CN105260785B - Logistics distribution vehicle path optimization method based on improved cuckoo algorithm - Google Patents

Logistics distribution vehicle path optimization method based on improved cuckoo algorithm Download PDF

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CN105260785B
CN105260785B CN201510521483.4A CN201510521483A CN105260785B CN 105260785 B CN105260785 B CN 105260785B CN 201510521483 A CN201510521483 A CN 201510521483A CN 105260785 B CN105260785 B CN 105260785B
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屈迟文
何伟
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Abstract

The invention relates to a logistics distribution vehicle path optimization method based on an improved cuckoo algorithm, which is characterized by comprising the following steps of: step 1: setting parameters for improving the cuckoo algorithm; step 2: initializing a population and calculating a fitness value; wherein the population randomly generates size number of parasitic nests with the nd dimension search space range of [1, number ] by adopting a uniform distribution function; calculating the fitness value, firstly, locally optimizing the path in each line by adopting a 2-opt algorithm, and solving the sum of the path values of each optimized line by adopting a piecewise penalty function method to serve as the fitness value of the scheme; and step 3: executing levy walking operation of the parasitic nest; and 4, step 4: performing a parasitic nest discovery operation; and 5: performing a parasitic nest mutation operation; step 6: the discovery probability is dynamically adjusted. The method is applied to the solution of the logistics distribution vehicle path problem by combining the improved cuckoo algorithm and the 2-opt algorithm, provides a new feasible and effective solution for solving the logistics distribution vehicle optimization problem, and enriches the method for solving the logistics distribution path optimization problem.

Description

Logistics distribution vehicle path optimization method based on improved cuckoo algorithm
Technical Field
The invention relates to a logistics distribution vehicle path optimization method, in particular to a logistics distribution vehicle path optimization method based on an improved cuckoo algorithm.
Background
With the rapid development of modern economy and network technology, the logistics industry has become the "third source of profit" for modern enterprises. The total logistics cost of China in 2011 is up to 8.5 trillion yuan, which accounts for 17.8% of GDP. In each link of logistics, the transportation and distribution cost accounts for about 60% of the total logistics cost, and the overhigh logistics cost restricts the development of national economy and simultaneously weakens the market competitiveness of enterprises. The logistics distribution vehicle path optimization problem (VRP) is one of the most critical links in the logistics distribution optimization. The logistics distribution vehicle path optimization problem is a typical NP-hard problem, which was proposed by DantZig and Ramser in 1959, and mainly researches how to realize optimization of vehicle distribution cost under the condition of meeting customer requirements and other constraint conditions (such as vehicle maximum load, vehicle maximum forming distance and the like) in the logistics vehicle distribution process, such as: shortest path, least cost and the like. The problem has become a research hotspot in the field of operational research and combinatorial optimization.
In recent years, research on the logistics vehicle distribution path problem has mainly focused on solving the problem by adopting various heuristic algorithms. The King-iron monarch and the like provide a chaotic particle swarm optimization algorithm for solving the optimization problem of the logistics distribution path by combining the advantages of chaotic ergodicity and rapidity of particle swarm; the method for solving the logistics distribution optimization problem by improving the genetic algorithm proposed by Audort and the like provides an effective way for solving the optimization problem related to the logistics distribution optimization problem; wuyuanchun provides a method for applying a self-adaptive variation particle swarm algorithm to the problem optimization of a logistics distribution path; wang Huadong, Li Wei and the like propose a logistics distribution path optimization method of a particle swarm algorithm. The research on the logistics distribution optimization problem is limited to the application of traditional intelligent colony algorithms such as a genetic algorithm, a particle swarm algorithm, an ant colony algorithm and the like in the logistics distribution optimization problem. However, in solving the problem of the logistics distribution vehicle path, the single algorithm is prone to be trapped in a local optimal value, and optimization accuracy is low. The cuckoo algorithm adopts a Levy searching mode, so that the implementation is simple, the required set parameters are few, and the optimization precision and the convergence speed are superior to those of a particle swarm algorithm and a genetic algorithm.
