CN106447024A - Particle swarm improved algorithm based on chaotic backward learning - Google Patents

Abstract

The invention discloses a particle swarm improved algorithm based on chaotic backward learning. The algorithm mainly comprises a backward learning strategy and chaotic particle swarm optimization. The basic principle of the backward learning strategy includes: the backward learning strategy generates a corresponding backward solution for each initial candidate solution, and selects the solutions with short distance (high fitness) from two kinds of solutions (candidate solutions and corresponding backward solutions) as members of an initial population so that the convergence rate in an optimization process can be increased. In order to maintain the diversity of the population and enable individuals of the initial population to be uniformly distributed as much as possible, the initial population is generated by employing the backward learning strategy.

Description

A kind of population innovatory algorithm based on chaos backward learning

Technical field

The present invention relates to the technical field of particle swarm optimization algorithm, specifically, it is related specifically to a kind of anti-based on chaos Population innovatory algorithm to study.

Background technology

Performance for particle swarm optimization algorithm is arranged by inherent parameters and is affected, and later stage speed is slow, be easily absorbed in local Minimum the problems such as.The research of PSO algorithm in recent years and its application mainly launch from the following aspects：The improvement of topological structure； The research of learning strategy, the research of PSO hybrid optimization algorithm, the application study of PSO algorithm.And the improved purpose of learning strategy is In order to strengthen information interchange between particle, strengthen the diversity of population, and then lift the ability that population jumps out locally optimal solution.A kind of Extensively the population (Comprehensive Learning Particle Swarm Optimizer, abbreviation CLPSO) of study is calculated Method is suggested, and " social part " particle all particles in addition to except itself of this algorithm are constituted, and substantially increase each particle Chance to other particle optimum inquiry learning；For improving the deficiency of CLPSO algorithm, a kind of adaptive learning strategy is suggested, According to the operation conditions of particle in population, dynamically assign learning sample for each particle, to strengthen interparticle information interchange. But these improvement strategies above-mentioned play a positive role to a certain extent, but still suffer from deficiency at aspects such as convergence precision.

Content of the invention

Present invention aims to deficiency of the prior art, provide a kind of population based on chaos backward learning Innovatory algorithm, to solve problems of the prior art.

Technical problem solved by the invention can employ the following technical solutions to realize：

A kind of population innovatory algorithm based on chaos backward learning, excellent including backward learning strategy and Chaos-Particle Swarm Optimization Change；

The comprising the following steps that of described backward learning strategy：

Produce initial solution X first_i, then obtain reverse solution X corresponding to each initial solution_i ¹,

And calculate the fitness value of all initial solutions, finally fitness value press to all solutions producing and sort, by fitness Value preferably top n solution is as solution Z of initial population_i ^dT () (d=1,2 ... D), it is used for improving the quality of solution and solves effect Rate；

Then it is incorporated into inertial factor, Studying factors, particle rapidity and position with reference to backward learning strategy and by chaos In renewal, idiographic flow is as follows：

Step 1：Initiation parameter, such as particle population size M, maximum iteration time T, the scope [W of inertial factor_min, W_max], typically take the scope [C of [0.4,0.9], Studying factors_min, C_max], typically take [1.4,2.0], population flying speed model Enclose [V_min, V_max], dimension be D, each optimization problem variable-value scope be [P^d _min,P^d _max] (d=1 ..., D), produced according to following formula Raw W, C₁、C₂、R₁And R₂Chaos time sequence；

W (t)=4.0W (t-1) (1-W (t-1))

W (t)=W_min+(W_max-W_min)W(t)

R_i(t)=4.0R_i(t-1)(1-R_i(t-1)), R_i∈(0,1)

C_i(t)=4.0C_i(t-1)(1-C_i(t-1))

C_i(t)=C_min+(C_max-C_min)C_i(t)

Step 2：The position of selected population and chaos intialization particle and speed；

Step 2.1 randomly generates D and ties up vector Z on (0,1) for each component values₀ ^d(t) (d=1,2 ..., D), D is to become Amount number, maps the chaos sequence Z producing N number of different tracks using typical Logistic_i ^dT () (d=1,2 ... D), pass through Backward learning policy selection optimum population, that is, as initial population；

Step 2.2 is according to Z_i ^d(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT initial population is carried out the standard of span by () Change；

Step 2.3 calculates the fitness value of population, and selects performance preferable M solution conduct from N number of initial population The initial position of particle, randomly generates M initial velocity；

Step 2.4 is by each particle individuality extreme value P^d _bestAs current location, calculate its fitness value, take adaptive value best Particle corresponding individuality extreme value as initial global extremum G^d _best；

Step 3:Judge whether convergence criterion meets, if met, exporting global optimum position and its fitness value, calculating Method terminates；If being unsatisfactory for, enter step 4；

