CN112149830A - IJAYAGA algorithm based on wavelet variation - Google Patents
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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
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:
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)And worst solutionGuiding 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
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness valueFitness value of original individualComparing, and selecting better individuals
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:
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
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:
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q:
Wherein:the genotype at the mth locus representing individual p,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:
step5.2 for each individual of P (k) in the populationCarrying out individual wavelet variation to obtain corresponding variant individuals
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 individualsThe fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recordedThe 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 calculationFraction S ofi:
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:
Step1.2, sorting all individual fitness values of the population P (k), and selecting the fitness values according to the individual fitness valuesAnd
step2 individual update:
step2.1 calculates the adaptive pilot operator w:
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)And worst solutionGuiding 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
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness valueFitness value of original individualComparing, and selecting better individuals
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:
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
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:
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q:
Wherein:the genotype at the mth locus representing individual p,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:
step5.2 for each individual of P (k) in the populationCarrying out individual wavelet variation to obtain corresponding variant individuals
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 individualsThe fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recordedThe 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 calculationFraction S ofi:
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:
wherein: k current iteration times, wherein K is the fixed total evolution times;
step2.2 uses the optimal solution in the population P (k)And worst solutionGuiding 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
Wherein: rand is a generated random number, and i is the ith individual in the population;
step2.3 to updated individual fitness valueFitness value of original individualComparing, and selecting better individuals
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:
Step3.2 calculation of the probability of each individual in the population P (k) being inherited into the next generation population
Step3.4 generates a random number gamma, wherein the gamma belongs to [0,1 ];
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:
Step4.3 calculating the similarity coefficient S of the individual p and the individual qp,q:
Wherein:the genotype at the mth locus representing individual p,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:
step5.2 for each individual of P (k) in the populationCarrying out individual wavelet variation to obtain corresponding variant individuals
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 individualsThe fitness of the individuals is compared with the fitness of Q individuals, and the individuals are recordedThe 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 calculationFraction S ofi:
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.
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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 |
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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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