CN112598153A - Traveler problem solving method based on longicorn stigma search algorithm - Google Patents

Traveler problem solving method based on longicorn stigma search algorithm Download PDF

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CN112598153A
CN112598153A CN202011319264.5A CN202011319264A CN112598153A CN 112598153 A CN112598153 A CN 112598153A CN 202011319264 A CN202011319264 A CN 202011319264A CN 112598153 A CN112598153 A CN 112598153A
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周宁宁
周一
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a traveler problem solving method based on a longicorn whisker search algorithm. Relates to the fields of combination optimization and path planning; the method comprises the following specific steps: 1. calculating the distance between each city to generate a distance matrix D; 2. initial parameters; 3. initializing a position X of a skynet herd; 4. obtaining the positions corresponding to the left and right beards in the current position respectively; 5. determining fitness value f (X) of left and right whiskersl),f(Xr) (ii) a 6. Obtaining a new position according to the position updating strategy, and performing correction operation; 7. calculating a fitness value f (X) of the current position and the obtained new positioni),
Figure DDA0002792310410000011
8. For random number r2Comparing with the local search probability p; 9. it is determined whether a maximum number of iterations has been reached. The invention applies the longicorn stigma search algorithm originally applied to the continuous domainThe problem of the traveling salesman is solved in a discrete domain, and the original thought of a longicorn must search algorithm is kept.

Description

Traveler problem solving method based on longicorn stigma search algorithm
Technical Field
The invention relates to the field of combination optimization and path planning, in particular to a traveler problem solving method based on a longicorn whisker search algorithm.
Background
The problem of the traveler:
the TSP Problem (tracking Salesman Problem) is translated into a Traveling Salesman Problem, a taro Problem, and is one of the well-known problems in the field of mathematics; it describes the following scenario: there is one traveler to visit each city, the number of cities is n, the restriction condition is that each city only visits once and all cities must all visit, the optimization goal is to minimize the total path length that the traveler walks through in the case of having visited all cities and eventually returning to the starting point. The classical TSP problem is that the path length between a point and a point is the linear distance between the point and the point.
The longicorn stigma search algorithm:
the longicorn stigma search algorithm is a novel biological heuristic intelligent optimization algorithm, which simulates the foraging behavior of the longicorn, the left and right tentacles can be used for sensing the odor intensity of food when the longicorn forages, if the odor intensity received by the left tentacle is large, the longicorn stigma search algorithm flies to the left with large odor intensity in the next step, otherwise, the longicorn stigma search algorithm flies to the right, the current position of the longicorn stigma search algorithm is a feasible solution of the problem, and the odor intensity of the food is a fitness function; the traditional longicorn stigma search algorithm is mostly used for solving the optimization problem of the continuity function and is difficult to solve the problem of dissociation and dispersion.
Disclosure of Invention
Aiming at the problems, the invention provides a traveler problem solving method based on a longicorn whisker search algorithm.