Step 4:Calculating, the speed of more new particle and position are iterated according to particle group velocity and location updating formula；

Step 5:Fitness function according to choosing compares fitness F (P^d _i) and F (P^d _best), if F is (P^d _i)<F (P^d _best), then update P^d _best；

Step 6:If F is (P^d _best)<F(G^d _best) it is updated G^d _best；

Step 7:Judge whether convergence criterion meets；If it is satisfied, then output global optimum position and its fitness value, calculate Method terminates；If being unsatisfactory for, enter step 8；

Step 8:Average grain is calculated away from Dis and Colony fitness variance according to following formula, and judges Dis<α and δ²<Whether H becomes Vertical, that is, whether evaluation algorithm is absorbed in local optimum, if not, go to step 4；

Wherein, L is the diagonal maximum length in search space；P_idRepresent the d dimensional coordinate values of i-th particle；Represent all The average of particle d dimensional coordinate values；M is the number of particles of population, and F is the fitness of particle i, F_avgCurrent for population Average fitness, F is normalization factor, for limiting δ²Size；

Step 9:Speed according to following formula more new particle and position, make particle jump out local optimum；

V^d _i(t+1)=W (t) V^d _i(t)+C₁(t)×R₁(t)×(P^d _best(t)-P^d _i(t))+C₂(t)×R₂(t)×(G^d _best (t)-P^d _i(t))

P^d _i(t+1)=P^d _i(t))+V^d _i(t+1))

Step 10:To optimal location G^d _bestCarry out chaos optimization；

Step 10.1 is according to G^d _best(t)=(G^d _best-P^d _min)/(P_max ^d-P_min ^d) by G^d _bestIt is mapped to (0,1)；

Step 10.2 is by G^d _bestIt is updated in the mapping of formula Logistic, iteration produces Chaos Variable sequence；

The Chaos Variable producing is passed through inverse mapping G by step 10.3^d _best(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT () arrives former Solution space；

Step 10.4 calculates its fitness value in former solution space to each feasible solution of Chaos Variable, obtains best performance Feasible solution G^d _best；

Step 11:Use G^d _bestSubstitute the position of any one particle in current group；

Step 12:Whether evaluation algorithm reaches maximum iteration time or meets solving precision requirement, if meeting, output is complete Office's optimal location and its fitness value, algorithm terminates；Otherwise return to step 3.

Compared with prior art, beneficial effects of the present invention are as follows：

Affected greatly by itself parameter setting for particle swarm optimization algorithm performance, and later stage speed is slow, is easily absorbed in Local minimum and premature convergence problem, the present invention propose chaos backward learning particle group optimizing method it is contemplated that chaos have right Initial value is sensitive, computational accuracy is high, easily jump out the features such as local minimum and globally asymptotical convergence, introduces chaology, and utilizes Backward learning strategy initialization population is distributed as evenly as possible search space so that initializing individuality, thus boosting algorithm Local search ability, is effectively prevented from Premature Convergence.

Brief description

Fig. 1 is the structured flowchart of the population innovatory algorithm based on chaos backward learning of the present invention.

Specific embodiment

Technological means, creation characteristic, reached purpose and effect for making the present invention realize are easy to understand, with reference to Specific embodiment, is expanded on further the present invention.

Referring to Fig. 1, the population innovatory algorithm based on chaos backward learning of the present invention, mainly include backward learning Strategy and chaotic particle swarm optimization.Backward learning strategy general principle：Backward learning strategy is that each initial candidate solution generates phase Corresponding reverse solution, and chosen distance is relatively nearly (i.e. fitness is more excellent) from this two classes solution (candidate solution and corresponding reverse solution) Solution as the member in initial population, it will help improve optimization process in rate of convergence.It is and keep the various of population Property and so that the individuality of initial population is uniformly distributed as far as possible, using backward learning strategy generating initial population.Produce initial first Solution X_i, then obtain reverse solution X corresponding to each initial solution_i ¹,

And calculate the fitness value of all initial solutions, finally fitness value press to all solutions producing and sort, by fitness Value preferably top n solution is as solution Z of initial population_i ^d(t) (d=1,2 ..., D), this will be helpful to improve the quality of solution and asks Solution efficiency.

The present invention is incorporated into inertial factor, Studying factors, particle rapidity and position with reference to backward learning strategy and by chaos Renewal in, idiographic flow is as follows

Step 1：Initiation parameter, such as particle population size M, maximum iteration time T, the scope [W of inertial factor_min, W_max], typically take the scope [C of [0.4,0.9], Studying factors_min,C_max], typically take [1.4,2.0], population flying speed model Enclose [V_min,V_max], dimension be D, each optimization problem variable-value scope be [P^d _min,P^d _max] (d=1 ..., D), produced according to following formula Raw W, C₁、C₂、R₁And R₂Chaos time sequence.

