CN104834957A - Method and device for solving nonlinear programming model based on cuckoo search algorithm - Google Patents

Abstract

The invention discloses a method for solving a nonlinear programming model based on a cuckoo search algorithm, which comprises the steps of A, randomly generating m bird's nests and calculating the fitness of each bird's nest; B randomly selecting one bird' nest, generating a new bird' nest through executing Levy flight, calculating the fitness of the new bird's nest, replacing the original bird's nest with the new bird's nest if the fitness of the new bird's nest is greater than the fitness of the original bird's nest; randomly selecting m*Pa bird's nests, generating m*Pa new bird's nests through executing sinusoidal carrier based Levy flight, calculating the fitness of the new bird's nests, and replacing the original bird's nests with the new bird's nests; D, acquiring the bird's nest with the fitness being the highest, and storing the bird's nest as the current optimal bird's nest if the fitness of the bird' nest is greater than the fitness of the current optimal bird's nest; and E, judging whether the number of iterations reaches a preset threshold value or not, if so, using the current optimal bird's nest to act as the optimal solution to output, and if not, returning back to the step B. The invention further discloses a device corresponding to the method and computing equipment comprising the device.

Description

A kind of method and apparatus solving Nonlinear programming Model based on cuckoo searching algorithm

Technical field

The present invention relates to the planning field of power distribution network, be specifically related to a kind of method and apparatus solving Nonlinear programming Model based on cuckoo searching algorithm.

Background technology

In recent years, along with the important breakthrough of the aggravation of environmental pollution, the shortage of fossil energy and new energy technology, the status of traditional energy generating is subject to great weakening, and simultaneously, as complementation, the development of new forms of energy is advanced by leaps and bounds, and especially sufficient the and parent that the wind-powered electricity generation of technology maturation is more and more subject to Utilities Electric Co. of various countries of the energy looks at.From the angle of planning, consideration rack and load that the planning of power distribution network can not be simple, wind-powered electricity generation should be considered into as the distributed power supply of one.

When building the Bi-level Programming Models of power distribution network, wind energy turbine set has leading position, thus as upper strata planning layer as planning main body.The upper strata planning layer in a distributed manner position of power supply (DWG), capacity and active management expense is control variable, its target is the maximization realizing oneself net proceeds, this net proceeds considers wind energy turbine set sale of electricity income and pays the active management expense of power distribution network company, has taken into account the wind-powered electricity generation cost of investment after annual operating and maintenance cost and year value in addition.Be limited by the factor such as floor area, space wind power concentration, installed capacity of wind-driven power must be less than certain value, and in addition, the minimum installation number of units of Wind turbines defines the lower limit of installed capacity of wind-driven power.

The objective function of this plan model is

$\begin{array}{c}\underset{x_k,{\mathrm{\ω}}_k^{\mathrm{DWG}},{\mathrm{\ρ}}^{\mathrm{AM}}}{\max }{B}_{\mathrm{DWG}}=({\mathrm{\ρ}}^{\mathrm{DWG}}-{\mathrm{\ρ}}^{\mathrm{AM}})\underset{t\∈T}{\mathrm{\Σ}}\mathrm{\Δt}\·\underset{k{\∈\mathrm{\Ω}}_{\mathrm{DWG}}}{\mathrm{\Σ}}(P_{k,t}^{\mathrm{DWG}}\·x_k)\\ -F(d,m)\·R_I^{\mathrm{DWG}}\·\underset{k{\∈\mathrm{\Ω}}_{\mathrm{DWG}}}{\mathrm{\Σ}}({\mathrm{\ω}}_k^{\mathrm{DWG}}\·x_k)\\ -R_O^{\mathrm{DWG}}\·\underset{k{\∈\mathrm{\Ω}}_{\mathrm{DWG}}}{\mathrm{\Σ}}(P_{k,t}^{\mathrm{DWG}}\·x_k)\end{array}---\left(1\right)$

The constraint condition of this plan model is

${\mathrm{\ω}}_{\min }^{\mathrm{DWG}}\≤{\mathrm{\ω}}_k^{\mathrm{DWG}}\≤{\mathrm{\ω}}_{\max }^{\mathrm{DWG}}---\left(2\right)$

x _k∈{0,1} (3)

