CN105426955A - Disturbance-based elite reverse learning particle swarm optimization implementation method - Google Patents

Abstract

The invention relates to a disturbance-based elite reverse learning particle swarm optimization implementation method. The technical scheme of the method comprises a first step of initializing a particle parameter, a second step of calculating particle fitness values and obtaining individual extrema and a global extremum, a third step of progressively decreasing inertia weight in a nonlinear manner, wherein a nonlinear progressive decrease manner not a linear progressive decrease manner is used to change the inertia weight so that a convergence speed and convergence precision of an algorithm are improved, a fourth step of determining a particle position updating mode, a fifth step of updating the individual extrema and the global extremum, and a sixth step of determining a particle continuing execution condition. The method is suitable for solving a function optimization problem, and the method has the high convergence speed and the high convergence precision and can effectively prevent from falling into a local optimum.

Description

A kind of implementation method of the elite's backward learning particle group optimizing based on disturbance

Technical field

The invention belongs to Intelligent Computation Technology field, particularly relate to a kind of implementation method of the elite's backward learning particle group optimizing based on disturbance.

Background technology

Particle swarm optimization algorithm (ParticleSwarmOptimization, PSO) be inspired in nineteen ninety-five a kind of optimization evolution algorithm of the overall situation proposed by flock of birds foraging behavior by scholar Kennedy and Eberhart, its main thought be by individuality between cooperation and information sharing realize solving target problem.

Particle cluster algorithm is a kind of Intelligent Optimal algorithm based on population, and all particles have an adaptive value determined by optimised function, are used for evaluating the quality of this particle current location.Particle finds optimum solution by the iteration of self, and in iterative process each time, particle upgrades oneself position by chasing individual extreme value pbest and global extremum gbest.If form a colony by N number of particle, tie up in search volume at D, vector x _i=(x _i1, x _i2..., x _id), i=1,2 ..., N, represents i-th position of particle in search volume, vector v _i=(v _i1, v _i2..., v _id) represent the speed of particle, i-th particle search to optimal location be p _i=(p _i1, p _i2..., p _id), the optimal location that whole particle group energy searches is p _g=(p _g1, p _g2..., p _gd).Then the equation of change of particle is as follows:

v _id(t+1)＝wv _id(t)+c ₁r ₁(p _id-x _id(t))+c ₂r ₂(p _gd-x _id(t))(1)

x _id(t+1)＝x _id(t)+v _id(t+1)(2)

Wherein: d=1,2 ..., D; W is called inertia weight; c ₁and c ₂be called Studying factors; r ₁and r ₂it is the random function of two changes in (0,1) scope; T is current iteration number of times.The part 1 of formula (1) is the previous speed of particle; Part 2 is " cognition " part, guides particle to self experience optimal direction motion; 3rd part is " society " part, guides particle to move to the direction of global optimum.

Because PSO algorithm flow is simple, be easy to realize, be widely used in multiple field.But PSO algorithm also exists and is easily absorbed in local extremum, speed of convergence is slow, optimizes the problem of low precision.

2005, professor Tizhoosh proposes backward learning (Opposition-basedlearning first, OBL) concept, the main thought of backward learning is: considering each candidate individual while, consider that it is oppositely individual, may obtain an individuality closer to optimum like this.Backward learning strategy effectively can improve population diversity, avoids algorithm Premature Convergence.General intelligence algorithm is all stochastic generation initial population, then by generation to optimum solution close to and finally to find or close to optimum solution.In search procedure, search for current solution simultaneously and oppositely separate, therefrom selecting good solution as follow-on colony, improve the efficiency of algorithm greatly.

2013, Zhou Xinyu etc. proposed elite's backward learning strategy, introduce elite's particle, in order to avoid population occurs that search is stagnated, adopted Differential Evolution Algorithm to strengthen the local producing capacity of algorithm.Elite's backward learning (EliteOpposition-basedParticleSwarmOptimization that Zhou Xinyu proposes, EOPSO) algorithm greatly improves the performance of algorithm from speed of convergence and convergence precision, but what adopt in literary composition is a kind of fixing inertia weight, upgrading what adopt to speed is the population speed more new formula of standard.Fixing inertia weight is unfavorable for that particle early stage search for accurately on a large scale by search and particle later stage, and the population speed of standard more new formula makes particle easily be absorbed in locally optimal solution.

Summary of the invention

The present invention is intended to overcome prior art defect, and object is to provide a kind of implementation method that can improve the elite's backward learning particle group optimizing based on disturbance of speed of convergence and convergence precision.

