CN104809500A - Efficient improved FSPSO (Particle Swarm Optimization based on prey behavior of Fish Schooling) - Google Patents

Abstract

The invention discloses an efficient improved FSPSO (Particle Swarm Optimization based on prey behavior of Fish Schooling). According to the efficient improved FSPSO, an intelligent behavior is simulated, and current globally-optimal particles search for current globally-superior positions through own optimal position information provided by a minority of other random particles. When fish schooling is attacked by other predators, weak fish which cannot escape quickly is eaten. The behaviors are simulated, weak particles close to current globally-worst particles are replaced with particles which are generated randomly, so that the diversity of the schooling is improved, and a local optimum can be effectively avoided by the FSPSO. The efficient improved FSPSO can be particularly applied to the solving process of complicated optimization problems such as function optimization and knapsack problems, traveling salesman problems, assembly line work problems and graph and image processing problems.

Description

A kind of improve PSO algorithm flutterring food behavior efficiently based on the shoal of fish

Technical field

The invention belongs to evolution algorithm technical field, relate to a kind of particle swarm optimization algorithm, be specifically related to a kind of improve PSO algorithm flutterring food behavior efficiently based on the shoal of fish.

Background technology

Particle swarm optimization algorithm (Particle Swarm Optimization, PSO) is by Kennedy and Eberhart by the observational study to some social action of flock of birds, the evolution algorithm of a kind of novelty of proposition.Because PSO parameters is few, easily realize, can be used for solving the complicated optimum problem of a large amount of non-linear, non-differentiability and multi-peak etc., be successfully applied to the numerous areas such as parameter optimization, feature extraction, traveling salesman problem, pattern-recognition.But in the optimization problem of complexity, particle cluster algorithm exists Premature Convergence, be easy to be absorbed in locally optimal solution.The people such as Angeline use for reference genetic algorithm idea and propose hybridization PSO algorithm concept, improve convergence of algorithm speed and precision.(the Fit ness-Distance-Ratio based Particle Swarm Optimization of the adaptive value-distance-proportional algorithm based on particle group optimizing that the people such as Peram proposed in 2003, FDR-PSO), in algorithm, each particle is according to certain adaptive value-distance-proportionality principle, carry out in various degree to neighbouring multiple particles with better adaptive value close, and best particle not only to current found is close.This algorithms to improve premature problem of PSO algorithm, in optimization complicated function, its performance obtains larger improvement.Bergh proposes collaborative PSO (Cooperative Particle Swarm Optimizer, CPSO), makes particle more easily jump out local minimum point, reaches higher convergence precision.Local optimum is absorbed in for preventing PSO algorithm, the people such as Liang proposed integrated learning particle swarm optimization algorithm (Comprehensive Learning ParticleSwarm Optimizer in 2006, CLPSO), make the renewal of the speed of each particle based on the history optimal location of other particles all, thus reach the object of integrated learning.Bergh proposes collaborative PSO (Cooperative ParticleSwarm Optimizer, CPSO), makes particle more easily jump out local minimum point, reaches higher convergence precision.Local optimum is absorbed in for preventing PSO algorithm, the people such as Liang proposed integrated learning particle swarm optimization algorithm (Comprehensive Learning Particle Swarm Optimizer in 2006, CLPSO), make the renewal of the speed of each particle based on the history optimal location of other particles all, thus reach the object of integrated learning.Wu Xiaojun is by analyzing the probability distribution of search center, propose search center equally distributed uniform search PSO (Uniform Search Particle Swarm Optimization between two extreme values, UPSO) algorithm, this algorithm search efficiency is high, good convergence.

Above-mentioned algorithm, when optimizing complicated higher-dimension multimodal function, is still easily absorbed in local optimum.

Summary of the invention

In order to solve above-mentioned technical matters, the present invention simulates the behavior that the shoal of fish flutters food, proposes a kind of improve PSO algorithm flutterring food behavior efficiently based on the shoal of fish.

