CN112149830A - IJAYAGA algorithm based on wavelet variation - Google Patents

IJAYAGA algorithm based on wavelet variation Download PDF

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CN112149830A
CN112149830A CN202010852795.4A CN202010852795A CN112149830A CN 112149830 A CN112149830 A CN 112149830A CN 202010852795 A CN202010852795 A CN 202010852795A CN 112149830 A CN112149830 A CN 112149830A
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李恩龙
袁志鹏
李振龙
赵海波
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CRRC Changchun Railway Vehicles Co Ltd
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Abstract

The technical scheme of the invention has the advantages of clear principle and simple design, and aims at solving the problems that the solving speed of the optimization problem in the engineering optimization field is low, the optimization problem is easy to fall into the local optimal solution and the like in the solving process, the IJAYAGA algorithm based on the wavelet variation is adopted, the improved JAYA algorithm is used for guiding the solution updating direction, the update towards the inferior solution direction is avoided, and the solving speed is accelerated; in the population variation process, wavelet variation is utilized to increase population diversity, and better populations are selected in a competitive mode to eliminate poor variation individuals, so that the diversity of solutions is increased, the probability that the solutions fall into local optimum in the solving process is reduced, the solutions are updated towards the direction of the global optimum solution at a higher speed, and a reliable and quick solution optimization scheme is provided for engineering optimization problems such as traffic flow prediction, traffic scheduling and the like.