For achieving the above object, the technical solution used in the present invention is:

The first step, initialization Fe coatings

First arranging population particle scale is N, and also carry out initialization to the position of each particle, speed, the size of initial setting up particle iterations is Iter, and the assessment number of times of particle is A, and the dimension of particle is the social learning ability C of D, particle simultaneously ₁with the ability of self-teaching C of particle ₂, wherein

C ₁＝C ₂＝1.193(3)

Second step, calculating particle fitness value

The fitness value that the quality of particle is produced by fitness function is evaluated, and the best values that particle each in N number of particle experiences, is also called individual extreme value P _i=(P _i1, P _i2..., P _id) represent, value best in N number of particle, be also called global extremum P _g=(P _g1, P _g2..., P _gd) represent.

3rd step, the non-linear inertia weight that successively decreases

Propose a kind of non-linear inertia weight successively decreased, be defined as follows

$w=w-\frac{(w_{max}-w_{min})}{sum(1:Iter)}\×({\mathrm{Iter}}_{max}-Iter)---\left(4\right)$

W _max, w _minfor the upper and lower limit of inertia weight, Iter _maxbe maximum iteration time, Iter is particle current iteration number of times, and inertia weight declines very fast early stage, and decreased later is slower.

4th step, determine the mode that particle position upgrades

Random number R between random generation one [0,1], compares with the probability P of initial setting, if R<P, performs by mode one; If R>P, perform by mode two;

Mode one: elite's backward learning

If the elite's individuality in current group is X _i=(x _{i, 1}, x _{i, 2}..., x _i,D), corresponding elite oppositely separates $X_i^{*}=(x_{i,1}^{*},x_{i,2}^{*},...,x_{i,D}^{*})$ Be defined as follows:

$X_{i,j}^{*}=k(a_j+b_j)-X_{i,j}---\left(5\right)$

Wherein X _i,j∈ [a _j, b _j], k ∈ [0,1], k is vague generalization coefficient, utilizes this coefficient can generate multiple different reverse elite individual.

Mode two: disturbed extremum

Introduce the scope that disturbed extremum expands particle search, avoid particle to be absorbed in local optimum, the more new formula of speed is changed into:

$v_{id}(t+1)={\mathrm{wv}}_{id}\left(t\right)+c_1{r}_1\left(\left(0.5+\frac{r_3}{2}\right)p_{id}-x_{id}\left(t\right)\right)+c_2{r}_2\left(\left(0.5+\frac{r_4}{2}\right)p_{gd}-x_{id}\left(t\right)\right)---\left(6\right)$

R in formula ₃and r ₄be equally distributed random number between (0,1), individual extreme value and global extremum can along with r ₃and r ₄value different and disturbance occurs, the size and Orientation of speed also can change, and the hunting zone of population expands, particle can fly to how new position, and particle easily finds the more figure of merit, by interparticle mutual study, particle can move to more excellent position, likely can jump out locally optimal solution.

5th step: upgrade individual extreme value and global extremum

After particle executes a location updating, for single particle, find the optimal-adaptive value that this particle has, as the individual extreme value of this particle, and particle position corresponding for adaptive value is upgraded, for N number of particle, find the global extremum of optimal-adaptive value as particle of all particles, upgrade the position of overall particle.

6th step: particle continues the determination of executive condition

The execution of each particle all can have a condition stopped, when particle initialization, set the iterations Iter of particle and the assessment number of times A of particle, when the number of times of particle iteration does not reach Iter, the number of times t of the current iteration of particle increases once, particle implementation continues to perform, until reach the iterations of initial setting, the implementation of particle stops.

Preferably, non-linearly successively decrease in inertia weight above-mentioned, the initial value of inertia weight w is set to 0.9.

The present invention gives the assessment of the implementation method performance of the above-mentioned elite's backward learning particle group optimizing based on disturbance, and the assessment of method performance adopts two kinds of methods below:

A. fixing evaluation number of times, the speed of convergence of appraisal procedure and convergence precision;

B. fix convergence precision desired value, appraisal procedure reaches this assessment number of times required for precision target.

The implementation method of the elite's backward learning particle group optimizing based on disturbance of the present invention, adopts the non-linear inertia weight that successively decreases, elite oppositely separates and disturbed extremum, achieve the optimization of the elite's backward learning population based on disturbance.The present invention compared with prior art, has higher speed of convergence and convergence precision, can effectively avoid being absorbed in local optimum, is applicable to the problem that solved function is optimized.

Accompanying drawing explanation

Fig. 1 is the step schematic diagram of the implementation method of the elite's backward learning particle group optimizing based on disturbance of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention will be further described, the restriction not to its protection domain.