The technical scheme of the invention is as follows: a traveler problem solving method based on a longicorn whisker search algorithm comprises the following specific steps:
step (1.1), initializing coordinates of M cities, calculating distances among the cities, and generating a distance matrix D;
step (1.2), initializing parameters; setting a skynet population scale row N, the maximum iteration number MAX and the update probability p1Longhorn beetle individual XiThe distance d between the middle left whisker and the middle right whisker and the local search probability p;
step (1.3), initializing the position X of the longicorn herd, and calculating the individual X of the longicorn in the longicorn herdiThe fitness value f (X) of the longhorn beetle is recordediIndividual history of (2) optimal PbstAnd population history optimality Gbst；
Step (1.4), obtaining the positions corresponding to the left and right whiskers in the current position respectively: taking the distance d between the left and right whiskers as the random transformation frequency, and carrying out comparison on the current longicorn individual XiD times of transformation are carried out, and the generated new individual is used as a left whisker XlThen for the current longhorn beetle individual XiD times of transformation to generate left whisker XlDifferent new individuals as right beard Xr；
Step (1.5), determining the fitness values of the left and right whiskers as f (X) respectivelyl),f(Xr): such as the left beard XlFitness value f (X)l) Smaller than the right whisker XrFitness value f (X)r) Then calculate the current position shift of individual to the left whisker XlThe motion vector of (2); otherwise, calculating the current position of the individual to shift to the right whisker XrThe motion vector of (2);
step (1.6) according to longicorn individual XiObtaining the longicorn individual X by the position updating strategyiNew position of
Figure BDA0002792310390000021
And for the new position obtained
Figure BDA0002792310390000022
Carrying out correction operation;
step (1.7), calculating the fitness values of the current position and the obtained new position to be f (X) respectivelyi),
Figure BDA0002792310390000023
If the fitness value f (X) of the current positioni) Fitness value greater than new position
Figure BDA0002792310390000024
Then the longicorn individual X is updatediTo move it to a new location
Figure BDA0002792310390000025
Otherwise, keeping the current position unchanged;
step (1.8), enabling longicorn individuals XiMove to a new position
Figure BDA0002792310390000026
Then, the random number r between (0, 1) is generated2Comparing with the local search probability p if the random number r2If the probability is greater than the local search probability P, the local search operation is carried out, and then the individual historical optimal P is updatedbstAnd population history optimality Gbst(ii) a Otherwise, directly updating the individual history optimal PbstAnd population history optimality Gbst；
Step (1.9), judging whether the maximum iteration number is reached; and (4) if the iteration is finished, outputting the global optimal solution and the corresponding position thereof, otherwise, updating the parameters and returning to the step (1.4) to the step (1.8).
Further, in step (1.5), the longicorn individual XiLeft and right whisker fitness value f (X)l),f(Xr) As shown in the following formula:
Figure BDA0002792310390000027
Figure BDA0002792310390000028
in the formula, d (X)ij,Xj+1) Is longicorn individual XiThe distance between the jth city and the j +1 th city.
Further, in the step (1.6), a specific operation method of the location update policy is as follows:
(1.6.1) traversing longhorn beetle individual XiWill generate a random number r between (0, 1)1And the update probability p1Carrying out comparison;
(1.6.2) when the random number r1Greater than partial update probability p1If the current element is less than the current element, the current element is set to 0, which is specifically expressed as the following formulaShown in the figure:
Figure BDA0002792310390000029
in the formula (I), the compound is shown in the specification,
Figure BDA00027923103900000210
denotes the ith longicorn individual X at the t iterationi，
Figure BDA00027923103900000211
Which represents the motion vector(s) of the motion vector,
Figure BDA00027923103900000212
represents the ith longicorn individual XiThe location of the update.
Further, in the step (1.6), the specific operation steps for performing the correction are as follows:
(1.7.1) randomly ordering cities which do not appear in the sequence;
(1.7.2) sequentially assigning the sorted cities to the elements of 0 so as to obtain a sequence meeting the requirement.
In the step (1.8), the specific operation steps of performing the local search operation are as follows:
(1.8.1) generating two random numbers a and b (0< a, b < M), taking the smaller value of a and b as the initial position, taking the larger value as the end position, and carrying out reverse operation on the sequence;
(1.8.2) calculating the fitness value f (X) of the sequence after the reverse order, if the fitness value f (X) is better than the original sequence, updating, otherwise, keeping the original sequence unchanged.
Further, in the step (1.9), the updated parameter is longicorn individual XiThe distance d between the two left and right whiskers in the current position is specifically shown as follows:
dtemp＝dtemp*0.996
d＝floor(1+dtemp)
wherein d istempRepresentation updateThe latter temporal distance, floor (x), represents a rounding down, i.e., taking the smallest integer no greater than x.