Disclosure of Invention
The invention aims to solve the problem of realizing the route optimization of the logistics distribution vehicle by adopting a method based on an improved cuckoo algorithm. The technical scheme is as follows:
a method for solving the problem of improving the route of a logistics distribution vehicle based on a cuckoo algorithm comprises the following steps:
step 1: setting parameters of an algorithm, setting a population size, the number nd of service customers, the number of vehicles required for solving the problem, the load CarrayCarCan of the vehicles, and the discovery probability of the bird eggs in the parasitic nests
Figure 178585DEST_PATH_IMAGE001
Algorithm search spatial Range [1, number ]]The number of times of population iteration Max _ iter, and the iteration counter N _ iter = 1;
step 2: initializing population and calculating fitness value, and randomly generating size nd dimension search space range of [1, number ] by adopting uniform distribution function]The position of the ith parasitic nest is recorded as
Figure 95726DEST_PATH_IMAGE002
And rounding each nest with a ceil function (i.e.
Figure 937780DEST_PATH_IMAGE003
) To ensure that each customer site is served by a vehicle and calculate its corresponding fitness value
Figure 332989DEST_PATH_IMAGE004
；
And step 3: performing levy walk operations of parasitic nests, using
Figure 147361DEST_PATH_IMAGE005
And the updating mode generates a new parasitic nest position, compares the position with the position before levy migration is executed, and selects a parasitic nest with a better position to be reserved to the next generation.
And 4, step 4: performing a parasitic nest discovery operation to generate random numbers
Figure 969824DEST_PATH_IMAGE006
If, if
Figure 299174DEST_PATH_IMAGE007
And disturbing the parasitic nest to generate a new parasitic nest, comparing the position with the corresponding position before disturbance, and reserving the parasitic nest with a better position.
And 5: performing parasitic nest mutation operations using
Figure 498074DEST_PATH_IMAGE008
And (5) carrying out mutation operation on the parasitic nests.
Step 6: dynamically adjusting discovery probability, using
Figure 166953DEST_PATH_IMAGE009
Dynamically adjusting parasitic nest discovery probability
Figure 160317DEST_PATH_IMAGE010
In the middle of the term
Figure 976963DEST_PATH_IMAGE011
Representing the probability of finding that the t-th iteration is carried out;
Figure 713975DEST_PATH_IMAGE012
、
Figure 237360DEST_PATH_IMAGE013
maximum discovery probability and minimum discovery probability respectively;
Figure 667204DEST_PATH_IMAGE014
is the maximum iteration number;
Figure 971147DEST_PATH_IMAGE015
is the current iteration number. This method ensures that at the early stage of the algorithm, a greater rate of change of position is required due to the individual being further from the optimum; at the later stages of the algorithm, a smaller rate of change of position is required, since most of the solution is concentrated around the optimal position.
And 7: keeping the optimal position and the fitness of each search, judging whether the search result meets the requirements, and if so, judging whether the search result meets the requirements
Figure 246270DEST_PATH_IMAGE016
Go to Step 8, otherwise go to Step 3.
And 8: and outputting the optimal parasitic nest position and the corresponding fitness value thereof to obtain the optimal logistics distribution vehicle path scheme.
Further, the calculation steps of the fitness value are as follows:
step 1: determine the vehicles required for any logistics distribution scheme x by roadindex = unique (x), by [ row, car _ index [ ]]= size (roadindex) determine vehicle number car _ index, set fitness value
Figure 889741DEST_PATH_IMAGE017
The optimal distribution path total _ road of the current scheme;
step 2: determining a customer point served by each vehicle by subRout = find (Zx = = roadindex (i)), and forming a distribution path subRout formed by the current vehicle according to the size of a distribution number;
and step 3: optimizing each distribution path subRout by adopting a 2-opt algorithm so as to obtain an optimal path road for single vehicle distribution, and recording the sequence of the vehicle distribution paths: total _ road (subrout) = road;
and 4, step 4: calculating the length of the path which is passed by the current vehicle optimal path road;
and 5: calculating the sum _ q of the customer demands of the current vehicle optimal path road;
step 6: punishing the load exceeding the maximum load of the current vehicle by adopting a sectional penalty function method, and setting the punishment amount as follows: fp;
and 7: calculating the fitness value of the current optimal vehicle path road as follows:
Figure 224908DEST_PATH_IMAGE018
，
Figure 13216DEST_PATH_IMAGE019
；
and 8: judgment of
Figure 92031DEST_PATH_IMAGE020
If the condition is met, turning to the step 2, otherwise, turning to the step 9;
and step 9: outputting fitness value of scheme x
Figure 590008DEST_PATH_IMAGE021
And the current scheme optimal delivery path total _ road.