$P_{i,t}^{\mathrm{Grid}}+P_{i,t}^{\mathrm{DWG}}-\underset{\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L}{\mathrm{\Σ}}{P}_{\mathrm{ij},t}^F-\underset{\left(\mathrm{ki}\right)\∈{\mathrm{\Ω}}_L}{\mathrm{\Σ}}{P}_{\mathrm{ki},t}^T=P_{i,t}^D,---\left(4\right)$

$\∀i\∈{\mathrm{\Ω}}_N,\∀t\∈T$

$P_{\mathrm{ij},t}^{\mathrm{Loss}}=P_{\mathrm{ij},t}^F+P_{\mathrm{ij},t}^T,\∀\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L,\∀t\∈T---\left(5\right)$

$P_{\mathrm{ij},t}^F=\frac{R_{\mathrm{ij}}}{Z_{\mathrm{ij}}^2}{U}_{i,t}(U_{i,t}-U_{j,t}),\∀\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L,\∀t\∈T---\left(6\right)$

$P_{\mathrm{ij},t}^T=\frac{R_{\mathrm{ij}}}{Z_{\mathrm{ij}}^2}{U}_{j,t}(U_{j,t}-U_{i,t}),\∀\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L,\∀t\∈T---\left(7\right)$

$I_{\mathrm{ij},t}=\frac{U_{i,t}-U_{j,t}}{Z_{\mathrm{ij}}},\∀\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L,\∀t\∈T---\left(8\right)$

$U_{\min }\≤U_{i,t}\≤U_{\max },\∀i\∈{\mathrm{\Ω}}_N,\∀t\∈T---\left(9\right)$

$-I_{\mathrm{ij}}^{\max }\≤I_{\mathrm{ij},t}\≤I_{\mathrm{ij}}^{\max },\∀\left(\mathrm{ij}\right)\∈{\mathrm{\Ω}}_L,\∀t\∈T---\left(10\right)$

$0\≤P_{g,t}^{\mathrm{Grid}}\≤P_{\max }^{\mathrm{Grid}},\∀g\∈{\mathrm{\Ω}}_G,\∀t\∈T---\left(11\right)$

In formula (1) ~ (12), B _dWGthe net proceeds of wind energy turbine set company, ρ ^dWGthe rate for incorporation into the power network of unit quantity of electricity wind-powered electricity generation, ρ ^aMbe the active management price of unit quantity of electricity, Δ t is the duration of a period in the working train family cycle, be in unit interval section a kth wind energy turbine set node place the power sent out, x _kbe two-valued variable, get 0 expression and wind-powered electricity generation is not installed, get 1 expression and wind-powered electricity generation is installed.T and Ω _dWGtime interval set and DWG candidate point set respectively.F (d, m) is a year value coefficient, F (d, m)=d (1+d) ^m/ [(1+d) ^m-1], d is damage rate, and m is the seeervice cycle of corresponding device. the cost of investment of wind energy turbine set unit installed capacity, it is the installed capacity of wind-driven power of k Nodes. it is the annual operating and maintenance cost of wind-powered electricity generation unit capacity. with the minimum and maximum installed capacity of wind energy turbine set respectively. the power that i-th Nodes t time period internal loading consumes. the power attenuation of circuit ij in t time period, the power that in t time period, major network provides.Ω _n, Ω _l, Ω _gload bus set in system, line set and the set of major network access point respectively. r _ijand Z _ijthe top of circuit ij, terminal active power and resistance, resistance value respectively.I _{ij, t}with electric current and the line energizing flow amount thereof of circuit ij in t time period respectively.U _i,tthe voltage of t time period interior nodes i, U _minand U _maxnode voltage bound respectively. it is maximum major network output power. a kth wind power that wind energy turbine set reality is available, ξ to exert oneself perunit value data according to the blower fan that calculates of typical case's day air speed data.

Above-mentioned plan model is a Nonlinear programming Model, can adopt cuckoo searching algorithm (CuckooSearch, CS) to solve.Cuckoo searching algorithm is a novel meta-heuristic algorithm found from the boarding reproductive behavior of cuckoo population, is integrated with row dimension offline mode (Levy flightpattern) method to generate new explanation in this algorithm.