W (t)=4.0W (t-1) (1-W (t-1))

W (t)=W_min+(W_max-W_min)W(t)

R_i(t)=4.0R_i(t-1)(1-R_i(t-1)), R_i∈(0,1)

C_i(t)=4.0C_i(t-1)(1-C_i(t-1))

C_i(t)=C_min+(C_max-C_min)C_i(t)

Step 2：The position of selected population and chaos intialization particle and speed.

Step 2.1 randomly generates D and ties up vector Z on (0,1) for each component values₀ ^d(t) (d=1,2 ..., D), D is to become Amount number, maps the chaos sequence Z producing N number of different tracks using typical Logistic_i ^dT () (d=1,2 ..., D), passes through Backward learning policy selection optimum population, that is, as initial population.

Step 2.2 is according to Z_i ^d(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT initial population is carried out the standard of span by () Change.

Step 2.3 calculates the fitness value of population, and selects performance preferable M solution conduct from N number of initial population The initial position of particle, randomly generates M initial velocity.

Step 2.4 is by each particle individuality extreme value P^d _bestAs current location, calculate its fitness value, take adaptive value best Particle corresponding individuality extreme value as initial global extremum G^d _best.

Step 3:Judge whether convergence criterion meets, if met, exporting global optimum position and its fitness value, calculating Method terminates.If being unsatisfactory for, enter step 4.

Step 4:Calculating, the speed of more new particle and position are iterated according to particle group velocity and location updating formula.

Step 5:Fitness function according to choosing compares fitness F (P^d _i) and F (P^d _best), if F is (P^d _i)<F (P^d _best), then update P^d _best.

Step 6:If F is (P^d _best)<F(G^d _best) it is updated G^d _best.

Step 7:Judge whether convergence criterion meets.If it is satisfied, then output global optimum position and its fitness value, calculate Method terminates.If being unsatisfactory for, enter step 8.

Step 8:Average grain is calculated away from Dis and Colony fitness variance according to following formula, and judges Dis<α and δ²<Whether H becomes Vertical, that is, whether evaluation algorithm is absorbed in local optimum, if not, go to step 4.

Wherein, L is the diagonal maximum length in search space；P_idRepresent the d dimensional coordinate values of i-th particle；Represent all The average of particle d dimensional coordinate values；M is the number of particles of population, and F is the fitness of particle i, F_avgCurrent for population Average fitness, F is normalization factor, for limiting δ²Size.

Step 9:Speed according to following formula more new particle and position, make particle jump out local optimum.

V^d _i(t+1)=W (t) V^d _i(t)+C₁(t)×R₁(t)×(P^d _best(t)-P^d _i(t))+C₂(t)×R₂(t)×(G^d _best (t)-P^d _i(t))

P^d _i(t+1)=P^d _i(t))+V^d _i(t+1))

Step 10:To optimal location G^d _bestCarry out chaos optimization.

Step 10.1 is according to G^d _best(t)=(G^d _best-P^d _min)/(P_max ^d-P_min ^d) by G^d _bestIt is mapped to (0,1).

Step 10.2 is by G^d _bestIt is updated in the mapping of formula Logistic, iteration produces Chaos Variable sequence.

The Chaos Variable producing is passed through inverse mapping G by step 10.3^d _best(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT () arrives former Solution space.

Step 10.4 calculates its fitness value in former solution space to each feasible solution of Chaos Variable, obtains best performance Feasible solution G^d _best.

Step 11:Use G^d _bestSubstitute the position of any one particle in current group.

Step 12:Whether evaluation algorithm reaches maximum iteration time or meets solving precision requirement, if meeting, output is complete Office's optimal location and its fitness value, algorithm terminates；Otherwise return to step 3.

General principle and principal character and the advantages of the present invention of the present invention have been shown and described above.The technology of the industry , it should be appreciated that the present invention is not restricted to the described embodiments, the simply explanation described in above-described embodiment and specification is originally for personnel The principle of invention, without departing from the spirit and scope of the present invention, the present invention also has various changes and modifications, these changes Change and improvement both falls within scope of the claimed invention.Claimed scope by appending claims and its Equivalent thereof.