The improved cuckoo algorithm is adopted for planning vehicle dispatching for grouping, and then 2-opt algorithm is adopted for optimizing each line so as to obtain an optimal distribution line in each group.
The method provides a feasible and effective solution for solving the logistics vehicle distribution optimization problem, and enriches the method for solving the logistics distribution path optimization problem.
Drawings
FIG. 1 is a flow chart of the algorithm for solving the logistics distribution vehicle routing problem;
fig. 2 is a flow chart for solving the fitness value for each logistics distribution scheme.
Detailed Description
The technical solutions of the present invention are further explained in detail by the drawings and the specific examples, but the scope of the present invention is not limited thereto.
The implementation method for solving the logistics distribution vehicle path problem based on the improved cuckoo algorithm is disclosed by the embodiment. Referring to fig. 1, fig. 1 is a schematic flow chart of the algorithm, which includes the following steps:
① set the parameters of the algorithm, set the size of the group, the number of service clients nd, the number of vehicles required to solve the problem at present, set the load of the vehicles carraycaran. the probability of finding a bird egg in a nest in the basic cuckoo algorithm is usually set to a constant value, so that when the algorithm executes the operation of finding a nest in the basic cuckoo algorithm, the nest in either the superior or inferior position is replaced with the same probability, if the cluster is in the superior or inferior position
Figure 361655DEST_PATH_IMAGE022
If the value is set too small, the poor solution convergence in the optimization process is slow, if it is too small
Figure 374610DEST_PATH_IMAGE023
The value is set too large, and the solution of a better position is difficult to converge to the optimal solution, so the invention adopts a dynamic discovery mechanism:
Figure 257116DEST_PATH_IMAGE024
in the middle of the term
Figure 609600DEST_PATH_IMAGE025
Algorithm search spatial Range [1, number ]]The number of times of population iteration Max _ iter, and the iteration counter t = 1;
② initialize the population and calculate the fitness value the cost of transportation between the distribution center and each customer demand point is calculated, in this example, by targeting the distance between the points as pseudo code:
for i=1:nd
for j=1:nd
cost(i,j)=sqrt((xy(i,1)-xy(j,1))^2+(xy(i,2)-xy(j,2))^2);
end
end
where xy is the coordinates of each point.
Randomly generating size nd dimension search space range of [1, number ] by using uniform distribution function]The position of the ith parasitic nest is recorded as
Figure 614465DEST_PATH_IMAGE026
And rounding each nest with a ceil function (i.e.
Figure 52399DEST_PATH_IMAGE027
) (ii) a To ensure that each customer site is served by a vehicle and calculate its corresponding fitness value
Figure 473017DEST_PATH_IMAGE028
；
③ carry out levy walk operations of parasitic nests
Figure 945586DEST_PATH_IMAGE029
And a new parasitic nest position is generated in an updating mode, and because Levy distribution integral is difficult, equivalent calculation is realized by adopting a Mantegana algorithm, and the equivalent calculation is compared with the position before Levy migration is executed, so that the parasitic nest with a better position is selected and reserved to the next generation.
④ perform a nest discovery operation
Figure 121353DEST_PATH_IMAGE030
If, if
Figure 46583DEST_PATH_IMAGE031
And disturbing the parasitic nest to generate a new parasitic nest, comparing the position with the corresponding position before disturbance, and reserving the parasitic nest with a better position.
⑤ executing the parasitic nest mutation operation
Figure 270891DEST_PATH_IMAGE032
To hostThe living nests are subjected to mutation operation.