The egg of oneself lives with in the Bird's Nest of other birds by cuckoo usually, and they can judge the quality of Bird's Nest by the instinct of oneself uniqueness thus select optimal boarding Bird's Nest.Once choose Bird's Nest, original bird egg will be thrown away to increase oneself offspring by the probability of bringing up by cuckoo.Some cuckoos even can by imitating the offspring of the morphological feature camouflage oneself of host's bird egg.Certainly, host bird also may find foreign invaders, and once be found, host bird will be removed foreign peoples or directly abandon original Bird's Nest.In general, the hatching of cuckoo slightly early than host bird, the meeting of these cuckoo birdling instincts other bird egg is released Bird's Nest thus increase oneself by nursing probability.Cuckoo searching algorithm is implemented based on above-mentioned behavior, and in the process implemented, some process need does idealized process certainly:

(1) in any case, can only have a bird egg in a Bird's Nest, Bird's Nest is equivalent to bird egg, and what they were all same is regarded as a solution.

(2) namely elite's bird egg represents current optimum solution and will be carried over into the next generation.

(3) host bird is with certain probability P _afind foreign peoples, once find namely to produce new explanation.

New explanation realizes by performing Levy flight, specific as follows:

$x_i^{T+1}=x_i^T+{\mathrm{\ω}}_i\⊗L_i\left(\mathrm{\λ}\right)---\left(13\right)$

Wherein, with t and the T+1 generation of i-th dimension of separating x respectively, i=1,2 ..., p, p are the dimension separating x, ω _i> 0 is the step-size factor relevant to Solve problems scope, dot product symbol, L _i(λ) be Levy flight step-length.Levy flight is a random walk process of obeying Levy distribution, and Levy distribution is shown below:

L(λ)～u＝t ^-λ,(1＜λ≤3) (14)

Wherein, u is heavy-tailed power-law distribution function, and λ is correlation of indices part.The method more effectively can search optimum solution in whole feasible zone.

But when adopting traditional cuckoo searching algorithm to solve nonlinear programming problem, its resource Searching efficiency is high not enough, to require further improvement and perfect.

Summary of the invention

In view of the above problems, the present invention is proposed to provide a kind of method and apparatus solving Nonlinear programming Model based on cuckoo searching algorithm overcoming the problems referred to above or solve the problem at least in part.

According to an aspect of the present invention, provide a kind of method solving Nonlinear programming Model based on cuckoo searching algorithm, be suitable for running in computing equipment, and comprise the steps:

A, a stochastic generation m Bird's Nest calculate the fitness of each Bird's Nest, each Bird's Nest represents a solution of Nonlinear programming Model;

B, from m Bird's Nest Stochastic choice Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest;

C, from m Bird's Nest Stochastic choice m × P _aindividual Bird's Nest, produces m × P by performing the flight of row dimension _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein 0 < P _a< 1;

The Bird's Nest that in D, acquisition m Bird's Nest, fitness is the highest, if the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, is then stored as current optimum Bird's Nest by this Bird's Nest; And

E, judge whether iterations reaches predetermined threshold value, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, return step B.

Alternatively, according to the method solving Nonlinear programming Model of the present invention, the flight of the row performed in step C dimension is the row dimension flight based on sinusoidal carrier.

Alternatively, according to the method solving Nonlinear programming Model of the present invention, in the row dimension based on sinusoidal carrier in-flight, determine the step-length y that flies in the following manner:

According to row dimension stochastic distribution determination arbitrary width t;

Change arbitrary width t according to sine function y=Asin (ω t)+b, obtain the step-length y that flies, wherein A is the amplitude of sine function, and ω is the angular frequency of sine function, and b is the offset distance of sine function.

Alternatively, solving in the method for Nonlinear programming Model according to of the present invention, determining A and b according to following formula:

$\left\{\begin{array}{c}b+A=L_{\max }\\ b-A=L_{\min }\end{array}\right.$

L _maxfor the upper limit of control variable value in Nonlinear programming Model, L _minfor the lower limit of control variable value in Nonlinear programming Model.

Alternatively, according to the method solving Nonlinear programming Model of the present invention, in step D, when the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, also perform step C and step D pre-determined number according to new sine function, wherein said new sine function is y=Asin (ω ' t+ θ)+b, ω '=ω/α, α > 1 t _nfor the arbitrary width of previous generation.