The invention has the beneficial effects that: the method for solving the problem of the traveling salesman based on the longicorn silk search algorithm applies the longicorn silk search algorithm originally applied to the continuous domain to the discrete domain to solve the problem of the traveling salesman, and simultaneously keeps the original idea of the longicorn silk search algorithm.
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FIG. 1 is a flow chart of the architecture of the present invention;
FIG. 2 is a comparative schematic of an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the technical solution of the present invention, the following detailed description is made with reference to the accompanying drawings:
as depicted in fig. 1; a traveler problem solving method based on a longicorn whisker search algorithm comprises the following specific steps:
step (1.1), initializing coordinates of M cities, calculating distances among the cities, and generating a distance matrix D, wherein the distance matrix D is (D)1,D2,...,DM)；
Step (1.2), initializing parameters of an algorithm; setting a skynet population scale row N, a maximum iteration number MAX and an update probability p1Longhorn beetle individual XiThe distance d between the middle left whisker and the middle right whisker and the local search probability p;
step (1.3) of initializing a position X of a longicorn group, wherein X is (X)1,X2,...Xi,XM) In the formula, XiIs a longicorn individual; calculating individual X of longhorn beetles in longhorn beetle groupiThe fitness value f (X) of the individual is recorded, and the optimal P of the individual history is recordedbstAnd population history optimality Gbst；
Step (1.4), obtaining the positions corresponding to the left and right whiskers in the current position respectively: taking the distance d between the left and right whiskers as the random transformation frequency, and carrying out comparison on the current longicorn individual XiPerforming secondary transformation to generate new individual as left whisker XlThen for the current longhorn beetle individual XiD times of transformation to generate left whisker XlDifferent new individuals are used as the right beard Xr；
Step (1.5), determining the fitness values of the left and right whiskers as f (X) respectivelyl),f(Xr): such as the left beard XlFitness value f (X)l) Smaller than the right whisker XrFitness value f (X)r) Then calculate the current position shift of individual to the left whisker XlThe motion vector of (2); otherwise, calculating the current position of the individual to shift to the right whisker XrThe motion vector of (2);
step (1.6) according to longicorn individual XiObtaining the longicorn individual X by the position updating strategyiNew position of
Figure BDA0002792310390000041
And for the new position obtained
Figure BDA0002792310390000042
Carrying out correction operation;
step (1.7), calculating the fitness values of the current position and the obtained new position to be f (X) respectivelyi),
Figure BDA0002792310390000043
If the fitness value f (X) of the current positioni) Fitness value greater than new position
Figure BDA0002792310390000044
Then the longicorn individual X is updatediTo move it to a new location
Figure BDA0002792310390000045
Otherwise, keeping the current position unchanged;
step (1.8), enabling longicorn individuals XiMove to a new position
Figure BDA0002792310390000046
Then, the random number r between (0, 1) is generated2Comparing with the local search probability p if the random number r2Is greater thanIf the local search probability P is high, the local search operation is carried out, and then the individual historical optimal P is updatedbstAnd population history optimality Gbst(ii) a Otherwise, directly updating the individual history optimal PbstAnd population history optimality Gbst；
Step (1.9), judging whether the maximum iteration number is reached; and (4) if the iteration is finished, outputting the global optimal solution and the corresponding position thereof, otherwise, updating the parameters and returning to the step (1.4) to the step (1.8).
Further, in step (1.5), the longicorn individual XiLeft and right whisker fitness value f (X)l),f(Xr) As shown in the following formula:
Figure BDA0002792310390000047
Figure BDA0002792310390000048
in the formula, d (X)ij,Xj+1) Is longicorn individual XiThe distance between the jth city and the j +1 th city.