The invention provides a kind of implementation method of the elite's backward learning particle group optimizing based on disturbance.In an one embodiment, the step of this implementation method comprises:

The first step, initialization Fe coatings

According to flow process of the present invention, a probability P can be set when parameter initialization, control the position of particle according to the mode more new particle of elite's backward learning or disturbance by probability, in particle implementation, P is set as 0.3.Also can set the specific object of particle simultaneously, initialization Population Size is N number of particle, also carries out initialization to position X, the speed V of each particle simultaneously, and the size of initial setting up particle iterations is Iter, the assessment number of times of particle is A, and the dimension of particle is the social learning ability C of D, particle ₁with the ability of self-teaching C of particle ₂, wherein

C ₁＝C ₂＝1.193(1)

Wherein, when the initialization of particle rapidity, can initial setting velocity range [v _min, v _max], when particle rapidity overruns, be maximum boundary scope v by the Speed Setting of particle _maxor minimum bounds v _min, run in iterative process at particle, what the present invention adopted speed is a kind of mode of dynamic change.

Second step, calculating particle fitness value

The fitness value that the quality of particle is produced by fitness function is evaluated, and the best values that particle each in N number of particle experiences, is also called individual extreme value P _i=(P _i1, P _i2..., P _id) represent, value best in N number of particle, be also called global extremum P _g=(P _g1, P _g2..., P _gd) represent.Fitness function represents with f (*) usually, in the optimizing process of function, can be tested by multiple trial function, when testing each trial function, and trial function namely fitness function here.Trial function is divided into unimodal trial function, is mainly used to speed of searching optimization and the convergence precision of trial function; Multimodal trial function, Solving Multimodal Function has multiple Local Extremum, is mainly used in the performance that testing algorithm avoids being absorbed in local extremum.

3rd step, the non-linear inertia weight that successively decreases

Basic particle cluster algorithm does not set inertia weight time the most initial, what utilize in particle implementation is the information sharing that social learning's ability of particle and ability of self-teaching realize particle, with the location updating not having the mode of inertia weight to perform particle, particle performed with same state iteration in early stage and later stage, and the concrete condition do not performed according to particle to change accordingly.The given fixing inertia weight when particle cluster algorithm of standard is initial, balances the execution feature of particle in early stage and later stage to a certain extent.On the basis of standard particle group, scholar is had to propose a kind of inertia weight particle cluster algorithm of linear decrease, further improve the performance of algorithm, the mode of linear decrease is adopted in algorithm implementation, inertia weight early stage and decreased later velocity contrast little, do not meet particle and early stage there is larger inertia weight in operation, run later stage inertia weight less.

The present invention proposes a kind of non-linear inertia weight successively decreased, and is defined as follows

$w=w-\frac{(w_{max}-w_{min})}{sum(1:Iter)}\&times;({\mathrm{Iter}}_{max}-Iter)---\left(2\right)$

W _max, w _minfor the upper and lower limit of inertia weight, Iter _maxbe maximum iteration time, Iter is particle current iteration number of times, and inertia weight declines very fast early stage, and decreased later is slower.

4th step, determine the mode that particle position upgrades

Random number R between random generation one [0,1], compares with the probability P of initial setting, if R<P, performs by mode one; If R>P, perform by mode two;

Mode one: elite's backward learning

In particle colony, the individuality of fitness optimum is considered as elite's individuality, particle can follow optimum Particles Moving in the process of iteration, produce elite by backward learning oppositely to separate, expand the hunting zone of particle, by information sharing between particle, be conducive to particle search to global optimum, strengthen the region of elite's individuality search, convergence of algorithm speed and ability of searching optimum will be improved.

If the elite's individuality in current group is X _i=(x _{i, 1}, x _{i, 2}..., x _i,D), corresponding elite oppositely separates $X_i^{*}=(x_{i,1}^{*},x_{i,2}^{*},...,x_{i,D}^{*})$ Be defined as follows:

$X_{i,j}^{*}=k\left(a_j+b_j\right)-X_{i,j}---\left(3\right)$

Wherein X _i,j∈ [a _j, b _j], k ∈ [0,1], k is vague generalization coefficient, utilizes this coefficient can generate multiple different reverse elite individual.

