CN103413173A - Particle swarm optimization method based on flight time linear decreasing - Google Patents

Abstract

The invention discloses a particle swarm optimization method based on flight time linear decreasing. The method reduces vibration phenomena generated in the flight process of particles, and improves the convergence rate of the method. The traditional particle swarm optimization methods hardly solve the vibration problem of the particles, and therefore the optimizing efficiency of the methods is influenced. Aiming at the problem, at the initial stage of the method, due to the fact that the particles are relatively far away from the optimal position, if the particles are required to reach the optimal position faster, the flight time should be longer, and otherwise, the flight time should be shorter. Therefore, a time parameter T is introduced to adjust the flight time of the particles at different stages, and the effects of effectively reducing the vibration phenomena and improving the convergence rate are finally achieved.

Description

Particle group optimizing method based on the flight time linear decrease

Technical field

The present invention relates to the population field, be specifically related to the research field of population flight time.

Background technology

Particle group optimizing method (PSO) is a kind of intelligent optimization method of widely paying close attention in recent years and studying, Ebrhart and Kennedy are in the common a kind of new method proposed of nineteen ninety-five, its basic thought is to be subjected in early days some swarm behaviors to be carried out to the inspiration of modeling and simulation result of study, and their model and emulation mode are mainly utilized the model of biologist Hepper.In his emulation, bird assembles near a habitat, and this piece habitat is attracting bird, until they all drop on this piece on the ground, in the model of Hepper, bird is until the position of habitat, but in actual conditions, birds are do not know food on-site just starting.So Kennedy thinks between bird the information of intercoursing that exists, so they have increased some contents in emulation: each individuality can be estimated by certain rule the adaptive value of self-position; Each individuality can be remembered the own current desired positions found, and is called local optimum pbest, remembers in addition the desired positions found in all birds in colony, is called the gbest of global optimum.These two optimum variablees make bird close towards these directions to a certain extent.Their comprehensive everything content, proposed the simplified model of actual flock of birds, i.e. our said particle swarm optimization.

As the important branch of intelligent optimization method, particle group optimizing method has many incomparable superior functions, as: easily realize, easily understanding, fast convergence rate, control parameter are few, stronger ability of searching optimum is arranged.At present, the method has been successfully applied to the numerous areas such as function optimization, neural network, pattern-recognition.

Particle group optimizing method is a kind of swarm intelligence method.Because it has many advantages, so once putting forward to receive extensive concern.Yet there are the problems such as easily to be absorbed in the speed of convergence that local optimum causes slow, and precision is low in elementary particle group method.

In recent years, to the improvement of PSO method, increase population diversity improvement, strengthen Local Search improvement, with global optimization method, combine, and deterministic local optimization methods fusion etc.Above-described is to discuss for the purpose of method improvement, the method of applying in actual augmentation has the improvement based on parameter, i.e. in form making improvements the iterative formula of PSO method, from the particle behavior pattern, improve in addition, be the information interchange mode between particle, as the improvement of topological structure, the improvement light that global schema combines with local mode; Also have the improvement of the particle swarm optimization merged based on method, method merges the shortcoming that the advantage that can introduce additive method makes up the PSO method, designs the optimization method that is more suitable for problem solving.

But, in the elementary particle group optimizing method, when particle is found optimum solution in search volume, the phenomenon that particle shakes back and forth can appear sometimes near optimum solution.Even also can't avoid this phenomenon by the regularized learning algorithm factor and the inertia weight factor, and this optimum solution may be exactly locally optimal solution.

Summary of the invention

Goal of the invention: the technical problem to be solved in the present invention is that the phenomenon of shaking in the particle flight course is reduced.

The technical scheme of invention:

Method flow:

1, Method And Principle

The basic thought of particle group optimizing method is to find optimum solution by the cooperation between individual in population and information sharing.In the PSO method, every bird is referred to as a particle, each particle means with its geometric position and velocity vector, and each particle is with reference to the set direction of oneself, the optimal direction experienced and whole flock of birds institute public awareness to optimal direction determine oneself flight.When elementary particle group method particle upgraded the positional information of oneself at every turn, the flight time of adopting was all 1.And at the initial period of method, particle from optimal location away from, the time of required flight will be grown partially, and to the later stage, particle from optimal location close to, so the required time is partially shorter again, if or as just starting flying for long time, just owing to may flying over optimal location, thereby cause the generation of oscillatory occurences.In order to reduce the phenomenon of shaking in the particle flight course, this method changes the time 1 into T, makes its linear decrease between (0,1).The main thought of method is as follows:

Supposing has m particle in the target search space of a D dimension.Wherein: i particle is expressed as the vector of a D dimension, x _i=(x _I1, x _I2..., x _ID) (i=1,2 ..., m) mean that i particle is at Zhong De position, this search volume, v _i=(x _I1, x _I2..., v _ID) (i=1,2 ..., the m) speed of circling in the air of i particle of expression.If the optimal location that i particle searches up to now is p _i=(p _I1, p _I2..., p _ID) (i=1,2 ..., m), the optimal location that whole population searches up to now is p _g=(p _G1, p _G2..., p _GD) (i=1,2 ..., m).