The technical solution adopted in the present invention is: a kind of improve PSO algorithm flutterring food behavior efficiently based on the shoal of fish, is characterized in that, comprise the following steps:

Step 1: the parameter of the improve PSO algorithm of food behavior is flutterred in initialization efficiently based on the shoal of fish, described parameter comprises colony number n, maximum iteration time maxk, inertia weight w, Studying factors c ₁and c ₂, search population m, search factor c ₃with range factor c ₄, wherein 0≤m≤n/10;

Step 2: the position and speed of improving each particle in population are upgraded;

Step 3: self the optimal location information that the particle of current global optimum is provided by m random particles, finds the position that the current overall situation is more excellent;

Step 4: the small and weak particle near the poorest particle of the current overall situation is replaced by the random particle produced;

Step 5: judge, is the improve PSO algorithm flutterring food behavior based on the shoal of fish efficiently restrained or reaches maximum iteration time?

If so, then export the position of globally optimal solution, this position is the solution of optimization problem;

If not, then the step 2 described in revolution execution.

As preferably, the specific implementation process of step 3 is, a Stochastic choice m particle, and they self optimal location is: P ₁, P ₂..., P _m, the position of a current global optimum particle jth direction search is:

XX _j=P _g+ r ₃c ₃(P _j-P _g), wherein 1≤j≤n, r ₃equally distributed random number between [0,1], c ₃it is search factor; Judge: if XX _jin optimal value be better than P _g, then P is substituted by this optimal value _g; Otherwise, P _gvalue constant.Current global optimum is learnt by self optimal value to minority particle, improves the ability of searching optimum of algorithm.

As preferably, the small and weak particle described in step 4, if the position of the poorest population of the overall situation is: P _b=(P _b1, P _b2..., P _bD), the position of a jth small and weak particle is Y _j, because small and weak particle is near the poorest particle of the overall situation, then Y _jand P _bdistance meet relational expression wherein c ₄be range factor, Range is the hunting zone of particle.The particle that small and weak particle is randomly generated substitutes, and this enhances the diversity of colony, effectively can avoid local optimum.

A kind of improve PSO algorithm (ParticleSwarm Optimization based on prey behavior of Fish Schooling is called for short FSPSO) flutterring food behavior efficiently based on the shoal of fish that the present invention proposes.The shoal of fish transmits heuristic information by ripples, to flutter in food by perception ripples information searching to better position.The present invention simulates this intelligent behavior, self the optimal location information that the particle of current global optimum is provided by other minority random particles, finds the position that the current overall situation is more excellent.When the shoal of fish by other flutter trencherman attack time, the small and weak fish that can not escape very soon will be eaten up.The present invention simulates these behaviors, and replaced by the random particle produced by the small and weak particle near the poorest particle of the current overall situation, this enhance the diversity of colony, FSPSO can avoid local optimum effectively.The present invention can be particularly applicable in the solution procedure of the complicated optimum problem such as function optimization, knapsack problem, traveling salesman problem, pipelining problem and graph and image processing.

Accompanying drawing explanation

Fig. 1: the global optimum's particle search directional diagram being the embodiment of the present invention;

Fig. 2: be the embodiment of the present invention the poorest particle of the overall situation near small and weak particle schematic diagram;

Fig. 3: be the embodiment of the present invention for function f ₂the convergence map of (x);

Fig. 4: be the embodiment of the present invention for function f ₇the convergence map of (x);

Fig. 5: the convergence map for knapsack problem being the embodiment of the present invention.

Embodiment

Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with drawings and Examples, the present invention is described in further detail, should be appreciated that exemplifying embodiment described herein is only for instruction and explanation of the present invention, is not intended to limit the present invention.

In hypothetical particle group algorithm, population is n, and search volume is D dimension, and position and the speed of i-th particle are respectively x _iand v _i, then:

x _i＝(x _i1,...,x _id,...,x _iD) (1)，

v _i＝(v _i1,...,v _id,...,v _iD) (2)；

The position in colony with optimal-adaptive degree particle is designated as:

P _g＝(P _g1,P _g2,...,P _gD) (3)；

I-th particle experience solution space desired positions be:

P _i＝(P _i1,P _i2,...,P _iD) (4)；

The equation that then particle cluster algorithm position and speed upgrade is:

$V_{\mathrm{id}}^{k+1}=w{V}_{\mathrm{id}}^k+c_1{r}_1(P_{\mathrm{id}}^k-X_{\mathrm{id}}^k)+c_2{r}_2(P_{\mathrm{gd}}^k-X_{\mathrm{id}}^k)---\left(5\right);$