Mode two: disturbed extremum

Basic particle cluster algorithm is easily absorbed in local optimum, particle populations has homoplasy, when particle cluster algorithm is absorbed in local optimum, namely the individual optimal value that experiences of particle and particle position are in one of globally optimal solution very little scope, speed then can be caused to be difficult to be upgraded, and particle can be searched for, because speed is very little within the scope of very little one of local optimum, particle is difficult to find more excellent position, and particle can be absorbed in local optimum.Larger hunting zone can allow particle be easy to jump out local optimum, therefore, introduces the scope that disturbed extremum expands particle search, avoids particle to be absorbed in local optimum, changed into by the more new formula of speed:

$v_{id}(t+1)={\mathrm{wv}}_{id}\left(t\right)+c_1{r}_1\left(\left(0.5+\frac{r_3}{2}\right)p_{id}-x_{id}\left(t\right)\right)+c_2{r}_2\left(\left(0.5+\frac{r_4}{2}\right)p_{gd}-x_{id}\left(t\right)\right)---\left(4\right)$

R in formula ₃and r ₄be equally distributed random number between (0,1), individual extreme value and global extremum can along with r ₃and r ₄value different and disturbance occurs, the size and Orientation of speed also can change, and the hunting zone of population expands, particle can fly to how new position, and particle easily finds the more figure of merit, by interparticle mutual study, particle can move to more excellent position, likely can jump out locally optimal solution.

5th step: upgrade individual extreme value and global extremum

After particle executes a location updating, for single particle, find the optimal-adaptive value that this particle has, as the individual extreme value of this particle, and particle position corresponding for adaptive value is upgraded, for N number of particle, find the global extremum of optimal-adaptive value as particle of all particles, upgrade the position of overall particle.Individual extreme value and global extremum are all upgraded in each iteration, can obtain more excellent particle, in upper iteration once, the information shared between particle can be more excellent, is more beneficial to particle and finds optimum solution.

6th step: particle continues the determination of executive condition

The execution of each particle all can have a condition stopped, when particle initialization, set the iterations Iter of particle and the assessment number of times A of particle, when the number of times of particle iteration does not reach Iter, the number of times t of the current iteration of particle increases once, particle implementation continues to perform, until reach the iterations of initial setting, the implementation of particle stops.

As shown in Figure 1, the technical scheme code flow adopted in the present embodiment is:

01) stochastic generation NP particle is as initial population N;

02)forIter＝1toIter _maxdo

03) inertia weight is upgraded by formula (4);

04)ifR≤Pthen

05) maximal value and the minimum value of particle motion interval scope is obtained;

06)fori＝1toNPdo

07) random coefficient k is generated;

08)forj＝1toDdo

09) the reverse solution of elite's particle is generated by formula (5);

10) if particle position is outside motion interval scope

11) renewal particle position is a random number within the scope of particle motion interval;

12)endif

13)endfor

14) particle fitness value is calculated;

15)endfor

16) from current individual and the reverse individuality of elite, select individuality as colony of future generation;

17)else

18) dynamic renewal maximal rate and minimum speed;

19) particle position is upgraded by formula (6);

20) particle fitness value is calculated;

21)fori＝1toNP

22) p is upgraded _bestand g _best;

23)endfor

24)endif

25) g is exported if reach maximum iteration time or meet accuracy requirement _best;

26)endfor

In order to test the method (DEOPSO) of the above-mentioned elite's backward learning particle group optimizing based on disturbance, the particle swarm optimization algorithm (PSO) of itself and standard and elite's backward learning particle swarm optimization algorithm (EOPSO) compare by we.Evaluate the performance of the inventive method, mainly from the evaluation number of times that (1) is fixing, the speed of convergence of assessment algorithm and convergence precision; (2) fixing convergence precision desired value, assessment algorithm reaches this assessment number of times required for precision target, and these two aspects are evaluated.

Adopt method of the present invention, test is optimized to function, trial function comprises the Solving Multimodal Function of unimodal trial function, simple Solving Multimodal Function, irrotational Solving Multimodal Function, band rotation, the global optimum of the function optimization provided is 0, dimension is 30 dimensions, and initialization population is 40, in order to the impact of elimination algorithm some enchancement factors in the process of implementation, by algorithm independent operating 30 times on each function, to obtain the evaluation of objective.

1) fixing evaluation number of times, the speed of convergence of assessment algorithm and convergence precision, concrete test result refers to table one.

2) fixing convergence precision desired value, assessment algorithm reaches this assessment number of times required for precision target, and concrete test result refers to table two.