⑥ dynamically adjusting the probability of discovery
Figure 394705DEST_PATH_IMAGE033
Dynamically adjusting parasitic nest discovery probability
Figure 679056DEST_PATH_IMAGE034
In the middle of the term
Figure 91583DEST_PATH_IMAGE035
Representing the discovery probability of performing the Nth iter iteration;
Figure 261793DEST_PATH_IMAGE036
、
Figure 443376DEST_PATH_IMAGE037
maximum discovery probability and minimum discovery probability respectively;
Figure 633049DEST_PATH_IMAGE038
is the maximum iteration number;
Figure 532872DEST_PATH_IMAGE039
is the current iteration number. This method ensures that at the early stage of the algorithm, a greater rate of change of position is required due to the individual being further from the optimum; at the later stages of the algorithm, a smaller rate of change of position is required, since most of the solution is concentrated around the optimal position.
⑦ keeping the optimal position and its fitness for each search, determining whether the search result meets the requirement, and if so, determining whether the result meets the requirement
Figure 161299DEST_PATH_IMAGE040
Go to ⑧, otherwise go to ③.
⑧ outputs the optimal parasitic nest position and the corresponding fitness value to obtain the optimal logistics distribution vehicle path scheme.
The fitness value involved in the above solving step
Figure 462968DEST_PATH_IMAGE041
Referring to fig. 2, fig. 2 is a schematic flowchart of the fitness value solving, including the following steps:
step 1: determining vehicles required by any logistics distribution scheme x by roadindex = unique (x), and setting a fitness value
Figure 823542DEST_PATH_IMAGE042
The optimal distribution path total _ road of the current scheme;
step 2: determining a customer point served by the ith vehicle by subRout = find (Zx = = roadindex (i)), and forming a distribution path subRout formed by the current vehicle according to the size of a distribution number;
and step 3: optimizing each distribution path subRout by adopting a 2-opt algorithm so as to obtain an optimal path road for the ith vehicle distribution, and recording the sequence of the vehicle distribution paths: total _ road (subrout) = road;
and 4, step 4: calculating the length of the path which is passed by the current vehicle optimal path road;
and 5: calculating the sum _ q of the customer demands of the current vehicle optimal path road;
step 6: punishing the load exceeding the maximum load of the current vehicle by adopting a sectional penalty function method, and setting the punishment amount as follows: fp, the specific calculation method is as follows:
Figure 210661DEST_PATH_IMAGE043
Figure 645709DEST_PATH_IMAGE044
the violation degree of the solution on the constraint condition is represented and calculated by the following formula:
Figure 536304DEST_PATH_IMAGE045
Figure 333359DEST_PATH_IMAGE046
and (3) representing the penalty intensity, and calculating by adopting the following formula:
Figure 4512DEST_PATH_IMAGE047
Figure 178004DEST_PATH_IMAGE048
determining different punishment degrees for the multi-segment mapping function according to different violation degrees, wherein the punishment mode is calculated by adopting the following formula:
Figure 188686DEST_PATH_IMAGE049
and 7: calculating the fitness value of the current optimal vehicle path road as follows:
Figure 156642DEST_PATH_IMAGE050
，
Figure 315090DEST_PATH_IMAGE051
；
and 8: judging whether the vehicle is the last vehicle, if so, turning to the step 2, otherwise, turning to the step 9;
and step 9: outputting fitness value of scheme x
Figure 26695DEST_PATH_IMAGE052
And the current scheme optimal delivery path total _ road.

Claims (2)

1. A logistics distribution vehicle path optimization method based on an improved cuckoo algorithm is characterized by comprising the following steps of:
solving:
step 1: setting parameters of an algorithm, setting a population size, the number nd of service customers, the number of vehicles required for solving the problem, the load CarrayCarCan of the vehicles, and the discovery probability of the bird eggs in the parasitic nests
Figure 327450DEST_PATH_IMAGE001
Algorithm search spatial Range [1, number ]]The number of times of population iteration Max _ iter, and the iteration counter N _ iter = 1;
step 2: initializing population and calculating fitness value, and randomly generating size nd dimension search space range of [1, number ] by adopting uniform distribution function]The position of the ith parasitic nest is recorded as
Figure 557181DEST_PATH_IMAGE002
And rounding each nest with a ceil function, i.e.