$X_{\mathrm{id}}^{k+1}=X_{\mathrm{id}}^k+V_{\mathrm{id}}^{k+1}---\left(6\right);$

Wherein, w is Inertia Weight, and k is iterations, c ₁and c ₂be all Studying factors, r ₁and r ₂all for being evenly distributed on the random number in interval [0,1].The variation range of d particle position and speed is respectively [XMIN _d, XMAX _d] and [VMIN _d, VMAX _d].If the value calculated by formula (5) and (6) has exceeded this scope, then it is set for boundary value.

Research finds that the shoal of fish can produce complicated ripples, and flutterring in food action process, the heuristic information flutterring food transmits by ripples.Simulate this intelligent behavior, self the optimal location information that the particle of current global optimum is provided by other minority random particles, find the position that the current overall situation is more excellent.

Without loss of generality, provide m particle Stochastic choice of heuristic information, they self optimal location is:

P ₁,P ₂,...,P _m(7)；

As shown in Figure 1, the position of a jth direction search of current global optimum particle search is in the direction of the more excellent particle of current global optimum particle search:

XX _j＝P _g+r ₃·c ₃·(P _j-P _g) (8)；

Wherein 1≤j≤n, r ₃equally distributed random number between [0,1], c ₃it is search factor.If XX _jin optimal value be better than P _g, then P is substituted by this optimal value _g; Otherwise, P _gvalue constant.For reducing calculated amount, the value of m is unsuitable excessive.Current global optimum is learnt by self optimal value to minority particle, improves the ability of searching optimum of algorithm.

The shoal of fish is flutterring in food process and can flutterred trencherman's attack by other, and according to Darwin's theory that the weak are the prey of the strong, the small and weak fish that can not escape very soon will be eaten up.The present invention simulates these behaviors, is replaced by the small and weak particle near the poorest particle of the current overall situation by the random particle produced.

The position of the poorest population of the overall situation is:

P _b＝(P _b1,P _b2,...,P _bD) (9)；

The position of a jth small and weak particle is Y _j, because small and weak particle is near the poorest particle of the overall situation, then Y _jand P _bdistance very little, the relation between them is as shown in Figure 2.Y _jwith P _bcentered by circle in, then the relation between them meet:

$\underset{i=1}{\overset{D}{\mathrm{\Σ}}}|Y_{\mathrm{ji}}-P_{\mathrm{bi}}|\≤c_4\·\mathrm{Range}---\left(10\right);$

Wherein c ₄be range factor, Range is the hunting zone of particle.The particle that small and weak particle is randomly generated substitutes, and this enhances the diversity of colony, and FSPSO can avoid local optimum effectively.

The present invention simulates the shoal of fish and flutters food behavior proposition FSPSO algorithm, and concrete steps are as follows:

Step 1: the parameter of initialization FSPSO algorithm, parameter comprises colony number n, maximum iteration time maxk, inertia weight w, Studying factors c ₁and c ₂, search population m, search factor c ₃with range factor c ₄, wherein 0≤m≤n/10;

Step 2: the position of particle each in colony and speed are upgraded by formula (5) and (6);

Step 3: self the optimal location information that the particle of current global optimum is provided by m random particles, finds the position that the current overall situation is more excellent, improves by formula (8);

Step 4: the small and weak particle near the poorest particle of the current overall situation is replaced by the random particle produced, improves by formula (10);

Step 5: judge, is FSPSO algorithm restrained or is reached maximum iteration time?

If so, then export the position of globally optimal solution, this position is the solution of optimization problem;

If not, then the step 2 described in revolution execution.

In FSPSO algorithm, calculate current optimal particle P _g, the poorest particle P _bwith each particle self optimal location P _itime complexity be O (n*D), the time complexity of the small and weak particle replaced near the poorest particle by random particles is O (n*D), and the time complexity of the more excellent position of current global optimum particle search is O (m*n*D).Because the value of m is smaller, so the time complexity of FSPSO is O (n*D*maxk), the same with the time complexity of PSO.In FSPSO, P _i, P _gand P _bposition need be stored.So the space complexity of FSPSO is O (n*D), the same with the space complexity of PSO.In sum, the Time & Space Complexity of FSPSO and the same of PSO, so the performance of FSPSO is fine.