Further, in the step (1.6), a specific operation method of the location update policy is as follows:
(1.6.1) traversing longhorn beetle individual XiWill generate a random number r between (0, 1)1And the update probability p1Carrying out comparison;
(1.6.2) when the random number r1Greater than the update probability p1If the current element is less than the current element, the current element is set to 0, which is specifically shown as the following formula:
Figure BDA0002792310390000049
in the formula (I), the compound is shown in the specification,
Figure BDA00027923103900000410
denotes the ith longicorn individual X at the t iterationi，
Figure BDA00027923103900000411
Which represents the motion vector(s) of the motion vector,
Figure BDA00027923103900000412
represents the ith longicorn individual XiThe location of the update.
Further, in the step (1.6), the specific operation steps for performing the correction are as follows:
(1.7.1) randomly ordering cities which do not appear in the sequence;
(1.7.2) sequentially assigning the sorted cities to the elements of 0 so as to obtain a sequence meeting the requirement.
Further, in the step (1.8), the specific operation steps of performing the local search operation are as follows:
(1.8.1) generating two random numbers a and b (0< a, b < M), taking the smaller value of a and b as the initial position, taking the larger value as the end position, and carrying out reverse operation on the sequence;
(1.8.2) calculating the fitness value f (X) of the sequence after the reverse order, if the fitness value f (X) is better than the original sequence, updating, otherwise, keeping the original sequence unchanged.
Further, in the step (1.9), the updated parameter is longicorn individual XiThe distance d between the two left and right whiskers in the current position is specifically shown as follows:
dtemp＝dtemp*0.996
d＝floor(1+dtemp)
wherein d istempIndicating the updated temporal distance, floor (x) indicates rounding down, i.e., taking the smallest integer no greater than x.
Aiming at the problem of the traveling salesman, the longicorn whisker algorithm is discretized, and a local search algorithm is added in the algorithm, so that the algorithm is prevented from falling into a local optimal solution in the later stage:
1. position of longicorn:
according to the characteristics of the TSP problem, the position of the ith longicorn is defined as the path of the traversed city, and is represented by the following form:
Xi＝(xi1,xi2,....,xin)
wherein n is the total number of cities, (i ═ 1,2, 3.. Q, Q is the population size); xiThe city path traversed by the ith longicorn is represented as x1→x2....→xn；(xi1,xi2,....,xin) X in (2)ijNumber representing the city traversed by the longicorn i-th time.
2. Fitness function:
define a solution X ═ X1,x2,...,xN) Representing the order of traversing the cities; taking the length of the traversal path as the fitness function F (x)
Figure BDA0002792310390000051
Wherein the content of the first and second substances,
Figure BDA0002792310390000052
being the distance between two cities, the performance of the solution is better when f (x) is smaller.
The specific embodiment is as follows:
(1) the experimental conditions were set as follows:
population number 100, city number 29, local search probability 0.5, update probability 0.5 and maximum iteration number 1000
(2) A fitness function of
Figure BDA0002792310390000061
Wherein d (X)ij,Xj+1) Is longicorn individual XiThe distance between the jth city and the j +1 th city.