Claims (1)

1. a kind of population innovatory algorithm based on chaos backward learning it is characterised in that：Including backward learning strategy and chaos Particle group optimizing；

The comprising the following steps that of described backward learning strategy：

Produce initial solution X first_i, then obtain reverse solution X corresponding to each initial solution_i ¹,

X_i ¹=rand (0,1) (X_max+X_min)-X_i

And calculate the fitness value of all initial solutions, finally fitness value press to all solutions producing and sort, by fitness value relatively Excellent top n solution is as solution Z of initial population_i ^dT () (d=1,2 ... D), it is used for improving quality and the solution efficiency of solution；

Then it is incorporated into the renewal of inertial factor, Studying factors, particle rapidity and position with reference to backward learning strategy and by chaos In, idiographic flow is as follows：

Step 1：Initiation parameter, such as particle population size M, maximum iteration time T, the scope [W of inertial factor_min,W_max], Typically take the scope [C of [0.4,0.9], Studying factors_Min,C_max], typically take [1.4,2.0], population flying speed scope [V_Min,V_max], dimension be D, each optimization problem variable-value scope be [P^d _min,P^d _max] (d=1 ..., D), produced according to following formula W、C₁、C₂、R₁And R₂Chaos time sequence；

W (t)=4.0W (t-1) (1-W (t-1))

W (t)=W_min+(W_max-W_min)W(t)

R_i(t)=4.0R_i(t-1)(1-R_i(t-1)), R_i∈(0,1)

C_i(t)=4.0C_i(t-1)(1-C_i(t-1))

C_i(t)=C_min+(C_max-C_min)C_i(t)

Step 2：The position of selected population and chaos intialization particle and speed；

Step 2.1 randomly generates D and ties up vector Z on (0,1) for each component values₀ ^d(t) (d=1,2 ..., D), D is variable Number, maps the chaos sequence Z producing N number of different tracks using typical Logistic_i ^dT () (d=1,2 ... D), by reverse Learning strategy selects optimum population, that is, as initial population；

Step 2.2 is according to Z_i ^d(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT initial population is carried out the standardization of span by ()；

Step 2.3 calculates the fitness value of population, and selects the preferable M solution of performance from N number of initial population as particle Initial position, randomly generate M initial velocity；

Step 2.4 is by each particle individuality extreme value P^d _bestAs current location, calculate its fitness value, take the grain that adaptive value is best Son corresponding individuality extreme value is as initial global extremum G^d _best；

Step 3:Judging whether convergence criterion meets, if met, exporting global optimum position and its fitness value, algorithm is tied Bundle；If being unsatisfactory for, enter step 4；

Step 4:Calculating, the speed of more new particle and position are iterated according to particle group velocity and location updating formula；

Step 5:Fitness function according to choosing compares fitness F (P^d _i) and F (P^d _best), if F is (P^d _i)<F(P^d _best), then Update P^d _best；

Step 6:If F is (P^d _best)<F(G^d _best) it is updated G^d _best；

Step 7:Judge whether convergence criterion meets；If it is satisfied, then output global optimum position and its fitness value, algorithm knot Bundle；If being unsatisfactory for, enter step 8；

Step 8:Average grain is calculated away from Dis and Colony fitness variance according to following formula, and judges Dis<α and δ²<Whether H sets up, that is, Whether evaluation algorithm is absorbed in local optimum, if being false, goes to step 4；

$Dis=\frac{1}{N\&times;L}\underset{i=1}{\overset{N}{\&Sigma;}}\sqrt{\underset{d=1}{\overset{D}{\&Sigma;}}{(P_{id}-{\stackrel{\&OverBar;}{P}}_d)}^2}$

${\mathrm{\&delta;}}^2=\underset{i=1}{\overset{m}{\&Sigma;}}\frac{F_i-F_{avg}}{F}$

Wherein, L is the diagonal maximum length in search space；P_idRepresent the d dimensional coordinate values of i-th particle；Represent all particles The average of d dimensional coordinate values；M is the number of particles of population, and F is the fitness of particle i, F_avgFor current average of population Fitness, F is normalization factor, for limiting δ²Size；

Step 9:Speed according to following formula more new particle and position, make particle jump out local optimum；

V^d _i(t+1)=W (t) V^d _i(t)+C₁(t)×R₁(t)×(P^d _best(t)-P^d _i(t))+C₂(t)×R₂(t)×(G^d _best(t)- P^d _i(t))

P^d _i(t+1)=P^d _i(t))+V^d _i(t+1))

Step 10:To optimal location G^d _bestCarry out chaos optimization；

Step 10.1 is according to G^d _best(t)=(G^d _best-P^d _min)/(P_max ^d-P_min ^d) by G^d _bestIt is mapped to (0,1)；

Step 10.2 is by G^d _bestIt is updated in the mapping of formula Logistic, iteration produces Chaos Variable sequence；

The Chaos Variable producing is passed through inverse mapping G by step 10.3^d _best(t)=P_min ^d+(P_max ^d-P_min ^d)Z_i ^dT () arrives former solution empty Between；

Step 10.4 calculates its fitness value in former solution space to each feasible solution of Chaos Variable, and obtain best performance can Row solution G^d _best；

Step 11:Use G^d _bestSubstitute the position of any one particle in current group；

Step 12:Whether evaluation algorithm reaches maximum iteration time or meets solving precision requirement, if meeting, the output overall situation is Excellent position and its fitness value, algorithm terminates；Otherwise return to step 3.