Adopt following formula to operate population:

v _ij(t+1)＝w*v _ij(t)+c ₁r ₁(p _i-x _ij(t))+c ₂r ₂(p _g-x _ij(t)) (1)

x _ij(t+1)＝x _ij(t)+v _ij(t+1)*T _t (2)

$T_t=T_{\max }-\frac{T_{\max }-T_{\min }}{\mathrm{it}\max }*t---\left(3\right)$

I=1 wherein, 2 ..., m; J=1,2 ..., D; T is the current iteration number of times of method, c ₁And c ₂For aceleration pulse, r ₁And r ₂For the random number on [0,1],, w is inertia weight; T is the particle flight time used, and zone is (0,1), T _maxFor the maximum duration of particle flight, T _minFor the particle flight shortest time used, itmax is the maximum iteration time of particle.In (1), first is the velocity inertial item of particle, and latter two are respectively autognosis item and social recognition item.Velocity inertial is in order to allow particle have certain Memorability to the speed of last time; c ₁The cognitive ability that means particle self experience, regulate the step-length of advancing that particle flies to the self-position direction; c ₂The cognitive ability that means the seat social experience, regulate the step-length that particle advances to overall desired positions.Inertial factor w, controlling the impact of last speed on present speed, and it can be regulated ability of searching optimum and the local search ability of algorithm, and the w value is larger, and global optimizing ability is stronger, and the local optimal searching ability is more weak; Otherwise the local optimal searching ability is stronger, global optimizing ability is more weak.In (2), flight time T _tAccording to (3), do linear decrease in time.Can make in the incipient stage like this, the flight time is long, and when particle from optimal location more and more close to the time, the flight time is also more and more less, reduces particle to fly over optimal location, and the oscillatory occurences caused.

2, the basic step of method:

Basic step based on the particle group optimizing method of flight time linear decrease is as follows:

(1) the position x of each particle in the random initializtion population _Ij(0) and speed v _Ij(0);

(2) calculate the fitness of each particle.The position of current particle and adaptive value are stored in to the pbest of each particle _IjIn, by all pbest _IjPosition and the adaptive value of middle adaptive value optimum individual are stored in gbest _IjIn;

(3) basis Flight time of new particle more; Wherein T is the particle flight time used, and zone is (0,1), T _maxFor the maximum duration of particle flight, T _minFor the particle flight shortest time used, t is the current iteration number of times of method, and itmax is the maximum iteration time of particle;

(4) according to x _Ij(t+1)=x _Ij(t)+v _Ij(t+1) * T _t, the speed of new particle more;

(5) according to v _Ij(t+1)=w*v _Ij(t)+c ₁r ₁(p _i-x _Ij(t))+c ₂r ₂(p _g-x _Ij(t)), the more displacement of new particle;

I=1 wherein, 2 ..., m; J=1,2 ..., D; T is the current iteration number of times of method, c ₁And c ₂For aceleration pulse, r ₁And r ₂For the random number on [0,1], w is inertia weight; c ₁The cognitive ability that means particle self experience, regulate the step-length of advancing that particle flies to the self-position direction; c ₂The cognitive ability that means the seat social experience, regulate the step-length that particle advances to overall desired positions; Inertial factor w, controlling the impact of last speed on present speed, and it can be regulated ability of searching optimum and the local search ability of method, and the w value is larger, and global optimizing ability is stronger, and the local optimal searching ability is more weak; Otherwise the local optimal searching ability is stronger, global optimizing ability is more weak;

(6), to each particle, calculate its current location adaptive value pbest _Ij

(7) the adaptive value pbest of more current all particles _IjWith its desired positions adaptive value gbest lived through _IjValue, upgrade gbest _Ij

(8) when t was greater than maximum iterations or result and is less than error precision, search stopped, the parameter using the parameter value of the historical optimal location of colony as optimum solution, and Output rusults, continue search otherwise turn back to step (3).

Beneficial effect: the phenomenon of shaking in the particle flight course is reduced.

The accompanying drawing explanation

Fig. 1 is method flow diagram;

Fig. 2 is that particle moves figure.

Embodiment

A kind of particle group optimizing method that improves the flight time.When particle upgraded the positional information of oneself at every turn, the flight time of employing, according to iterations linear decrease between (0,1), was then found optimum solution by the cooperation between individual in population and information sharing.This method can significantly reduce the phenomenon of shaking in the particle flight course.