Specifically, 1, loading 29 city coordinates, calculating the distance between each city, and generating a distance matrix;
2. setting the number of the population as 100, updating the probability p10.5, longicorn individual XiThe distance d between the left whisker and the right whisker is 20, and the local search probability p is 0.5;
3. initializing the position X ═ X of the longicorn herd (X)1,X2,...,XM) In the formula, XiIs a longicorn individual; calculating the fitness value f (X) of the individuals in the cow group according to the initialization result, and simultaneously recording the optimal historical P of the individualsbstAnd population history optimality Gbst；
4. For current longhorn beetle individual XiD times of transformation are carried out, and the generated new individual is used as a left whisker XlThen for the current individual XiD times of transformation generation and left whisker XlDifferent individuals as right whiskers Xr；
5. If f isleft≤frightThen the current position X is calculatediAnd the left palpus XlIf f is a motion vector ofright<fleftThen the current position X is calculatediAnd the right palpus XrA motion vector between;
Figure BDA0002792310390000062
v＝Xi-Xtemp
wherein v represents a number from XiTo XtempAt the time of transfer, XiThe motion vector of the element in (1) shifted to the right, fleftIs the fitness value of the left beard, frightThe fitness value of the right beard;
6. traversing each element in an individual, generating a random number r between (0, 1)1And the update probability p1Making a comparison if r1>p1If so, the current element is updated, otherwise, the current element is updated
Figure BDA0002792310390000063
Set the current element in (1) to 0;
Figure BDA0002792310390000064
7. to pair
Figure BDA0002792310390000065
Performing a correction operation, will not appear in
Figure BDA0002792310390000066
Randomly arranging the middle cities, and sequentially assigning the arranged cities to the elements of 0;
8. computing
Figure BDA0002792310390000067
And position
Figure BDA0002792310390000068
Respectively has a fitness value of
Figure BDA0002792310390000069
If it is
Figure BDA00027923103900000610
Figure BDA00027923103900000611
Then the individual location is updated to
Figure BDA00027923103900000612
Otherwise, keeping the position of the individual unchanged;
9. generating a random number r between (0, 1)2Comparing with the local search probability p if r2>p, local search is carried out, otherwise, the step 10 is carried out;
10. calculating the fitness value f (X) of the current individual and the historical optimal P of the individualbstAnd population history optimality GbstMaking a comparison if f (X)<PbstIf so, updating the individual historyPreferably f (X), if f (X)<GbstIf the updated group history is optimal to be f (X);
if f(X)<Pbst Then Pbst＝f(X)
if f(X)<Gbst Then Gbst＝f(X)
11. judging whether the maximum iteration times is reached, if so, outputting the optimal population and the corresponding individual, otherwise, updating the distance between the left and right whiskers of the longicorn, and then turning to the step (1.4); the result is shown in fig. 2 by computer simulation.
Finally, it should be understood that the embodiments described herein are merely illustrative of the principles of embodiments of the present invention; other variations are possible within the scope of the invention; thus, by way of example, and not limitation, alternative configurations of embodiments of the invention may be considered consistent with the teachings of the present invention; accordingly, the embodiments of the invention are not limited to the embodiments explicitly described and depicted.

Claims (6)

1. A traveler problem solving method based on a longicorn whisker search algorithm is characterized by comprising the following specific steps:
step (1.1), initializing coordinates of M cities, calculating distances among the cities, and generating a distance matrix D;
step (1.2), initializing parameters; setting a skynet population scale row N, a maximum iteration number MAX and an update probability p1Longhorn beetle individual XiThe distance d between the middle left whisker and the middle right whisker and the local search probability p;
step (1.3), initializing the position X of the longicorn herd, and calculating the individual X of the longicorn in the longicorn herdiFitness value f (X)i) Recording longicorn individuals XiIndividual history of (2) optimal PbstAnd population history optimality Gbst；
Step (1.4), obtaining the positions corresponding to the left and right whiskers in the current position respectively: taking the distance d between the left and right whiskers as the random transformation frequency, and carrying out comparison on the current longicorn individual XiD times of transformation are carried out, and the generated new individual is used as a left whisker XlThen for the current longhorn beetle individual XiIs carried out d timesTransforming, generating and left whisker XlDifferent new individuals as right beard Xr；
Step (1.5), determining the fitness values of the left and right whiskers as f (X) respectivelyl),f(Xr): such as the left beard XlFitness value f (X)l) Smaller than the right whisker XrFitness value f (X)r) Then calculate the current position shift of individual to the left whisker XlThe motion vector of (2); otherwise, calculating the current position of the individual to shift to the right whisker XrThe motion vector of (2);
step (1.6) according to longicorn individual XiObtaining the longicorn individual X by the position updating strategyiNew position of
Figure FDA0002792310380000011
And for the new position obtained
Figure FDA0002792310380000012
Carrying out correction operation;
step (1.7), calculating the fitness value of the current position and the obtained fitness value of the new position respectively
Figure FDA0002792310380000013
If the fitness value f (X) of the current positioni) Fitness value greater than new position
Figure FDA0002792310380000014
Then the longicorn individual X is updatediTo move it to a new location
Figure FDA0002792310380000015
Otherwise, keeping the current position unchanged;
step (1.8), enabling longicorn individuals XiMove to a new position
Figure FDA0002792310380000016
Then, the random number r between (0, 1) is generated2In contrast to the local search probability p,if a random number r2If the probability is greater than the local search probability P, the local search operation is carried out, and then the individual historical optimal P is updatedbstAnd population history optimality Gbst(ii) a Otherwise, directly updating the individual history optimal PbstAnd population history optimality Gbst；
Step (1.9), judging whether the maximum iteration number is reached; and (4) if the iteration is finished, outputting the global optimal solution and the corresponding position thereof, otherwise, updating the parameters and returning to the step (1.4) to the step (1.8).
