CN112330006A - Optimal path planning method applied to logistics distribution based on improved ant colony algorithm - Google Patents

Optimal path planning method applied to logistics distribution based on improved ant colony algorithm Download PDF

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CN112330006A
CN112330006A CN202011182041.9A CN202011182041A CN112330006A CN 112330006 A CN112330006 A CN 112330006A CN 202011182041 A CN202011182041 A CN 202011182041A CN 112330006 A CN112330006 A CN 112330006A
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许琼
郝晓玲
谢季峰
王坤
李艳
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Southwest Petroleum University
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Abstract

The invention discloses an optimal path planning method based on an improved ant colony algorithm applied to logistics distribution in the technical field of path planning, which comprises the following steps: redefining the initial distribution of the pheromone content on each path, so that the initial distribution is not only related to the length of the path, but also related to the diversity of road choices connecting the transit points of the path; in addition, the invention also redefines the pheromone updating rule, so that the pheromone updating rule is limited by the iteration times and the historical optimal path length. Through the measures, the improved ant colony algorithm has high convergence speed and good optimizing performance, the optimal path can be found out quickly, and the distribution cost is reduced.

Description

Optimal path planning method applied to logistics distribution based on improved ant colony algorithm
Technical Field
The invention relates to the technical field of path planning, in particular to an ant colony algorithm aiming at the path planning problem, and specifically relates to an optimal path planning method applied to logistics distribution based on an improved ant colony algorithm.
Background
The classical ant colony algorithm has the problems of long search time and easy falling into local optimum in path planning. The invention redefines the initial distribution of pheromone content on each path, so that the initial distribution is not only related to the length of the path, but also related to the diversity of road choices connecting transfer points of the path; in addition, the invention also redefines the pheromone updating rule so that the pheromone updating rule is restricted by the iteration times and the historical optimal path length. Through the measures, the improved ant colony algorithm has high convergence speed and good optimizing performance, the optimal path can be found out quickly, and the distribution cost is reduced.
Disclosure of Invention
The present invention is directed to providing an optimal path planning method applied to logistics based on an improved ant colony algorithm to solve the above-mentioned problems.
In order to achieve the purpose, the invention provides the following technical scheme: the optimal path planning method applied to logistics distribution based on the improved ant colony algorithm comprises the following steps:
s1: parameters of the ant colony algorithm are improved, including the number M of ants, the constant quantity M of pheromone, and the maximum iteration number NCmaxIntensity Q of pheromone, minimum value τ of pheromone amountminAnd maximum value τmaxCarrying out initialization;
s2: calculating the quantity of pheromones on each path at the initial time, i.e. on the path (i, j)
Figure BDA0002750433910000011
The calculation formula of (2) is as follows:
Figure BDA0002750433910000021
in the formula (1), diTotal length of all paths to connect transit points i, djTotal length of all paths connecting transit points j, dijIs the distance between paths (i, j), M is the pheromone quantity constant;
s3: placing ants at randomThe city is initialized and added into a tabu corresponding to each antkPerforming the following steps;
s4: ant k allowed in optional citykWithin range, the cities to be transferred are calculated according to formulas and put into corresponding tabu tableskProbability of transfer of ant k from transfer point i to transfer point j
Figure BDA0002750433910000022
The calculation formula of (2) is as follows:
Figure BDA0002750433910000023
in the formula (2), s belongs to allowedkWhere alpha denotes an information elicitation factor, beta denotes a desired elicitation factor,
Figure BDA0002750433910000024
representing heuristic information values on the path (i, j),
Figure BDA0002750433910000025
the amount of residual pheromone on the path (i, j) at time t;
s5: if allowedkIf there are not found cities, the process continues to S4, otherwise, the process goes to S6,
s6: updating the pheromone persistence rho, wherein the pheromone persistence rho is calculated by the following formula:
Figure BDA0002750433910000026
NC in the formula (3) is the iteration number of the current loop, and NCmaxIs the maximum iteration number;
s7: updating pheromone concentration on each path
Figure BDA0002750433910000027
In the ant colony path node optimizing process, the real-time pheromone content range of each node follows the following rule:
Figure BDA0002750433910000031
in the formula (4), τminAnd τmaxFor the algorithm initial information, minimum and maximum values of the pheromone quantity are specified,
concentration of pheromone
Figure BDA0002750433910000032
The calculation formula is as follows:
Figure BDA0002750433910000033
Figure BDA0002750433910000034
in the formulae (5) and (6), m represents the number of ant colonies, ρ represents the pheromone persistence, (1- ρ) represents the pheromone attenuation, and Δ τijRepresenting the increment of the pheromone on the path (i, j) in the current cycle,
Figure BDA0002750433910000035
the pheromone quantity of the ant k left on the path (i, j) in the current cycle is represented by the following calculation formula:
when ant k passes (i, j) in this cycle:
Figure RE-GDA0002870251890000034
when ant k does not pass (i, j) in this cycle:
Figure RE-GDA0002870251890000035
in the formula (7), Q represents pheromone intensity,Lkrepresents the length of the path traveled by ant k in the current search, LbestThe optimal solution in the last iteration process is obtained;
s8: recording the optimal solution of the iteration, judging whether the optimal solution obtained by continuously iterating for 10 times from the beginning of the iteration has change, if not, changing the pheromones on all paths into the pheromone concentration of the latest improved result;