Concrete implementation step based on the particle group optimizing method of flight time linear decrease is as follows:

(1) the position x of each particle in the random initializtion population _Ij(0) and speed v _Ij(0);

(2) calculate the fitness of each particle.The position of current particle and adaptive value are stored in to the pbest of each particle _IjIn, by all pbest _IjPosition and the adaptive value of middle adaptive value optimum individual are stored in gbest _IjIn;

(3) basis

Flight time of new particle more; Wherein T is the particle flight time used, and zone is (0,1), T _maxFor the maximum duration of particle flight, T _minFor the particle flight shortest time used, t is the current iteration number of times of method, and itmax is the maximum iteration time of particle;

(4) according to x _Ij(t+1)=x _Ij(t)+v _Ij(t+1) * T _t, the speed of new particle more;

(5) according to v _Ij(t+1)=w*v _Ij(t)+c ₁r ₁(p _i-x _Ij(t))+c ₂r ₂(p _g-x _Ij(t)), the more displacement of new particle;

I=1 wherein, 2 ..., m; J=1,2 ..., D; T is the current iteration number of times of method, c ₁And c ₂For aceleration pulse, r ₁And r ₂For the random number on [0,1], w is inertia weight; c ₁The cognitive ability that means particle self experience, regulate the step-length of advancing that particle flies to the self-position direction; c ₂The cognitive ability that means the seat social experience, regulate the step-length that particle advances to overall desired positions; Inertial factor w, controlling the impact of last speed on present speed, and it can be regulated ability of searching optimum and the local search ability of method, and the w value is larger, and global optimizing ability is stronger, and the local optimal searching ability is more weak; Otherwise the local optimal searching ability is stronger, global optimizing ability is more weak;

(6), to each particle, calculate its current location adaptive value pbest _Ij

(7) the adaptive value pbest of more current all particles _IjWith its desired positions adaptive value gbest lived through _IjValue, upgrade gbest _Ij

(8) when t was greater than maximum iterations or result and is less than error precision, search stopped, the parameter using the parameter value of the historical optimal location of colony as optimum solution, and Output rusults, continue search otherwise turn back to step (3).

Above demonstration and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should be appreciated that; the present invention is not restricted to the described embodiments; that in above-described embodiment and instructions, describes just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications; these changes and improvements all fall in the claimed scope of the invention, and the claimed scope of the present invention is defined by its equivalent of appending claims.

Claims (1)

1. particle group optimizing method that improves the flight time.When particle upgraded the positional information of oneself at every turn, the flight time of employing, according to iterations linear decrease between (0,1), was then found optimum solution by the cooperation between individual in population and information sharing;

Concrete implementation step based on the particle group optimizing method of flight time linear decrease is as follows:

(1) the position x of each particle in the random initializtion population _Ij(0) and speed v _Ij(0);

(2) calculate the fitness of each particle.The position of current particle and adaptive value are stored in to the pbest of each particle _IjIn, by all pbest _IjPosition and the adaptive value of middle adaptive value optimum individual are stored in gbest _IjIn;

(3) basis

Flight time of new particle more; Wherein T is the particle flight time used, and zone is (0,1), T _maxFor the maximum duration of particle flight, T _minFor the particle flight shortest time used, t is the current iteration number of times of method, and itmax is the maximum iteration time of particle;

(4) according to x _Ij(t+1)=x _Ij(t)+v _Ij(t+1) * T _t, the speed of new particle more;

(5) according to v _Ij(t+1)=w*v _Ij(t)+c ₁r ₁(p _i-x _Ij(t))+c ₂r ₂(p _g-x _Ij(t)), the more displacement of new particle;

I=1 wherein, 2 ..., m; J=1,2 ..., D; T is the current iteration number of times of method, c ₁And c ₂For aceleration pulse, r ₁And r ₂For the random number on [0,1], w is inertia weight; c ₁The cognitive ability that means particle self experience, regulate the step-length of advancing that particle flies to the self-position direction; c ₂The cognitive ability that means the seat social experience, regulate the step-length that particle advances to overall desired positions; Inertial factor w, controlling the impact of last speed on present speed, and it can be regulated ability of searching optimum and the local search ability of method, and the w value is larger, and global optimizing ability is stronger, and the local optimal searching ability is more weak; Otherwise the local optimal searching ability is stronger, global optimizing ability is more weak;

(6), to each particle, calculate its current location adaptive value pbest _Ij

(7) the adaptive value pbest of more current all particles _IjWith its desired positions adaptive value gbest lived through _IjValue, upgrade gbest _Ij

(8) when t was greater than maximum iterations or result and is less than error precision, search stopped, the parameter using the parameter value of the historical optimal location of colony as optimum solution, and Output rusults, continue search otherwise turn back to step (3).

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