CN102479338A - Particle swarm optimization algorithm utilizing sine function to describe nonlinear inertia weight - Google Patents

Abstract

Provided is a particle swarm optimization algorithm utilizing sine function to describe nonlinear inertia weight so as to improve inertia weight of particle swarm. The particle swarm optimization algorithm includes steps of firstly, regulating parameters of a standard particle swarm optimization algorithm completely and describing the inertia weight of the particle swarm optimization algorithm by sine function; and secondly, performing self-adaptive nonlinear regulation of position and speed of particles, so that the particle swarm optimization algorithm has higher convergence rate in the prior period while local search capacity is enhanced in the later period, the probability of local extremum of particles is reduced, results can be converged into the global optimal solution, and good test effect is realized.

Description

The particle swarm optimization of nonlinear inertial weight is described with sine function

One, technical field

Particle swarm optimization is according to the flock of birds one type of emerging random optimization algorithm that is used to solve optimization problem that proposes with cluster model of migrating in the process of looking for food, and it is advantageous that simple realize easily and powerful.Generally speaking, the more potential application of particle swarm optimization comprises system design, multiple-objection optimization, classification, pattern-recognition, scheduling, signal Processing, decision-making, robot application etc.Wherein concrete application example has: design of Fuzzy Controller, Job Shop Scheduling, robot real-time route planning, automatic target detection, time frequency analysis etc.

Two, background technology

The particle swarm optimization algorithm is a kind of evolutionary computing based on the colony intelligence method.Particle swarm optimization is similar with genetic algorithm, is a kind of optimization tool based on colony.System initialization is one group of RANDOM SOLUTION, searches optimal value through iteration.But do not have intersection and mutation operation that genetic algorithm is used, but the particle that particle (potential separates) is followed optimum in solution space is searched for.Compare with genetic algorithm, the advantage of particle swarm optimization is the simple deep intelligent background that realizes easily having again simultaneously, and both suitable scientific research is particularly suitable for practical applications again.Therefore, particle swarm optimization one proposes, and has caused the scholars' in fields such as EVOLUTIONARY COMPUTATION extensive concern at once, and in short several years, a large amount of achievements in research occurs, has formed a research focus.

Particle swarm optimization is proposed in nineteen ninety-five by Kennedy and Eberhart the earliest, and the result of study that receives artificial life inspires, and the key concept of particle swarm optimization comes from the research to the flock of birds predation.Imagine such scene: bevy is at random search food.In this zone, has only a food.All birds are not all known food there.But they know how far current position also has from food.What the optimal strategy that finds food so is.The most simple and effective is exactly to search present peripheral region from the nearest bird of food.Particle swarm optimization takes a hint from this model and is used to solve optimization problem.In the particle swarm optimization, potential the separating of each optimization problem all is a bird in the search volume, is referred to as " particle ".All particles all have an adaptive value by optimised function decision, and each particle also has a speed to determine direction and distance that they circle in the air.Particles are just followed current optimal particle and in solution space, are searched for then.Particle swarm optimization is initialized as a group random particles (RANDOM SOLUTION).Find optimum solution through iteration then.In iteration each time, particle upgrades oneself through following the tracks of two " extreme values ".First is exactly the optimum solution that particle itself is found.This is separated and is called individual extreme value.Another extreme value is the optimum solution that whole population is found at present.This extreme value is a global extremum.In addition also can whole population and just with wherein a part is as the neighbours of particle, the extreme value in all neighbours is exactly a local extremum so.

Owing to recognize the wide application prospect that particle swarm optimization contains in fields such as function optimizations, a lot of scholars have carried out the research of this respect after Kennedy and Eberhart.At present, proposed multiple particle swarm optimization and improved algorithm, and particle swarm optimization has been widely used in function optimization, neural metwork training, pattern classification, fuzzy system control and other application.

Three, summary of the invention

The object of the present invention is to provide a kind of intelligent algorithm of more optimizing.Concrete implementation procedure is on particulate crowd existed algorithms, to improve, and makes algorithm have speed of convergence faster at preliminary stage, strengthens local search ability during the late stages of developmet, reduces the chance that particulate is absorbed in local extremum, makes the result converge on globally optimal solution.

Description of drawings

Fig. 1 is the new inertia weight figure of this method;

Fig. 2 separates movement locus for this method individuality;

Fig. 3 is a contrast test result

Fig. 4 is for adopting the contrast test result of Levy No.5 function

Fig. 5 is for adopting the contrast test result of Shaffer ' s F6 function

Embodiment:

Below in conjunction with accompanying drawing and instantiation the present invention is further specified:

1, at first provides the algorithm model of standard particle swarm optimization algorithm.

Supposing has n particulate in M dimension region of search, they form a colony.X _i=(x _I1, x _I2..., x _Im), i=1,2 ..., n is the position vector of particulate i, V _i=(v _I1, v _I2,, v _Im) be the velocity vector of particulate i, they all are the M dimensions.P _i=(p _I1, p _I2... P _Im) be particulate i in optimizing process the position with best adaptive value of process; P _g=(p _G1, p _G2... P _Gm) be the optimal location that whole particulate group hunting arrives.