s9: emptying a tabukTable, iteration number NC + 1;
s10: and judging whether the current iteration number reaches a specified algebra or the solved number is not improved in a plurality of iterations, if so, outputting the obtained result, and otherwise, turning to S3 to perform a new search.
Compared with the prior art, the invention has the beneficial effects that: the invention improves the distribution condition of each path pheromone at the initial moment, so that the distribution of the pheromones is not only related to the length of the path, but also related to the number of paths connected with nodes at two ends, and the shorter the path, the more the number of the paths are connected, the larger the initial pheromone amount of the path is, thus realizing the rapid convergence of the algorithm; in addition, the improved pheromone updating mode and the pheromone persistence self-adaptive method can reduce local optimal interference of the algorithm and ensure that the optimal solution is rapidly output.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
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 only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the present invention provides a technical solution: the optimal path planning method applied to logistics distribution based on the improved ant colony algorithm comprises the following steps:
s1: parameters of the ant colony algorithm are improved, including the number M of ants, the constant quantity M of pheromone, and the maximum iteration number NCmaxMinimum value of pheromone intensity Q pheromone amount tauminAnd maximum value τmaxCarrying out initialization;
s2: calculating the quantity of pheromones on each path at the initial time, i.e. on the path (i, j)
Figure BDA0002750433910000041
The calculation formula of (2) is as follows:
Figure BDA0002750433910000051
in the formula (1), diTotal length of all paths to connect transit points i, djTotal length of all paths connecting transit points j, dijIs the distance between paths (i, j), M is the pheromone quantity constant; front half part
Figure BDA0002750433910000052
The number of cities connecting the transfer points i and j is considered, and the larger the number is, the larger the initial pheromone amount of the path is; the second half part
Figure BDA0002750433910000053
It indicates that the smaller the distance between the paths (i, j), the larger the amount of pheromone. By the method, the convergence speed of the algorithm can be effectively improved.
S3: randomly placing ants in an initial city, and simultaneously adding the city into a tabu corresponding to each antkPerforming the following steps;
s4: ant kAllowed in optional citieskCalculating the city to be transferred according to the formula (2) in the range, and putting the city into the corresponding tabu tablekProbability of transfer of ant k from transfer point i to transfer point j
Figure BDA0002750433910000054
The calculation formula of (2) is as follows:
Figure BDA0002750433910000055
in the formula (2), s belongs to allowedkWhere α denotes an information heuristic, β denotes an expected heuristic, and path (i, j) is the path between transit point i and transit point j,
Figure BDA0002750433910000056
representing heuristic information values on the path (i, j),
Figure BDA0002750433910000057
the amount of residual pheromone on the path (i, j) at time t; the present invention only considers the distance between two cities (or equivalently the cost of converted transportation).
S5: if allowedkIf there are not found cities, the process continues to S4, otherwise, the process goes to S6,
s6: updating the pheromone persistence rho, wherein the calculation formula of rho is as follows:
Figure BDA0002750433910000061
NC in the formula (3) is the iteration number of the current loop, and NCmaxIs the maximum iteration number;
when rho value is low, the pheromone is high in residue, the overall positive feedback effect of the pheromone is weakened, the randomness of the algorithm is increased, the method is suitable for the initial stage of the algorithm, and the aim of reducing the interference of a local optimal path can be achieved; when rho is large, the pheromone is low in residue, the algorithm can be quickly converged under the enhanced positive feedback effect, the randomness of the algorithm can be reduced, the method is suitable for later use, and the optimal solution is quickly output.
S7: updating pheromone concentration on each path
Figure BDA0002750433910000062
In the ant colony path node optimizing process, the real-time pheromone content range of each node follows the following rule:
Figure BDA0002750433910000063
in the formula (4), τminAnd τmaxFor the algorithm initial information, minimum and maximum values of the pheromone quantity are specified,
concentration of pheromone
Figure BDA0002750433910000064
The calculation formula is as follows:
Figure BDA0002750433910000065
Figure BDA0002750433910000066
in the formulae (5) and (6), m represents the number of ant colonies, ρ represents the pheromone persistence, (1- ρ) represents the pheromone attenuation, and Δ τijRepresenting the increment of the pheromone on the path (i, j) in the current cycle,
when ant k passes (i, j) in this cycle:
Figure RE-GDA0002870251890000067
when ant k does not pass (i, j) in this cycle:
Figure RE-GDA0002870251890000068
q represents pheromone intensity, LkRepresents the length of the travel path, L, in the current search of ant kbestAnd the optimal solution in the last iteration process is obtained. Wherein the length L of the travel path of the pheromone intensity Q along with the current search of the ant k is representedkIs increased and decreased, and arccot (L)best-Lk) The pheromone increment is dynamically adjusted by comparing the distance difference between the current search path of the ant k and the optimal path of the last iteration.
S8: recording the optimal solution of the iteration, judging whether the optimal solution obtained by continuously iterating for 10 times from the beginning of the iteration has change, if not, changing the pheromones on all paths into the pheromone concentration of the latest improved result;
s9: emptying a tabukTable, iteration number NC + 1;
s10: and judging whether the current iteration number reaches a specified algebra or the solved number is not improved in a plurality of iterations, if so, outputting the obtained result, and otherwise, turning to S3 to perform a new search.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, a schematic representation of the above terms does not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (1)