Description

IJAYAGA algorithm based on wavelet variation
Technical Field
The invention relates to the field of intelligent algorithm optimization, in particular to a self-adaptive regeneration genetic algorithm based on population similarity.
Background
Optimization problems are one of the major problems in engineering practice and scientific research. The solution of the optimization problem mainly comprises an analytic method and an intelligent bionic algorithm:
the analytical method is only suitable for the condition that the target function and the constraint condition have obvious analytical expressions. The solving method comprises the following steps: the optimal necessary conditions are firstly solved to obtain a set of equations or inequalities, then the set of equations or inequalities is solved, the necessary conditions are generally solved by a derivative method or a variational method, and the problem is simplified through the necessary conditions. However, the optimization problem in real life is complex or cannot be described by a variable display function, and an optimal point can be searched by adopting an intelligent bionic algorithm through a plurality of iterations. However, most intelligent bionic algorithms, such as genetic algorithms, have gradually reduced population diversity along with the continuous evolution process, have high probability of falling into local optimum, and are easy to lose the optimum solution.
Disclosure of Invention
The invention aims to provide an IJAYAGA algorithm based on wavelet variation, which can reduce the probability of local optimum of the traditional genetic algorithm and accelerate the convergence speed of the optimization algorithm under the condition of not losing the optimal solution, and provides a reliable and rapid solution optimization scheme for the engineering optimization problems of traffic flow prediction, traffic scheduling and the like.
In order to achieve the above object, the present invention provides an IJAYAGA algorithm based on wavelet variation, which is characterized by comprising the following steps:
step1 evaluation: calculating individual fitness values, sequencing the individual fitness values, and selecting an optimal individual and a worst individual;
step2 individual update: calculating a self-adaptive guiding operator, and updating individuals to generate a new population;
step3 population selection: calculating individual fitness, and selecting individuals to generate a selected population by roulette;
step4 intersection: calculating a crossover operator, and generating a crossover population by crossing individuals;
step5 wavelet mutation: calculating wavelet mutation operators, generating a variant population by individual mutation, and mixing a cross population and the variant population to generate a new population;
step6 random competition selection: randomly selecting a plurality of individuals, calculating the scores of the individuals, and carrying out competitive comparison to generate a new population.
Further, the specific process of individual update is as follows:
step2.1 calculates the adaptive pilot operator w:
Figure BDA0002645321440000021
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)
Figure BDA0002645321440000022
And worst solution
Figure BDA0002645321440000023
Guiding the individual to update towards the direction of the optimal solution, avoiding the update towards the direction of the inferior solution, and calculating the updated individual
Figure BDA0002645321440000024
Figure BDA0002645321440000025
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness value
Figure BDA0002645321440000026
Fitness value of original individual
Figure BDA0002645321440000027
Comparing, and selecting better individuals
Figure BDA0002645321440000028
Figure BDA0002645321440000029
Step2.4 updates the count value, i.e. i is equal to i + 1. If the condition that i is less than or equal to N is met, executing the step Step2.1, and taking N newly generated individuals as a new population.
Further, the specific process of population selection is as follows:
step3.1 calculate fitness value for each individual in the population P (k)
Figure BDA0002645321440000031
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Figure BDA0002645321440000032
Figure BDA0002645321440000033
Step3.3 calculation of cumulative probability of Each individual in the population P (k)
Figure BDA0002645321440000034
Figure BDA0002645321440000035
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
step3.5 amino acid sequence
Figure BDA0002645321440000036
Then individual 1 is selected; if it is
Figure BDA0002645321440000037
Selecting an individual i;
step3.6 Step3.4 and Step3.5 were repeated until N individuals were selected, which were called the selection population.
Further, the specific process of interleaving is as follows:
step4.1 randomly selects two individuals p and q from the population P (k), and p is not equal to q;
step4.2 computing adaptive crossover operator Pc
Figure BDA0002645321440000038
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q
Figure BDA0002645321440000039
Wherein:
Figure BDA00026453214400000310
the genotype at the mth locus representing individual p,
Figure BDA00026453214400000311
denotes the genotype of the M-th locus of an individual q, M being the length of each individual in the population.
Step4.4 Generation of random number γcSatisfy 0. ltoreq. gammac≤1;
If Step4.5 satisfies Sp,qLess than or equal to gammac≤pcIf yes, the step Step4.6 is executed, otherwise, the step Step4.1 is executed;
step4.6 generates a random number n, wherein n is more than or equal to 1 and less than or equal to M;
step4.7 performing a single point crossover operation on individuals p and q at the nth locus;
step4.8 performed Step4.1-Step4.7 a total of N/2 times.
Further, the specific process of wavelet mutation is as follows:
step5.1 calculation of the population P (k) for each individual
Figure BDA0002645321440000041
Wavelet mutation operator:
Figure BDA0002645321440000042
wherein:
Figure BDA0002645321440000043
Figure BDA0002645321440000044
is a variation constant;
step5.2 for each individual of P (k) in the population
Figure BDA0002645321440000045
Carrying out individual wavelet variation to obtain corresponding variant individuals
Figure BDA0002645321440000046
Figure BDA0002645321440000047
Step5.3 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step Step5.1 is carried out to execute the mutation process. Generating a new variant population;
step5.4 adds a new variant population to the original population, generating a new population with 2N individuals.
Further, the specific process of random competition selection is as follows:
step6.1 randomly selecting Q individuals from 2N individuals to form a test population, and combining the individuals
Figure BDA0002645321440000048
The fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recorded
Figure BDA0002645321440000049
The times of the individuals in the Q are better than or equal to the times of the individuals in the Q, and the individuals are obtained by calculation
Figure BDA00026453214400000410
Fraction S ofi
Figure BDA00026453214400000411
