CN102682203A - Method for improving particle memorability in gravity search optimization algorithm - Google Patents

Abstract

The invention relates to the field of an intelligent optimization algorithm, and discloses a gravity search optimization algorithm for improving particle memorability, which mainly comprises the following steps: 1, an adaptive value of the current position of each particle is compared with the adaptive value of the best position of the individual particle in a movement historical process, and if the adaptive value of the current position is superior to the adaptive value of the best position of the individual particle in the movement historical process, the current position value is endowed to the individual best position value; 2, the adaptive value of the current position of each particle is compared with the adaptive value of the best position of the whole process undergone by a particle group, and if the adaptive value of the current position is superior to the adaptive value of the best position of the whole process, the current position value is endowed to the best position value of the whole process; and 3, the individual optimal solution of the particle and the optimal solution of the whole process are introduced into a speed updating formula of the particle to revise the speed updating formula of the particle, and the concept of a coordinating factor is introduced for adjusting the influence proportion of the memorized historical information in an optimization process. The memorability of the particle in the algorithm is improved, and the search capability of the algorithm is improved.

Description

A kind of to the improved method of particle Memorability in the gravitation search optimized Algorithm

Technical field

The present invention relates to a kind ofly, belong to the intelligent optimization algorithm field the improved method of particle Memorability in the gravitation search optimized Algorithm.

Background technology

Gravitation search optimized Algorithm is a kind of colony intelligence optimized Algorithm; Its essential idea is based on newton's the law of universal gravitation: " between universe; each particle attracts owing to gravitational effect each other; the size of gravitation is directly proportional with the quality of particle, and the distance between them is inversely proportional to ".

Owing to only have only current position information in the iteration renewal process, to work in the gravitation searching algorithm; Can know that the gravitation searching algorithm is a kind of algorithm that lacks Memorability, when particle movement is perhaps compared near optimum solution to optimum solution, particle's velocity is constantly to accelerate (according to the universal gravitation formula; The size of gravitation is and the distance relation of being inversely proportional to); During when the arrival optimum solution or near optimum solution, is big (there is randomness in particle's velocity) very, can know according to the kinematics rule; This situation can cause near particle concussion back and forth repeatedly optimum solution; Cause whole optimized Algorithm search precision not high, particularly higher-dimension function optimization performance is not good, the phenomenon that optimizing process is precocious easily.

Summary of the invention

To the deficiency of above technology, the objective of the invention is to the thought of particle Memorability is incorporated in the gravitation searching algorithm, to improve the individual Memorability of particle in this algorithm, improve the search capability of algorithm.

A kind of mainly is that the historical optimal value of population particle and the individual historical optimal value of particle are incorporated in the gravitation searching algorithm to the improved method of particle Memorability in the gravitation search optimized Algorithm, main step comprise following some:

Step 1: for each particle; The adaptive value of its current location and the adaptive value of its individuality desired positions in the motion history process are compared; If the adaptive value of current location is superior to the adaptive value of its individuality desired positions in the motion history process, then give individual desired positions value with current positional value.Step 2:,,, then give overall desired positions value with current positional value if the adaptive value of current location is superior to the adaptive value of overall desired positions with the adaptive value of its current location and the adaptive value of particle overall desired positions that colony experiences for each particle.Step 3: individual optimum solution of particle and globally optimal solution are incorporated into particle rapidity more in the new formula, revise more new formula of particle's velocity, and the notion of introducing coordinating factor, be used for adjusting the historical information remembered the ratio that influences at optimizing process.

The invention has the advantages that:

The thought of particle Memorability is incorporated in the gravitation searching algorithm; In order to improve the individual Memorability of particle in this algorithm; The particle's velocity update mode is revised; The acting in conjunction of depending on other particles in the total system is not just won in the particle's velocity information updating like this, also receives the influence that it is remembered self, makes it have good search capability to optimum solution.

Description of drawings

Optimized Algorithm process flow diagram after Fig. 1 the inventive method is improved

Fig. 2 particle Memorability improvement part structural representation

Embodiment

Further specify below in conjunction with the accompanying drawing specific embodiments of the invention.

A kind of to the improved gravitation of particle Memorability search optimized Algorithm method, step mainly comprise following some:

Step 1: the search volume of clear and definite whole gravitational field.From target problem, obtain the spatial dimension of whole problem.

Step 2: each particle position in the random initializtion population, set number of particles and maximum iteration time in the gravitational field.The initialization spatial positional information mainly be according in the step 1 clear and definite search volume, the number of particle is N, maximum iteration time is T.

Step 3: according to target problem, calculate the adaptive value of each particle, the historical optimum position of memory particle information.Each particle position is exactly potential separating, with X _iThe substitution objective function just can calculate its adaptive value, and the best values of the individual experience of particle is designated as The desired positions that all particles of whole colony live through is designated as gbest=(gbest ¹, gbest ²..., gbest ^D), and the Memorability of particle just has been embodied in pbest and these two amounts of gbest.