1. The optimal path planning method applied to logistics distribution based on the improved ant colony algorithm is characterized by comprising the following steps of: the method comprises the following steps:
s1: parameters of the ant colony algorithm are improved, including the number M of ants, the constant quantity M of pheromone, and the maximum iteration number NCmaxIntensity Q of pheromone, minimum value τ of pheromone amountminAnd maximum value τmaxCarrying out initialization;
s2: calculating the quantity of pheromones on each path at the initial time, i.e. on the path (i, j)
Figure RE-FDA0002870251880000011
The calculation formula of (2) is as follows:
Figure RE-FDA0002870251880000012
in the formula (1), diTotal length of all paths to connect transit points i, djTotal length of all paths connecting transit points j, dijIs the distance between paths (i, j), M is the pheromone quantity constant;
s3: randomly placing ants in an initial city, and simultaneously adding the city into a tabu corresponding to each antkPerforming the following steps;
s4: ant k allowed in optional citykWithin range, the cities to be transferred are calculated according to the formula and put into corresponding tabu tableskProbability of transfer of ant k from transfer point i to transfer point j
Figure RE-FDA0002870251880000013
The calculation formula of (2) is as follows:
Figure RE-FDA0002870251880000014
in the formula (2), s belongs to allowedkWhere alpha denotes an information elicitation factor, beta denotes a desired elicitation factor,
Figure RE-FDA0002870251880000015
representing heuristic information values on the path (i, j),
Figure RE-FDA0002870251880000016
the amount of residual pheromone on the path (i, j) at time t;
s5: if allowedkIf there are not found cities, the process continues to S4, otherwise, the process goes to S6,
s6: updating the pheromone persistence rho, wherein the pheromone persistence rho is calculated by the following formula:
Figure RE-FDA0002870251880000021
NC in the formula (3) is the iteration number of the current loop, and NCmaxIs the maximum iteration number;
s7: updating pheromone concentration on each path
Figure RE-FDA0002870251880000022
In the ant colony path node optimizing process, the real-time pheromone content range of each node follows the following rules:
Figure RE-FDA0002870251880000023
in the formula (4), τminAnd τmaxFor the algorithm initial information, minimum and maximum values of the pheromone quantity are specified,
concentration of pheromone
Figure RE-FDA0002870251880000024
The calculation formula is as follows:
Figure RE-FDA0002870251880000025
Figure RE-FDA0002870251880000026
in the formulae (5) and (6), m represents the number of ant colonies, ρ represents the pheromone persistence, (1- ρ) represents the pheromone attenuation, and Δ τijRepresenting the increment of the pheromone on the path (i, j) in the current cycle,
Figure RE-FDA0002870251880000027
the pheromone quantity of the ant k left on the path (i, j) in the current cycle is represented by the following calculation formula:
when ant k passes (i, j) in this cycle:
Figure RE-FDA0002870251880000028
when ant k does not pass (i, j) in this cycle:
Figure RE-FDA0002870251880000029
in the formula (7), Q represents pheromone intensity, LkRepresents the length of the path traveled by ant k in the current search, LbestThe optimal solution in the last iteration process is obtained;
s8: recording the optimal solution of the iteration, judging whether the optimal solution obtained by continuously iterating for 10 times from the beginning of the iteration has change, if not, changing the pheromone on all paths into the pheromone concentration of the latest improved result;
s9: emptying tabukTable, iteration number NC + 1;
s10: and judging whether the current iteration number reaches a specified algebra or the solved number is not improved in a plurality of iterations, if so, outputting the obtained result, and otherwise, turning to S3 to perform a new search.
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CN114610045A (en) * 2022-05-12 2022-06-10 南京铉盈网络科技有限公司 Robot path planning method and system based on improved ant colony algorithm
CN115032997A (en) * 2022-06-22 2022-09-09 江南大学 Fourth logistics transportation path planning method based on ant colony algorithm

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Application publication date: 20210205