Step6.2 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step is changed to step Step6.1 to calculate the score S of each individuali
Step6.3 score S for individuals in population P (k)iAnd sorting, and selecting N individuals with higher scores to form a next generation new population.
The technical scheme has the advantages of clear principle and simple design, and aiming at the problems that the solving speed is low, the local optimal solution is easy to fall into and the like in the solving process of the optimization problem in the engineering optimization field, the IJAYAGA algorithm based on wavelet variation is adopted, the improved JAYA algorithm is utilized to guide the solution updating direction, the update towards the inferior solution direction is avoided, and the solving speed is accelerated; in the population variation process, wavelet variation is utilized to increase population diversity, and better populations are selected in a competitive mode to eliminate poor variation individuals, so that the diversity of solutions is increased, the probability that the solutions fall into local optimum in the solving process is reduced, the solutions are updated towards the direction of the global optimum solution at a higher speed, and a reliable and quick solution optimization scheme is provided for engineering optimization problems such as traffic flow prediction, traffic scheduling and the like.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
In order to more clearly illustrate the invention, the invention is further described below with reference to preferred embodiments and the accompanying drawings. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
As shown in fig. 1, an IJAYAGA algorithm based on wavelet mutation includes the following steps:
step0 initializes:
and designing the current iteration number K to be 0 and the maximum evolution algebra K, and randomly generating N individuals as an initial population P (0) according to the constraint condition of the variable to be optimized. And setting a population individual evaluation function f (X).
Step1 individual evaluation:
step1.1 calculation of fitness value for each individual in the population P (k)
Figure BDA0002645321440000061
Step1.2, sorting all individual fitness values of the population P (k), and selecting the fitness values according to the individual fitness values
Figure BDA0002645321440000062
And
Figure BDA0002645321440000063
step2 individual update:
step2.1 calculates the adaptive pilot operator w:
Figure BDA0002645321440000064
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)
Figure BDA0002645321440000065
And worst solution
Figure BDA0002645321440000066
Guiding the individual to update towards the direction of the optimal solution, avoiding the update towards the direction of the inferior solution, and calculating the updated individual
Figure BDA0002645321440000067
Figure BDA0002645321440000068
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness value
Figure BDA0002645321440000069
Fitness value of original individual
Figure BDA00026453214400000610
Comparing, and selecting better individuals
Figure BDA00026453214400000611
Figure BDA00026453214400000612
Step2.4 updates the count value, i.e. i is equal to i + 1. If the condition that i is less than or equal to N is met, executing the step Step2.1, and taking N newly generated individuals as a new population;
step3 population selection:
step3.1 calculate fitness value for each individual in the population P (k)
Figure BDA00026453214400000613
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Figure BDA0002645321440000071
Figure BDA0002645321440000072
Step3.3 calculation of cumulative probability of Each individual in the population P (k)
Figure BDA0002645321440000073
Figure BDA0002645321440000074
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
step3.5 amino acid sequence
Figure BDA0002645321440000075
Then individual 1 is selected; if it is
Figure BDA0002645321440000076
Selecting an individual i;
step3.6 Step3.4 and Step3.5 were repeated until N individuals were selected, which were called the selection population.
Step4 intersection:
step4.1 randomly selects two individuals p and q from the population P (k), and p is not equal to q;
step4.2 computing adaptive crossover operator Pc
Figure BDA0002645321440000077
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q
Figure BDA0002645321440000078
Wherein:
Figure BDA0002645321440000079
the genotype at the mth locus representing individual p,
Figure BDA00026453214400000710
denotes the genotype of the M-th locus of an individual q, M being the length of each individual in the population.
Step4.4 Generation of random number γcSatisfy 0. ltoreq. gammac≤1;
If Step4.5 satisfies Sp,qLess than or equal to gammac≤pcIf yes, the step Step4.6 is executed, otherwise, the step Step4.1 is executed;
step4.6 generates a random number n, wherein n is more than or equal to 1 and less than or equal to M;
step4.7 performing a single point crossover operation on individuals p and q at the nth locus;
step4.8 performed Step4.1-Step4.7 a total of N/2 times.
And (4) obtaining a new population through the crossing process, namely the crossing population.
Step5 wavelet mutation:
step5.1 calculation of the population P (k) for each individual
Figure BDA0002645321440000081
Wavelet mutation operator:
Figure BDA0002645321440000082
wherein:
Figure BDA0002645321440000083
Figure BDA0002645321440000084
is a variation constant;
step5.2 for each individual of P (k) in the population
Figure BDA0002645321440000085
Carrying out individual wavelet variation to obtain corresponding variant individuals
Figure BDA0002645321440000086
Figure BDA0002645321440000087
Step5.3 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step Step5.1 is carried out to execute the mutation process. Generating a new variant population;
step5.4 adds a new variant population to the original population, generating a new population with 2N individuals.
Step6 random Q-competition selection:
step6.1 randomly selecting Q individuals from 2N individuals to form a test population, and combining the individuals
Figure BDA0002645321440000088
The fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recorded
Figure BDA0002645321440000089
The times of the individuals in the Q are better than or equal to the times of the individuals in the Q, and the individuals are obtained by calculation
Figure BDA00026453214400000810
Fraction S ofi
Figure BDA00026453214400000811
Step6.2 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step is changed to step Step6.1 to calculate the score S of each individuali
Step6.3 score S for individuals in population P (k)iAnd sorting, and selecting N individuals with higher scores to form a next generation new population.
Step7 executes a loop:
the count value is updated, i.e. k equals k + 1. If K is less than or equal to K, go to Step2 to execute the evolution process. Otherwise, the whole evolution process is ended.
The above-mentioned embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations may be made on the basis of the above description, and all embodiments may not be exhaustive.

