following steps:
step S1, carrying out network modeling on the cable laying path, and determining node information corresponding to the equipment and the connection relation between nodes;
and step S2, based on pheromone limitation and self-adaptive adjustment of pheromone volatilization factors, calculating by adopting an ant colony path optimization algorithm to obtain the shortest path between the corresponding nodes of any two devices and the length of the shortest path.
2. The ant colony algorithm-based cable laying path optimization method according to claim 1, wherein the step S1 specifically includes:
the three-dimensional cable is projected to a horizontal plane, each device and the intersection are equivalent to form a node, an edge between two nodes represents that a cable channel exists between the devices, and an edge weight represents the length of the cable channel.
3. The ant colony algorithm-based cable laying path optimization method according to claim 2, wherein the cable channel comprises a bridge, a cable trench and a pipeline.
4. The ant colony algorithm-based cable laying path optimizing method according to claim 1, wherein the step S2 comprises the following sub-steps:
step S21: initializing an ant colony path optimizing algorithm;
step S22, calculating the node transfer probability of ant colony path selection, and moving;
step S23, performing pheromone updating based on pheromone limitation and pheromone volatilization factor self-adaptive adjustment;
and S24, repeating the steps S22-S23, iteratively optimizing the ant colony path until the iteration times reach the maximum iteration times, and outputting the shortest path and the length of the shortest path.
5. The ant colony algorithm-based cable laying path optimization method according to claim 4, wherein the step S21 specifically includes: and initializing relevant parameters of the ant colony path optimization algorithm, wherein the relevant parameters comprise the ant colony number M, the maximum iteration number N, the pheromone enhancement coefficient Q, the pheromone influence factor alpha and the visibility influence factor beta.
6. The ant colony algorithm-based cable laying path optimizing method according to claim 4, wherein the node transfer probability expression in the step S22 is as follows:
Figure FDA0003367050430000011
wherein the content of the first and second substances,
Figure FDA0003367050430000021
probability of selecting node j for ant k at node i
Figure FDA0003367050430000022
α is a pheromone influence factor, β is a visibility influence factor; tau isij(t)、τis(t) is a pheromone, the range of which is limited to a closed interval [ tau ]min,τmax]In which τ isminAnd τmaxRespectively representing a pheromone minimum value and a pheromone maximum value; etaij、ηis(t) is the visibility value, related to the distance between nodes; allowedkThe ant k is a set of nodes that have not been passed before the path to the target node.
7. The ant colony algorithm-based cable laying path optimization method as claimed in claim 6, wherein the visibility value ηijComprises the following steps:
Figure FDA0003367050430000023
wherein d isijIs the distance between node i and node j.
8. The ant colony algorithm-based cable laying path optimizing method according to claim 6, wherein in the step S23, the pheromone updating expression is as follows:
Figure FDA0003367050430000024
wherein rho is an pheromone volatilization factor, and the value range is between 0 and 1;
Figure FDA0003367050430000025
the sum of the left-over pheromones left between node i and node j in the iterative process of M ants.
9. The ant colony algorithm-based cable laying path optimization method as claimed in claim 8, wherein the pheromone volatility factor p is adaptively adjusted by using a Gompertz growth function, and the expression is as follows:
Figure FDA0003367050430000026
wherein a, b and c are set constants; and x is the current iteration number.
10. The ant colony algorithm-based cable laying path optimization method according to claim 8, wherein the legacy pheromones
Figure FDA0003367050430000027
The ant period model is adopted for calculation, and the expression is as follows:
Figure FDA0003367050430000028
wherein Q is a pheromone enhancement coefficient and is a set value; l iskThe length of all paths that the kth ant has traveled during the current iteration.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270377A (en) * 2022-09-26 2022-11-01 浙江华东工程数字技术有限公司 Multi-cable optimal path planning method based on improved ant colony algorithm
CN116505435A (en) * 2023-04-15 2023-07-28 无锡广盈集团有限公司 Intelligent cable installation process correction method and system

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270377A (en) * 2022-09-26 2022-11-01 浙江华东工程数字技术有限公司 Multi-cable optimal path planning method based on improved ant colony algorithm
CN116505435A (en) * 2023-04-15 2023-07-28 无锡广盈集团有限公司 Intelligent cable installation process correction method and system
CN116505435B (en) * 2023-04-15 2024-04-26 无锡广盈集团有限公司 Intelligent cable installation process correction method and system

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