According to a further aspect in the invention, provide a kind of device solving Nonlinear programming Model based on cuckoo searching algorithm, reside in computing equipment, and comprise:

Initialization module, be suitable for a stochastic generation m Bird's Nest and calculate the fitness of each Bird's Nest, each Bird's Nest represents a solution of Nonlinear programming Model;

First row dimension flight module, is suitable for Stochastic choice Bird's Nest from m Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest;

Secondary series dimension flight module, is suitable for Stochastic choice m × P from m Bird's Nest _aindividual Bird's Nest, produces m × P by performing the flight of row dimension _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein 0 < P _a< 1;

Update module, is suitable for obtaining the Bird's Nest that in m Bird's Nest, fitness is the highest, if the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, then this Bird's Nest is stored as current optimum Bird's Nest; And

Judge module, is suitable for judging whether iterations reaches predetermined threshold value, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, trigger secondary series dimension flight module and update module.

Alternatively, solving in the device of Nonlinear programming Model according to of the present invention, the row dimension flight that secondary series dimension flight module performs is the row dimension flight based on sinusoidal carrier.

Alternatively, according to the device solving Nonlinear programming Model of the present invention, secondary series dimension flight module in the row dimension based on sinusoidal carrier in-flight, determines the step-length y that flies in the following manner:

According to row dimension stochastic distribution determination arbitrary width t;

Change arbitrary width t according to sine function y=Asin (ω t)+b, obtain the step-length y that flies, wherein A is the amplitude of sine function, and ω is the angular frequency of sine function, and b is the offset distance of sine function, and determines A and b according to following formula:

$\left\{\begin{array}{c}b+A=L_{\max }\\ b-A=L_{\min }\end{array}\right.$

L _maxfor the upper limit of control variable value in Nonlinear programming Model, L _minfor the lower limit of control variable value in Nonlinear programming Model.

Alternatively, solving in the device of Nonlinear programming Model according to of the present invention, when update module determines that the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, secondary series dimension flight module and update module are also according to the process of new sine function pre-determined number, wherein said new sine function is y=Asin (ω ' t+ θ)+b, ω '=ω/α, α > 1 t _nfor the arbitrary width of previous generation.

According to another aspect of the invention, provide a kind of computing equipment, the resident with good grounds device solving Nonlinear programming Model based on cuckoo searching algorithm of the present invention in this computing equipment.

Solving in the scheme of Nonlinear programming Model according to of the present invention, existing cuckoo searching algorithm is being improved, improves the efficiency of search.Further, by improving the mechanism of cuckoo searching algorithm more new explanation, add sinusoidal carrier, not only automatically meet the constraint requirements of decision variable, and carrier extend method making fine search become possibility, increasing the probability finding optimum solution.

Above-mentioned explanation is only the general introduction of technical solution of the present invention, in order to technological means of the present invention can be better understood, and can be implemented according to the content of instructions, and can become apparent, below especially exemplified by the specific embodiment of the present invention to allow above and other objects of the present invention, feature and advantage.

Accompanying drawing explanation

By reading hereafter detailed description of the preferred embodiment, various other advantage and benefit will become cheer and bright for those of ordinary skill in the art.Accompanying drawing only for illustrating the object of preferred implementation, and does not think limitation of the present invention.And in whole accompanying drawing, represent identical parts by identical reference symbol.In the accompanying drawings:

Fig. 1 shows the process flow diagram of the method solving Nonlinear programming Model according to an embodiment of the invention based on cuckoo searching algorithm;

Fig. 2 shows the Levy Flight track of two dimensional surface;

Fig. 3 shows the schematic diagram of the sinusoidal carrier adopted in the embodiment of the present invention;

Fig. 4 shows in the embodiment of the present invention schematic diagram expanding sinusoidal carrier local precise search;

Fig. 5 shows the structural drawing of the device solving Nonlinear programming Model according to an embodiment of the invention based on cuckoo searching algorithm; And

Fig. 6 is arranged as to realize according to the block diagram solving the Example Computing Device of the device of Nonlinear programming Model based on cuckoo searching algorithm of the present invention.

Embodiment

Below with reference to accompanying drawings exemplary embodiment of the present disclosure is described in more detail.Although show exemplary embodiment of the present disclosure in accompanying drawing, however should be appreciated that can realize the disclosure in a variety of manners and not should limit by the embodiment set forth here.On the contrary, provide these embodiments to be in order to more thoroughly the disclosure can be understood, and complete for the scope of the present disclosure can be conveyed to those skilled in the art.