Claims (6)

1. An IJAYAGA algorithm based on wavelet variation is characterized by comprising the following steps:
step1 evaluation: calculating individual fitness values, sequencing the individual fitness values, and selecting an optimal individual and a worst individual;
step2 individual update: calculating a self-adaptive guiding operator, and updating individuals to generate a new population;
step3 population selection: calculating individual fitness, and selecting individuals to generate a selected population by roulette;
step4 intersection: calculating a crossover operator, and generating a crossover population by crossing individuals;
step5 wavelet mutation: calculating wavelet mutation operators, generating a variant population by individual mutation, and mixing a cross population and the variant population to generate a new population;
step6 random competition selection: randomly selecting a plurality of individuals, calculating the scores of the individuals, and carrying out competitive comparison to generate a new population.
2. The wavelet-variant-based IJAYAGA algorithm as claimed in claim 1, wherein the specific process of individual update is as follows:
step2.1 calculates the adaptive pilot operator w:
Figure FDA0002645321430000011
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)
Figure FDA0002645321430000012
And worst solution
Figure FDA0002645321430000013
Guiding the individual to update towards the direction of the optimal solution, avoiding the update towards the direction of the inferior solution, and calculating the updated individual
Figure FDA0002645321430000014
Figure FDA0002645321430000015
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness value
Figure FDA0002645321430000016
Fitness value of original individual
Figure FDA0002645321430000017
Comparing, and selecting better individuals
Figure FDA0002645321430000018
Figure FDA0002645321430000021
Step2.4 updates the count value, i.e. i is equal to i + 1. If the condition that i is less than or equal to N is met, executing the step Step2.1, and taking N newly generated individuals as a new population.
3. The wavelet-variant-based IJAYAGA algorithm as claimed in claim 1, wherein the specific process of population selection is as follows:
step3.1 calculate fitness value for each individual in the population P (k)
Figure FDA0002645321430000022
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Figure FDA0002645321430000023
Figure FDA0002645321430000024
Step3.3 calculation of cumulative probability of Each individual in the population P (k)
Figure FDA0002645321430000025
Figure FDA0002645321430000026
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
step3.5 amino acid sequence
Figure FDA0002645321430000027
Then individual 1 is selected; if it is
Figure FDA0002645321430000028
Selecting an individual i;
step3.6 Step3.4 and Step3.5 were repeated until N individuals were selected, which were called the selection population.
4. The wavelet-variant-based IJAYAGA algorithm as claimed in claim 1, wherein the specific process of crossing is as follows:
step4.1 randomly selects two individuals p and q from the population P (k), and p is not equal to q;
step4.2 computing adaptive crossover operator Pc
Figure FDA0002645321430000031
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q
Figure FDA0002645321430000032
Wherein:
Figure FDA0002645321430000033
the genotype at the mth locus representing individual p,
Figure FDA0002645321430000034
denotes the genotype of the M-th locus of an individual q, M being the length of each individual in the population.
Step4.4 Generation of random number γcSatisfy 0. ltoreq. gammac≤1;
If Step4.5 satisfies Sp,qLess than or equal to gammac≤pcIf yes, the step Step4.6 is executed, otherwise, the step Step4.1 is executed;
step4.6 generates a random number n, wherein n is more than or equal to 1 and less than or equal to M;
step4.7 performing a single point crossover operation on individuals p and q at the nth locus;
step4.8 performed Step4.1-Step4.7 a total of N/2 times.
5. The IJAYAGA algorithm based on wavelet variation as claimed in claim 1, wherein the wavelet variation is implemented by the following steps:
step5.1 calculation of the population P (k) for each individual
Figure FDA0002645321430000035
Wavelet mutation operator:
Figure FDA0002645321430000036
wherein:
Figure FDA0002645321430000037
Figure FDA0002645321430000038
is a variation constant;
step5.2 for each individual of P (k) in the population
Figure FDA0002645321430000039
Carrying out individual wavelet variation to obtain corresponding variant individuals
Figure FDA00026453214300000310
Figure FDA00026453214300000311
Step5.3 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step Step5.1 is carried out to execute the mutation process. Generating a new variant population;
step5.4 adds a new variant population to the original population, generating a new population with 2N individuals.
6. The wavelet-variant-based IJAYAGA algorithm as claimed in claim 1, wherein the specific process of random competition selection is as follows:
step6.1 randomly selecting Q individuals from 2N individuals to form a test population, and combining the individuals
Figure FDA0002645321430000041
The fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recorded
Figure FDA0002645321430000042
The times of the individuals in the Q are better than or equal to the times of the individuals in the Q, and the individuals are obtained by calculation
Figure FDA0002645321430000043
Fraction S ofi
Figure FDA0002645321430000044
Step6.2 updates the count value, i.e. i is equal to i + 1. If i is less than or equal to N, the step is changed to step Step6.1 to calculate the score S of each individuali
Step6.3 score S for individuals in population P (k)iAnd sorting, and selecting N individuals with higher scores to form a next generation new population.
CN202010852795.4A 2020-08-22 2020-08-22 IJAYAGA algorithm based on wavelet variation Pending CN112149830A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112948971A (en) * 2021-03-04 2021-06-11 北京交通大学 Energy-saving optimization method for speed curve of magnetic suspension train
CN113867368A (en) * 2021-12-03 2021-12-31 中国人民解放军陆军装甲兵学院 Robot path planning method based on improved gull algorithm

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112948971A (en) * 2021-03-04 2021-06-11 北京交通大学 Energy-saving optimization method for speed curve of magnetic suspension train
CN112948971B (en) * 2021-03-04 2023-09-29 北京交通大学 Energy-saving optimization method for speed curve of maglev train
CN113867368A (en) * 2021-12-03 2021-12-31 中国人民解放军陆军装甲兵学院 Robot path planning method based on improved gull algorithm

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Application publication date: 20201229