In order to assess the performance of FSPSO, utilize the trial function of this algorithm to 9 standards to be optimized, trial function is as shown in table 1, and the development environment of experiment is as follows: Matlab R2012b, CPU are i7-2600k3.4GHz.

Table 1 trial function

F in table 1 ₁(x)-f ₆x () is single mode function, f ₇(x)-f ₉x () is multi-modal function.In these functions, N is the dimension of function, and these functional minimum value are all 0, and optimum solution is [0] ⁿ.FSPSO, PSO and GA are used to optimize above-mentioned function, and in these three kinds of algorithms, dimension is 30 (N=D=30), and population number is 50, and maximum iteration time is 1000.In PSO, c ₁=c ₂=2, inertial factor w along with iterations is from 0.9 to 0.7 linear decrease.The parameter searching out FSPSO suitable by comparative experiments is as follows: the setting of other parameters of stepa=1.5, stepb=0.0001, m=4, FSPSO is the same with in PSO.The optimum configurations of GA is as follows: crossover probability is 0.95, and adopt Stochastic choice mechanism, the probability of Gaussian mutation is 0.1.The Optimal Experimental of each function runs 30 times, and the optimal value of separating for 30 times, mean value, intermediate value, variance are as shown in table 2.

The result of table 2 three kinds of algorithm optimization functions

As shown in Table 2, to good all than GA and PSO of the optimum solution of all function F SPSO, so the ability of searching optimum of FSPSO is better than other two kinds of algorithms.All PSO is better than, except f to the mean value of all function F SPSO ₁(x), f ₃(x) and f ₈x () outward, the mean value of FSPSO is all better than GA.So the overall search performance of FSPSO is better than other two kinds of algorithms.Except f ₇x () outward, the intermediate value of FSPSO is all less than PSO, except f ₃(x) and f ₈x () outward, the intermediate value of FSPSO is all less than GA.Except f ₇x () outward, the variance of FSPSO is all less than PSO, except f ₁(x), f ₃(x) and f ₈x () outward, the variance of FSPSO is all less than GA.So the stability of FSPSO is better than other two kinds of algorithms.

Convergence curve for evaluating the performance of three kinds of algorithms, in order to without loss of generality, Stochastic choice single mode function f ₂(x) and multi-modal function f ₇x () is analyzed.In order to analyze convergence curve better, the value of separating in iteration is taken the logarithm, and three kinds of convergence of algorithm curves as shown in Figure 3 and Figure 4.From convergence curve, be compared to other two kinds of algorithms, FSPSO has better ability of searching optimum and convergence.FSPSO finds the iterations of global optimum to be less than other algorithms, so the efficiency of convergence is higher.Compare PSO, FSPSO is more effective.So FSPSO shows obvious improvement effect in majorized function, overall performance is also fine.

Knapsack problem is typical np hard problem, and GA, PSO and FSPSO are for optimizing a knapsack problem, and in this problem, cost matrix c and volume matrix w is as follows:

c＝[220,208,198,192,180,180,165,162,160,158,155,130,125,122,120,118,115,110,105,101,100,100,98,96,95,90,88,82,80,77,75,73,72,70,69,66,65,63,60,58,56,50,30,20,15,10,8,5,3,1]

w＝[80,82,85,70,72,70,66,50,55,25,50,55,40,48,50,32,22,60,30,32,40,38,35,32,25,28,30,22,50,30,45,30,60,50,20,65,20,25,30,10,20,25,15,10,10,10,4,4,2,1]

The limit value of volume is 1000.Because knapsack problem is a discrete problem, in the present invention, the discretization method of each particle position is:

$X_{\mathrm{id}}^k=\left\{\begin{array}{ccc}1& \mathrm{if}& r_4<\mathrm{sig}\left(V_{\mathrm{id}}^k\right)\\ 0& \mathrm{else}& \end{array}\right.---\left(11\right);$

$\mathrm{sig}\left(V_{\mathrm{id}}^k\right)=\frac{1}{1+\exp (-V_{\mathrm{id}}^k)}---\left(12\right);$

Wherein r ₄it is equally distributed random number between [0,1].Experimental situation is the same with arranging in sum functions optimization problem of algorithm parameter, and the iterativecurve of three kinds of Algorithm for Solving knapsack problems as shown in Figure 5.As shown in Figure 5, the ability of searching optimum of FSPSO is better than other two kinds of algorithms.The experiment of three kinds of these knapsack problems of algorithm optimization runs 30 times, and the optimal value of separating for 30 times, worst-case value, mean value, intermediate value, variance are as shown in table 3.