Fig. 1 shows the process flow diagram of the method solving Nonlinear programming Model according to an embodiment of the invention based on cuckoo searching algorithm, and the method is suitable for running in computing equipment.

With reference to Fig. 1, the method starts from step S102, and step S102 is initialization step.In step s 102, for Nonlinear programming Model to be solved, such as, Nonlinear programming Model shown in formula (1) ~ formula (12), carries out the initialization of algorithm parameter, comprises and arranges total iterations T _max, primary iteration number of times T=1, the bound of control variable, the population quantity m etc. that adopts in algorithm.Such as, for control variable its upper limit is lower limit is

In step S104, stochastic generation m Bird's Nest X ₁, X ₂..., X _m, m be greater than 0 integer, such as m=100, and the fitness calculating each Bird's Nest, wherein each Bird's Nest represents a solution of Nonlinear programming Model.The dimension of the solution of Nonlinear programming Model is d, and namely each solution comprises d control variable.The fitness of Bird's Nest is the value of the objective function of Nonlinear programming Model, such as, is the B calculated on the right that d control variable substitutes into formula (1) _dWG.

In step s 106, Stochastic choice Bird's Nest from m Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest.

As previously mentioned, the solution of Nonlinear programming Model may have d to tie up, then all perform for each dimension in d dimension or partial dimensional and arrange dimension flight, the result of flying according to row dimension is afterwards combined into a new solution, and calculates the fitness of new solution.

Levy flight gives a name from French mathematician Paul Pierre Levy, is a kind of markov (Markov) process, and the step-length of walking meets the Levy distribution of heavy-tailed (heavy-tailed).In embodiments of the present invention, Levy stochastic distribution can occur in simplified form, as follows:

L(s)～|s| ^-1-β,0＜β≤2 (15)

In formula: s is random Levy step-length.On search the unknown, large-scale space problem, LevyFlight is more effective than Blang random motion.One of them reason is that the variance of Levy Flight can than the variances sigma of Blang random motion ²s () ~ s increases faster, as follows:

σ ²(s)～s ^3-β0＜β≤2 (16)

Be illustrated in figure 2 the Levy Flight track of two dimensional surface.In Levy Flight, the walking of short-range exploratory Local Search and once in a while longer distance is alternate, and therefore some solutions are searched near current optimal value, thus accelerate Local Search; Another part solution can from current optimal value enough away from space search for, thus ensure that system can not sink into local optimum.In intelligent optimization algorithm, adopt LevyFlight, can hunting zone be expanded, increase population diversity, more easily jump out local best points.

In embodiments of the present invention, the arbitrary width s of Levy Flight can also be obtained by following formula:

$s=\frac{\mathrm{\&mu;}}{{\left|v\right|}^{1/\mathrm{\&beta;}}},0<\mathrm{\&beta;}\&le;2---\left(17\right)$

μ and v obtains respectively from following normal distribution:

$\mathrm{\&mu;}~N(0,{\mathrm{\&sigma;}}_{\mathrm{\&mu;}}^2),v~N(0,{\mathrm{\&sigma;}}_v^2)---\left(18\right)$

In formula:

${\mathrm{\&sigma;}}_{\mathrm{\&mu;}}={\left\{\frac{\mathrm{\&Gamma;}(1+\mathrm{\&beta;})\sin (\mathrm{\&pi;\&beta;}/2)}{\mathrm{\&Gamma;}[(1+\mathrm{\&beta;})/2]{\mathrm{\&beta;}2}^{(\mathrm{\&beta;}-1)/2}}\right\}}^{1/\mathrm{\&beta;}},{\mathrm{\&sigma;}}_v=1---\left(19\right)$

In step S108, Stochastic choice m × P from m Bird's Nest _aindividual Bird's Nest, by performing the flight of row dimension to selected each Bird's Nest respectively, produces corresponding m × P _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein P _afor host bird probability in cuckoo searching algorithm finds the probability of foreign peoples, 0 < P _a< 1.Such as, P _a=0.2, m=100, then m × P _a=20, namely often perform a deuterzooid step, all 20 Bird's Nests are upgraded.Certainly, m × P _awhen not being integer, process can also be rounded to it.