Step 4: the optimum value and the worst-case value that upgrade particle position in the gravitation coefficient in the universal gravitation formula, the inertial mass of particle, the whole population.According to formula (1) and formula (2), can calculate the inertial mass M of each particle _i(t):

$m_i\left(t\right)=\frac{{\mathrm{fitness}}_i\left(t\right)-\mathrm{worst}\left(t\right)}{\mathrm{best}\left(t\right)-\mathrm{worst}\left(t\right)}---\left(1\right)$

$M_i\left(t\right)=\frac{m_i\left(t\right)}{{\mathrm{\Σ}}_{j=1}^N{m}_j\left(t\right)},$ i＝1，2，...，N (2)

Wherein, N is a number of particles, m _i(t) for calculating the intermediate variable of mass particle, fitness _i(t) be particle i in t adaptive value constantly, and worst (t) and best (t) are meant respectively in the worst adaptive value of t whole population of the moment and best adaptive value.

When ferret out function minimum problem, the worst and best adaptive value is respectively:

$\mathrm{best}\left(t\right)=\underset{j\∈\{1,...,N\}}{\min }{\mathrm{fitness}}_j\left(t\right),$ $\mathrm{worst}\left(t\right)=\underset{j\∈\{1,...,N\}}{\max }{\mathrm{fitness}}_j\left(t\right)$

When ferret out function max problem, the worst and best adaptive value is respectively:

$\mathrm{best}\left(t\right)=\underset{j\∈\{1,...,N\}}{\max }{\mathrm{fitness}}_j\left(t\right),$ $\mathrm{worst}\left(t\right)=\underset{j\∈\{1,..,N\}}{\min }{\mathrm{fitness}}_j\left(t\right)$

G (t) is the gravitation coefficient: $G\left(t\right)=G_0{e}^{-\mathrm{\α}\frac{t}{T}}.---\left(3\right)$

Wherein, G ₀With α be constant, T is a maximum iteration time.

Step 5: calculate the summation of each particle power in different directions, and calculate the acceleration of particle.Use the universal gravitation formula after the conversion, can calculate each particle each other gravitation on each dimension space, the gravitation between particle i on the d dimension space and particle j:

$F_{\mathrm{ij}}^d\left(t\right)=G\left(t\right)\frac{M_i\left(t\right)\×M_j\left(t\right)}{R_{\mathrm{ij}}\left(t\right)+\mathrm{\ϵ}}(x_j^d\left(t\right)-x_i^d\left(t\right))---\left(4\right)$

Wherein,

Be meant the position of particle i in the d dimension space,

Be meant the position of particle j in the d dimension space, ε is meant very little constant, R _Ij(t) be Euclidean distance between particle i and the particle j: R _Ij(t)=|| x _i(t), x _j(t) || ₂

Calculate on each dimension space the acceleration of particle i constantly according to Newton's laws of motion then, in the gravitation searching algorithm, in order to increase the random character of algorithm, at acting force at t Before add rand _jRandom function supposes that total acting force is the summation from other all particle acting forces on i the particle acting on the d dimension space, and the inertial mass of particle i is M _Ii(t), the acceleration of particle is so:

$a_i^d\left(t\right)=\frac{\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}{\mathrm{rand}}_j{F}_{\mathrm{ij}}^d\left(t\right)}{M_{\mathrm{ii}}\left(t\right)}---\left(5\right)$

Step 6: upgrade particle's velocity, and upgrade each particle position information.At last, particle i in the speed in next moment and the evolutionary equation of position is:

$V_i^d(t+1)={\mathrm{rand}}_1*V_i^d\left(t\right)+c_1*{\mathrm{rand}}_2*({\mathrm{pbest}}_i^d\left(t\right)-X_i^d\left(t\right))+$

$c_2*{\mathrm{rand}}_3*({\mathrm{gbest}}_i^d\left(t\right)-X_i^d\left(t\right))+a_i^d\left(t\right)---\left(6\right)$

$X_i^d(t+1)=X_i^d\left(t\right)+V_i^d(t+1)---\left(7\right)$

Wherein, rand ₁, rand ₂Be equally distributed separate random number sequence between (0,1), c ₁And c ₂As coordinating factor, the scope of setting (does not comprise 0 and 1) between 0 to 1.

Step 7: continuous search iteration, until reach iterations or the precision that meets the demands till.

Claims (1)

1. one kind to the improved method of particle Memorability in the gravitation search optimized Algorithm, it is characterized in that:

The thought of remembering the historical optimum solution of particle movement preservation is incorporated in the gravitation searching algorithm, and the memory capability of particle in the gravitation searching algorithm is improved, and can remember optimum solution and globally optimal solution in the displacement process.Improve the Velocity Updating mode of particle with this, improve the search capability of algorithm in evolutionary process.The particle rapidity of band memory more new formula is:

$V_i^d(t+1)={\mathrm{rand}}_1*V_i^d\left(t\right)+c_1*{\mathrm{rand}}_2*({\mathrm{Pbest}}_i^d\left(t\right)-X_i^d\left(t\right))+$

$c_2*{\mathrm{rand}}_3*({\mathrm{gbest}}_i^d\left(t\right)-X_i^d\left(t\right))+a_i^d\left(t\right)$

Wherein,

Be particle i t speed constantly in the d dimension space,

Particle i t is constantly remembered in the d dimension space self historical optimum solution,

Be the particle i global history optimum solution that t is remembered constantly in the d dimension space,

Be meant particle i t positional information constantly in the d dimension space, Be particle i t acceleration constantly in the d dimension space, rand ₁, rand ₂And rand ₃Be equally distributed separate random number sequence between (0,1), parameter c ₁And c ₂Can be defined as coordinating factor, c ₁And c ₂Value (does not comprise 0 and 1) between 0 to 1.

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