Figure 612862DEST_PATH_IMAGE003
To ensure that each customer site is served by a vehicle and calculate its corresponding fitness value
Figure 429508DEST_PATH_IMAGE004
And step 3: performing levy walk operations of parasitic nests, using
Figure 228837DEST_PATH_IMAGE005
The updating mode generates a new parasitic nest position, compares the position with the position before levy walk execution, and selects the parasitic nest with better position to be reserved to the next generation, wherein
Figure 316004DEST_PATH_IMAGE006
Which represents a step-size control factor,
Figure 745848DEST_PATH_IMAGE007
as a function of column dimension distribution
Figure 49790DEST_PATH_IMAGE009
The parameters of (1);
and 4, step 4: performing a parasitic nest discovery operation to generate random numbers
Figure 387231DEST_PATH_IMAGE010
Disturbing the parasitic nest to generate a new parasitic nest, comparing the new parasitic nest with the corresponding position before disturbance, and reserving the parasitic nest with a better position;
and 5: performing parasitic nest mutation operations using
Figure DEST_PATH_IMAGE011
Carrying out mutation operation on the parasitic nests;
step 6: dynamically adjusting discovery probability, using
Figure 671449DEST_PATH_IMAGE012
Dynamically adjusting parasitic nest discovery probability
Figure DEST_PATH_IMAGE013
In the middle of the term
Figure 68932DEST_PATH_IMAGE014
Representing the probability of finding that the t-th iteration is carried out;
Figure DEST_PATH_IMAGE015
maximum discovery probability and minimum discovery probability respectively;
Figure 922488DEST_PATH_IMAGE016
is the maximum iteration number;
Figure DEST_PATH_IMAGE017
the current iteration number is; this method ensures that at the early stage of the algorithm, a greater rate of change of position is required due to the individual being further from the optimum; at the later stages of the algorithm, a smaller rate of change of position is required, since most of the solution is concentrated around the optimal position;
and 7: keeping the optimal position and the fitness of each search, judging whether the search result meets the requirements, and if so, judging whether the search result meets the requirements
Figure 627401DEST_PATH_IMAGE018
Then, the process goes to Step 8,otherwise, turning to Step 3;
and 8: and outputting the optimal parasitic nest position and the corresponding fitness value thereof to obtain the optimal logistics distribution vehicle path scheme.
2. The logistics distribution vehicle path optimization method based on the improved cuckoo algorithm as claimed in claim 1, wherein the calculation steps of the involved fitness values are as follows:
step 1: determine the vehicles required for any logistics distribution scheme x by roadindex = unique (x), by [ row, car _ index [ ]]= size (roadindex) determine vehicle number car _ index, set fitness value
Figure DEST_PATH_IMAGE019
The optimal distribution path total _ road of the current scheme;
step 2: determining a customer point served by each vehicle by subRout = find (Zx = = roadindex (i)), and forming a distribution path subRout formed by the current vehicle according to the size of a distribution number;
and step 3: optimizing each distribution path subRout by adopting a 2-opt algorithm so as to obtain an optimal path road for single vehicle distribution, and recording the sequence of the vehicle distribution paths: total _ road (subrout) = road;
and 4, step 4: calculating the length of the path which is passed by the current vehicle optimal path road;
and 5: calculating the sum _ q of the customer demands of the current vehicle optimal path road;
step 6: punishing the load exceeding the maximum load of the current vehicle by adopting a sectional penalty function method, and setting the punishment amount as follows: fp;
and 7: calculating the fitness value of the current optimal vehicle path road as follows:
Figure 187695DEST_PATH_IMAGE020
；
and 8: judgment of
Figure 21659DEST_PATH_IMAGE022
If the condition is met, turning to the step 2, otherwise, turning to the step 9;
and step 9: outputting fitness value of scheme x
Figure DEST_PATH_IMAGE023
And the current scheme optimal delivery path total _ road.
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CN106127295A (en) * 2016-06-21 2016-11-16 湘潭大学 A kind of Optimal Design of Pressure Vessel method based on self adaptation cuckoo Yu fireworks hybrid algorithm
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CN108388250B (en) * 2018-03-30 2021-03-05 哈尔滨工程大学 Water surface unmanned ship path planning method based on self-adaptive cuckoo search algorithm
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