In step s 110, sort according to fitness, obtain the Bird's Nest that in m Bird's Nest, fitness is the highest, judge whether the fitness of the Bird's Nest that fitness is the highest is greater than the fitness of current optimum Bird's Nest, if, then this Bird's Nest is stored as current optimum Bird's Nest, otherwise, the current optimum Bird's Nest stored is not upgraded.

Wherein, in execution according in the cuckoo searching algorithm of the embodiment of the present invention, in first time iterative process, Bird's Nest the highest for fitness in m Bird's Nest is stored as current optimum Bird's Nest; In second time iterative process, the fitness of the current optimum Bird's Nest of Bird's Nest the highest for fitness in m Bird's Nest and storage is compared, determine whether to upgrade to the current optimum Bird's Nest stored according to comparative result; The like

In step S112, judge whether iterations T reaches predetermined threshold value T _max, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, after making T=T+1, return step S106, perform next iteration process.

In addition, in cuckoo searching algorithm, if directly produce new explanation by Levy flight, this is for very applicable unrestricted variable solves.But solve for belt restraining variable, need to increase variable and cross the border treatment step to ensure the validity of separating, this process is more loaded down with trivial details and consuming time.Such as, for above-mentioned Nonlinear programming Model, control variable there is bound to limit, namely should meet constraint condition ${\mathrm{\&omega;}}_{\min }^{\mathrm{DWG}}\&le;{\mathrm{\&omega;}}_k^{\mathrm{DWG}}\&le;{\mathrm{\&omega;}}_{\max }^{\mathrm{DWG}}.$

For this reason, the Levy that the embodiment of the present invention also proposed based on sinusoidal carrier flies, and RANDOM SOLUTION can well be limited in restriction range, and can support local accurately optimizing.Namely perform in step S108 row dimension flight for based on sinusoidal carrier row dimension flight.

Be an amplitude such as formula function (11) Suo Shi be A, angular frequency is ω, and the cycle is the sine function of T=2 π/ω:

y＝Asin(ωt)+b (20)

From the character of sine function, when independent variable (being such as the time), t is within the scope of real number during consecutive variations, and the span of this sine function is always [b-A, b+A], can not cross the border, as shown in Figure 3.Make the independent variable t of sine function like this with Levy flight result, and be defined as b-A by under the decision variable of Nonlinear programming Model, be above defined as b+A, thus try to achieve b, A, after ω is set as required, just determine sine function.Make a functional transformation by Levy flight result, the value after converting is not crossed the border, thus does not need the treatment step that crosses the border increasing variable, also reduce the complexity of algorithm simultaneously.

Specifically, A and b can be determined according to following formula:

$\left\{\begin{array}{c}b+A=L_{\max }\\ b-A=L_{\min }\end{array}\right.---\left(21\right)$

Wherein, L _maxfor the upper limit of control variable value in Nonlinear programming Model, L _minfor the lower limit of control variable value in Nonlinear programming Model.Such as, for control variable corresponding L _minfor corresponding L _maxfor

In addition, as can be seen from Figure 3, the constant amplitude change of independent variable t can cause the not constant amplitude of y to change, and this can strengthen the elasticity of variable search.Because this value covers the whole region of search, so search belongs to global search.

It should be noted that, above process refers to the process carried out a dimension of separating, similar to the process of other dimensions of separating.

In other embodiments of the invention, sinusoidal expansion carrier wave local precise search can also be adopted.Particularly, on the basis of above-mentioned analysis, when decision variable is at t _nmoment (i.e. the n-th generation) searches the possible extreme value points p than having optimal value fitness larger (supposing that optimal value gets maximal value) before _n=(y _n1, y _n2..., y _nd) after, just carry out local accurately optimizing, d is the dimension of separating.Its principle as shown in Figure 4.