Table one is fixing evaluates the convergence precision of number of times algorithm on trial function

Function name	DEOPSO	PSO	EOPSO
				Sphere (unimodal)	0.00E+00	9.78E-03	0.00E+00
Rosenbrock (simple multimodal)	2.55E+01	2.93E+01	3.74E-02
				Ackley (non-rotating multimodal)	8.88E-16	3.94E-14	3.99E-15
Weierstrass (non-rotating multimodal)	0.00E+00	1.30E-04	7.36E-10
				Rotated Weierstrass (rotation multimodal)	0.00E+00	6.66E-01	1.17E-09
Rotated Rastrigin (rotation multimodal)	0.00E+00	9.90E+00	0.00E+00

Table two is fixed convergence precision desired value and assess number of times on trial function

Function name	DEOPSO	EOPSO
			Sphere (unimodal)	2260	6354
Rosenbrock (simple multimodal)	200000	200000
			Ackley (non-rotating multimodal)	3820	9840
Weierstrass (non-rotating multimodal)	4460	12568
			Rotated Weierstrass (rotation multimodal)	4596	12676
Rotated Rastrigin (rotation multimodal)	2616	8804

Claims (3)

1., based on an implementation method for elite's backward learning particle group optimizing of disturbance, it is characterized in that, comprise the steps:

The first step, initialization Fe coatings

First arranging population particle scale is N, and also carry out initialization to the position of each particle, speed, the size of initial setting up particle iterations is Iter, and the assessment number of times of particle is A, and the dimension of particle is the social learning ability C of D, particle simultaneously ₁with the ability of self-teaching C of particle ₂, wherein

C ₁＝C ₂＝1.193(1)

Second step, calculating particle fitness value

The fitness value that the quality of particle is produced by fitness function is evaluated, and the best values that particle each in N number of particle experiences, is also called individual extreme value P _i=(P _i1, P _i2..., P _id) represent, value best in N number of particle, be also called global extremum P _g=(P _g1, P _g2..., P _gd) represent;

3rd step, the non-linear inertia weight that successively decreases

Propose a kind of non-linear inertia weight successively decreased, be defined as follows

$w=w-\frac{(w_{max}-w_{min})}{sum(1:Iter)}\&times;({\mathrm{Iter}}_{max}-Iter)---\left(2\right)$

Wherein, w _max, w _minfor the upper and lower limit of inertia weight, Iter _maxbe maximum iteration time, Iter is particle current iteration number of times, and inertia weight declines very fast early stage, and decreased later is slower;

4th step, determine the mode that particle position upgrades

Random number R between random generation one [0,1], compares with the probability P of initial setting, if R<P, performs by mode one; If R>P, perform by mode two;

Mode one: elite's backward learning

If the elite's individuality in current group is X _i=(x _{i, 1}, x _{i, 2}..., x _i,D), corresponding elite oppositely separates $X_i^{*}=(x_{i,1}^{*},x_{i,2}^{*},...,x_{i,D}^{*})$ Be defined as follows:

$X_{i,j}^{*}=k\left(a_j+b_j\right)-X_{i,j}---\left(3\right)$

Wherein X _i,j∈ [a _j, b _j], k ∈ [0,1], k is vague generalization coefficient, utilizes this coefficient can generate multiple different reverse elite individual;

Mode two: disturbed extremum

Introduce the scope that disturbed extremum expands particle search, avoid particle to be absorbed in local optimum, the more new formula of speed is changed into:

$v_{id}(t+1)={\mathrm{wv}}_{id}\left(t\right)+c_1{r}_1\left(\left(0.5+\frac{r_3}{2}\right)p_{id}-x_{id}\left(t\right)\right)+c_2{r}_2\left(\left(0.5+\frac{r_4}{2}\right)p_{gd}-x_{id}\left(t\right)\right)---\left(4\right)$

R in formula ₃and r ₄be equally distributed random number between (0,1), individual extreme value and global extremum can along with r ₃and r ₄value different and disturbance occurs;

5th step: upgrade individual extreme value and global extremum

After particle executes a location updating, for single particle, find the optimal-adaptive value that this particle has, as the individual extreme value of this particle, and particle position corresponding for adaptive value is upgraded, for N number of particle, find the global extremum of optimal-adaptive value as particle of all particles, upgrade the position of overall particle;

6th step: particle continues the determination of executive condition

The execution of each particle all can have a condition stopped, when particle initialization, set the iterations Iter of particle and the assessment number of times A of particle, when the number of times of particle iteration does not reach Iter, the number of times t of the current iteration of particle increases once, particle implementation proceeds, until reach the iterations of initial setting, the implementation of particle stops.

2. the implementation method of the elite's backward learning particle group optimizing based on disturbance according to claim 1, is characterized in that: successively decrease in inertia weight non-linear, the initial value of inertia weight w is set to 0.9.

3. the assessment of the implementation method performance of the elite's backward learning particle group optimizing based on disturbance according to claim 1 and 2, is characterized in that: the assessment of method performance adopts two kinds of methods below:

A. fixing evaluation number of times, the speed of convergence of appraisal procedure and convergence precision;

B. fix convergence precision desired value, appraisal procedure reaches this assessment number of times required for precision target.