I the particulate in t generation evolve to t+1 for the time, the speed of j dimension and position are with following evolution equation calculating:

v _ij(t+1)＝ω·v _ij(t)+c ₁·r ₁·(p _ij(t)-x _ij(t))

(1)

+c ₂·r ₂·(p _gj(t)-x _ij(t))

x _ij(t+1)＝x _ij(t)+v _ij(t+1)

(2)

Each dimension of particle rapidity all can be limited in a maximal rate v _Max(v _Max＞0) in, if the speed after certain one dimension upgrades surpasses the v that the user sets _MaxThe time, the speed of this one dimension just is restricted to v so _Max, that is: if v _Ij＞v _MaxThe time, v _Ij=v _Max, or v _Ij＜-v _MaxThe time, v _Ij=-v _Max

Optimizing early stage, can be in order to make particulate with bigger speed near optimal location; Optimizing the later stage, in order not make the excessive disengaging optimal location of particle speed, carry out the self-adaptation adjustment to the formula in the standard particle swarm optimization (1) (2), formula (2) becomes:

x _ij(t+1)＝x _ij(t)+η(t)·v _ij(t+1) (3)

2, its algorithm is improved

Value and the inertia weight that the present invention proposes a kind of accelerator coefficient combines, inertia weight increases the improvement particle cluster algorithm that afterwards subtracts earlier along sinusoidal curve such as Fig. 1; And speed is carried out the parameter adaptive adjustment; Preliminary stage at algorithm has speed of convergence faster like this, and has good local search ability in the algorithm later stage, has both kept to have the advantage that increases progressively the inertia weight and the inertia weight particle swarm optimization that successively decreases; Also overcome their shortcoming, obtained reasonable experiment effect.

Dynamically adjustment inertia weight ω can make the particle swarm optimization algorithm have stronger global convergence ability in the early stage, has stronger local convergence ability in the later stage.Therefore, formula (1) can be expressed as:

v _ij(t+1)＝ω(t)·v _ij(t)+c ₁·r ₁·[p _ij(t)-x _ij(t)]+c ₂·r ₂·[p _gj(t)-x _ij(t)] (4)

Make λ ₁=c ₁r ₁, λ ₂=c ₂r ₂, inertia weight ω and accelerator coefficient λ ₁, λ ₂Between satisfy following relational expression algorithm convergence

Be λ ₁+ λ ₂＜2 (ω+1) make λ ₁=(ω+1) * rand1, λ ₂=(ω+1) * (2-rand1) * rand2.

So this paper is to parameter ω (t), η (t) carries out self-adaptation and dynamically adjusts.So that make the convergence of algorithm better effects if.

The adjustment law of parameter is respectively:

$\mathrm{\ω}\left(t\right)=\sin (\frac{2}{3}\mathrm{\π}\×\frac{k}{\max \mathrm{number}}+\frac{1}{3}\mathrm{\π})---\left(5\right)$

$\mathrm{\η}\left(t\right)=\frac{({\mathrm{\η}}_{\max }-{\mathrm{\η}}_{\min })}{1+\exp [\mathrm{\α}\×(t-\max \mathrm{number}/2)]}+{\mathrm{\η}}_{\min }---\left(6\right)$

In the formula (6), η _Max, η _MinBe maximal value and the minimum value that η (t) changes, generally get η _Max∈ [1.0,1.8], η _Min∈ [0.4,0.8]; T is an optimizing algebraically, and max number is a maximum iteration time; α is a constant, generally gets α ∈ [0.005,0.015].

3, emulation experiment

Transfer the performance of joining tactful improvement particle swarm optimization for what propose above verifying based on nonlinear s in function, adopt Shaffer ' s F6 and Levy No.5 function that it is tested, and experimental result is analyzed.

1)Shaffer’s?F6?Function：

$\min F(x,y)=\frac{{\sin }^2\sqrt{x^2+y^2}-0.5}{{(1+0.001(x^2+y^2))}^2}-0.5---\left(7\right)$

2)Levy?No.5?Function：

$\min F(x,y)=\underset{i=1}{\overset{5}{\mathrm{\Σ}}}[i\×\cos ((i-1)\×x+i)]$

$\×\underset{j=1}{\overset{5}{\mathrm{\Σ}}}[j\×\cos ((j+1)\×y+j)]---\left(8\right)$

$+{(x+1.42513)}^2+{(y+0.80032)}^2$

At first, test with Shaffer ' s F6 function.In test process, getting particle number is 50, and maximum iteration time is 2000, and the γ value is 0.0085, and the optimizing termination condition is that particulate crowd's the difference of optimal-adaptive value and optimum solution is less than 0.00001.L-G simulation test has been done 4 times altogether, in each experiment, carries out 100 times optimizing process altogether.Experimental result such as table 1, Fig. 2 separates the individual movement track for it.

From table 1, can find out, adopt nonlinear s in function that inertia weight is carried out the self-adaptation adjustment, help searching process to flee from the local optimum point, avoid particle swarm optimization to be easy to be absorbed in local optimum.Secondly, test with the LevyNo.5 function.Function is tested.Done many groups of experiments equally, Fig. 3 is single test result's wherein a contrast test.

For this improved validity of demonstration further, contrast with basic particle swarm optimization (Normal particle swarm optimization), the linear nonlinear inertial weight particle swarm optimization (Nonlinear weight particle swarm optimization) of transferring ginseng particle swarm optimization (Linear weight particle swarm optimization) and this paper to propose.The result of single test such as Fig. 4,5.

From Fig. 4, can find out in 5, carry out the initial stage at algorithm, propose in the literary composition based on the inertia weight of sin function and combine the particle swarm optimization of speed parameter self-adaptation adjustment all faster than other speed of convergence of two kinds; Carry out the later stage at algorithm, its speed of convergence decreases, and can make searching process move closer to optimum solution, thereby has avoided search to shake.

Table 1 is transferred ginseng method test result contrast for two kinds

Claims (2)

1. the parameter of standard particle swarm optimization is carried out all fronts adjustment, the inertia weight in the particle swarm optimization is described with sine function;

2. through particle position and speed are carried out the self-adaptation nonlinear adjustment, make algorithm have speed of convergence faster, strengthen local search ability during the late stages of developmet, reduce the chance that particulate is absorbed in local extremum, make the result converge on globally optimal solution at preliminary stage.

Images