The result of table 3 three kinds of algorithm optimization knapsack problems

Algorithm	Optimum	The poorest	On average	Middle	Variance
						GA	2909	2670	2788.5	2787	49.5
PSO	2955	2687	2820.3	2812	58.7
						FSPSO	3030	2899	2957.4	2961	31.8

As shown in Table 3, the optimal value that FSPSO obtains, worst-case value, mean value and intermediate value are greater than the analog value that GA and PSO obtains, and the variance that FSPSO obtains then is less than other two kinds of algorithms.So the ability of searching optimum of FSPSO and convergence are better than other two kinds of algorithms, illustrate for knapsack problem FSPSO more effective.

The present invention proposes a kind of improve PSO algorithm FSPSO flutterring food behavior based on the shoal of fish, the position that self optimal location information searching that the particle of current global optimum is provided by other minority random particles is more excellent, the ability of searching optimum of such algorithm enhances.Small and weak particle near the poorest particle of the current overall situation is replaced by the random particle produced, which increases the diversity of population and avoid locally optimal solution.By trial function and the typical knapsack problem of optimizing criterion, demonstrate FSPSO for solve continuously and discrete optimization problems of device has higher efficiency.

Should be understood that, the part that this instructions does not elaborate all belongs to prior art.

Should be understood that; the above-mentioned description for preferred embodiment is comparatively detailed; therefore the restriction to scope of patent protection of the present invention can not be thought; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that the claims in the present invention protect; can also make and replacing or distortion, all fall within protection scope of the present invention, request protection domain of the present invention should be as the criterion with claims.

Claims (3)

1. flutter an improve PSO algorithm for food behavior efficiently based on the shoal of fish, it is characterized in that, comprise the following steps:

Step 1: the parameter of the improve PSO algorithm of food behavior is flutterred in initialization efficiently based on the shoal of fish, described parameter comprises colony number n, maximum iteration time maxk, inertia weight w, Studying factors c ₁and c ₂, search population m, search factor c ₃with range factor c ₄, wherein 0≤m≤n/10;

Step 2: the position and speed of improving each particle in population are upgraded;

Step 3: self the optimal location information that the particle of current global optimum is provided by m random particles, finds the position that the current overall situation is more excellent;

Step 4: the small and weak particle near the poorest particle of the current overall situation is replaced by the random particle produced;

Step 5: judge, is the improve PSO algorithm flutterring food behavior based on the shoal of fish efficiently restrained or reaches maximum iteration time?

If so, then export the position of globally optimal solution, this position is the solution of optimization problem;

If not, then the step 2 described in revolution execution.

2. the improve PSO algorithm flutterring efficiently food behavior based on the shoal of fish according to claim 1, is characterized in that: the specific implementation process of step 3 is, a Stochastic choice m particle, and they self optimal location is: P ₁, P ₂..., P _m, the position of a current global optimum particle jth direction search is: XX _j=P _g+ r ₃c ₃(P _j-P _g), wherein 1≤j≤n, r ₃equally distributed random number between [0,1], c ₃it is search factor; Judge: if XX _jin optimal value be better than P _g, then P is substituted by this optimal value _g; Otherwise, P _gvalue constant.

3. the improve PSO algorithm flutterring food behavior efficiently based on the shoal of fish according to claim 1, is characterized in that: the small and weak particle described in step 4, if the position of the poorest population of the overall situation is: P _b=(P _b1, P _b2..., P _bD), the position of a jth small and weak particle is Y _j, because small and weak particle is near the poorest particle of the overall situation, then Y _jand P _bdistance meet relational expression wherein c ₄be range factor, Range is the hunting zone of particle.