2. The method for solving the problem of traveling salesman based on longicorn silk search algorithm as claimed in claim 1, wherein in step (1.5), said longicorn individual XiLeft and right whisker fitness value f (X)l),f(Xr) As shown in the following formula:
Figure FDA0002792310380000017
Figure FDA0002792310380000018
in the formula, d (X)ij,Xj+1) Is longicorn individual XiThe distance between the jth city and the j +1 th city.
3. The method for solving the traveling salesman problem based on the longitudian whisker search algorithm as claimed in claim 1, wherein in the step (1.6), the specific operation method of the location update strategy is as follows:
(1.6.1) traversing longhorn beetle individual XiWill generate a random number r between (0, 1)1And the update probability p1Carrying out comparison;
(1.6.2) when the random number r1Greater than the update probability p1When the position is changed, the corresponding element in the position is updated to generate a temporary individualAnd if the current element is less than the position, setting the current element to be 0, which is specifically shown as the following formula:
Figure FDA0002792310380000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002792310380000022
denotes the ith longicorn individual X at the t iterationi，
Figure FDA0002792310380000023
Which represents the motion vector(s) of the motion vector,
Figure FDA0002792310380000024
denotes the ith longicorn individual XiUpdated position, r1Is a random number between (0, 1) and is used to compare with the update probability.
4. The method for solving the problem of the traveling salesman based on the longicorn whisker search algorithm as claimed in claim 1, wherein in the step (1.6), the concrete operation steps for correction are as follows:
(1.7.1) randomly ordering cities which do not appear in the sequence;
(1.7.2) sequentially assigning the sorted cities to the elements of 0 so as to obtain a sequence meeting the requirement.
5. The method for solving the traveling salesman problem based on the longicorn whisker search algorithm as claimed in claim 1, wherein in the step (1.8), the specific operation steps for performing the local search operation are as follows:
(1.8.1) generating two random numbers a and b (0< a, b < M), taking the smaller value of a and b as the starting position, taking the larger value as the ending position, and carrying out reverse operation on the sequence;
(1.8.2) calculating the fitness value f (X) of the sequence after the reverse order, if the fitness value f (X) is better than the original sequence, updating, otherwise, keeping the original sequence unchanged.
6. The method for solving the traveling salesman problem based on longicorn silk search algorithm as claimed in claim 1, wherein in said step (1.9), said updated parameter is longicorn individual XiThe distance d between the two left and right whiskers in the current position is specifically shown as follows:
dtemp＝dtemp*0.996
d＝floor(1+dtemp)
wherein d istempIndicating the updated temporal distance, floor (x) indicates rounding down, i.e., taking the smallest integer no greater than x.
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CN113434982A (en) * 2021-07-07 2021-09-24 合肥工业大学 Inverse kinematics solution method of electric intelligent bionic climbing robot
CN113434982B (en) * 2021-07-07 2022-09-27 合肥工业大学 Inverse kinematics solution method of electric intelligent bionic climbing robot

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