If the sinusoidal carrier of decision variable kth dimension is Wave1, then p _nmiddle kth dimension is at current time t _ncorresponding functional value (i.e. the current location of kth dimension) is y _nk, and y _nk=A _ksin (ω t _n)+b _k.Keep t _nthe functional value y in moment _nkconstant, the cycle increasing sinusoidal carrier is original α (α > 1) times, even its angular frequency is reduced into 1/ original α doubly.As shown in Figure 4, t on Wave1 is kept _nthe value y in moment _nkwhen constant, reduce the angular frequency of carrier wave Wave1, expanded to carrier wave Wave2.Under the effect of this expansion, the y value variable quantity that same time interval Δ t causes will reduce.In Fig. 4, under waiting the Δ t time interval, the y value variation delta y on Wave2 ₂=y _nk-y ₂will much smaller than y value variation delta y on Wave1 ₁=y _nk-y ₁, the differentiation namely during variable update search will reduce, and realize the object of carrying out precise search in less scope with this.

Above-mentioned at t for realizing _nmoment keeps y _nkbe worth constant (y _nk=y ' _nk), and the map function of carrier extend (ω '=ω/α, α > 1), should make:

A _ksin(ωt _n)+b _k＝A _ksin(ω′t _n+θ)+b _k(22)

Namely have:

$\mathrm{\&theta;}=\frac{\mathrm{\&alpha;}-1}{\mathrm{\&alpha;}}{\mathrm{\&omega;t}}_n---\left(23\right)$

Meanwhile, experiment shows: when α value is along with deeply the increasing gradually of precise search, can improve constantly the precision of Local Search, close to local optimum (also may be exactly global optimum).Certainly, low optimization accuracy is higher, and the carrier extend step number of needs is also more, and corresponding optimal time is also longer.In order to balance low optimization accuracy and optimal time, first carrier extend multiple can be less, then successively increase (increasing as become multiple), make the local optimal searching scope of variable from large to small, and fitness value no longer marked change time terminate the local optimal searching of this position, to meet accuracy requirement.Secondly, suitable maximum local optimal searching step number can be set in algorithm, terminate the local optimal searching of this position equally when local optimal searching reaches this step number limit value, to meet time requirement.

Local optimal searching terminates, then by before the angular frequency of carrier wave ' return to local optimal searching, proceed to carry out global optimizing on a large scale.

Like this, by improving the mechanism of meta-heuristic intelligent algorithm cuckoo searching algorithm more new explanation, adding sinusoidal carrier, not only automatically meeting the constraint requirements of decision variable, and carrier extend method makes fine search become possibility, increase the probability finding optimum solution.

Fig. 5 shows the structural drawing of the device solving Nonlinear programming Model according to an embodiment of the invention based on cuckoo searching algorithm, and this device resides in computing equipment.With reference to Fig. 5, this device comprises initialization module 10, first row dimension flight module 20, the flight of secondary series dimension module 30, update module 40 and judge module 50.

Initialization module 10 is suitable for a stochastic generation m Bird's Nest and calculates the fitness of each Bird's Nest, and each Bird's Nest represents a solution of Nonlinear programming Model.Process and the step S102 and step S104 of initialization module 10 execution are similar, do not repeat here.

First row dimension flight module 20 is suitable for Stochastic choice Bird's Nest from m Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest.Process and the step S106 of the execution of first row dimension flight module 20 are similar, do not repeat here.

Secondary series dimension flight module 30 is suitable for Stochastic choice m × P from m Bird's Nest _aindividual Bird's Nest, produces m × P by performing the flight of row dimension _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein 0 < P _a< 1.Wherein, the row dimension flight that secondary series dimension flight module 30 performs can be the row dimension flight based on sinusoidal carrier.Process and the step S108 of the execution of secondary series dimension flight module 30 are similar, do not repeat here.

Update module 40 is suitable for obtaining the Bird's Nest that in m Bird's Nest, fitness is the highest, if the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, then this Bird's Nest is stored as current optimum Bird's Nest.

Alternatively, when update module 40 determines that the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, secondary series dimension flight module and update module are also according to the process of new sine function pre-determined number, wherein said new sine function is y=Asin (ω ' t+ θ)+b, ω '=ω/α, α > 1 t _nfor the arbitrary width of previous generation.

Process and the step 110 of update module 40 execution are similar, do not repeat here.

Judge module 50 is suitable for judging whether iterations reaches predetermined threshold value, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, trigger secondary series dimension flight module 30 and update module 40.Process and the step S112 of judge module 50 execution are similar, do not repeat here.

Fig. 6 is arranged as to realize according to the block diagram solving the Example Computing Device 900 of the device of Nonlinear programming Model based on cuckoo searching algorithm of the present invention.In basic configuration 902, computing equipment 900 typically comprises system storage 906 and one or more processor 904.Memory bus 908 may be used for the communication between processor 904 and system storage 906.

Depend on the configuration of expectation, processor 904 can be the process of any type, includes but not limited to: microprocessor (μ P), microcontroller (μ C), digital information processor (DSP) or their any combination.Processor 904 can comprise the high-speed cache of one or more rank of such as on-chip cache 910 and second level cache 912 and so on, processor core 914 and register 916.The processor core 914 of example can comprise arithmetic and logical unit (ALU), floating-point unit (FPU), digital signal processing core (DSP core) or their any combination.The Memory Controller 918 of example can use together with processor 904, or in some implementations, Memory Controller 918 can be an interior section of processor 904.

Depend on the configuration of expectation, system storage 906 can be the storer of any type, includes but not limited to: volatile memory (such as RAM), nonvolatile memory (such as ROM, flash memory etc.) or their any combination.System storage 906 can comprise operating system 920, one or more application 922 and routine data 924.Application 922 can comprise the device 926 solving Nonlinear programming Model based on cuckoo searching algorithm being configured to realize solving the method for Nonlinear programming Model based on cuckoo searching algorithm.Routine data 924 can comprise and can be used for Bird's Nest as described here and fitness 928.In some embodiments, application 922 can be arranged as and utilize routine data 924 to operate on an operating system.

Computing equipment 900 can also comprise the interface bus 940 communicated contributed to from various interfacing equipment (such as, output device 942, Peripheral Interface 944 and communication facilities 946) to basic configuration 902 via bus/interface controller 930.The output device 942 of example comprises Graphics Processing Unit 948 and audio treatment unit 950.They can be configured to contribute to communicating with the various external units of such as display or loudspeaker and so on via one or more A/V port 952.Example Peripheral Interface 944 can comprise serial interface controller 954 and parallel interface controller 956, they can be configured to the external unit contributed to via one or more I/O port 958 and such as input equipment (such as, keyboard, mouse, pen, voice-input device, touch input device) or other peripheral hardwares (such as printer, scanner etc.) and so on and communicate.The communication facilities 946 of example can comprise network controller 960, and it can be arranged to is convenient to via one or more communication port 964 and the communication of one or more other computing equipments 962 by network communication link.

Network communication link can be an example of communication media.Communication media can be presented as computer-readable instruction, data structure, program module in the modulated data signal of such as carrier wave or other transmission mechanisms and so on usually, and can comprise any information delivery media." modulated data signal " can be such signal, the change of one or more or it of its data centralization can the mode of coded message in the signal be carried out.As nonrestrictive example, communication media can comprise the wire medium of such as cable network or private line network and so on, and such as sound, radio frequency (RF), microwave, infrared (IR) or other wireless medium are at interior various wireless mediums.Term computer-readable medium used herein can comprise both storage medium and communication media.

Computing equipment 900 can be implemented as a part for small size portable (or mobile) electronic equipment, and these electronic equipments can be such as cell phone, personal digital assistant (PDA), personal media player equipment, wireless network browsing apparatus, individual helmet, application specific equipment or the mixing apparatus that can comprise any function above.Computing equipment 900 can also be embodied as the personal computer comprising desktop computer and notebook computer configuration.

Intrinsic not relevant to any certain computer, virtual system or miscellaneous equipment with display at this algorithm provided.Various general-purpose system also can with use based on together with this teaching.According to description above, the structure constructed required by this type systematic is apparent.In addition, the present invention is not also for any certain programmed language.It should be understood that and various programming language can be utilized to realize content of the present invention described here, and the description done language-specific is above to disclose preferred forms of the present invention.

In instructions provided herein, describe a large amount of detail.But can understand, embodiments of the invention can be put into practice when not having these details.In some instances, be not shown specifically known method, structure and technology, so that not fuzzy understanding of this description.

Similarly, be to be understood that, in order to simplify the disclosure and to help to understand in each inventive aspect one or more, in the description above to exemplary embodiment of the present invention, each feature of the present invention is grouped together in single embodiment, figure or the description to it sometimes.But, the method for the disclosure should be construed to the following intention of reflection: namely the present invention for required protection requires feature more more than the feature clearly recorded in each claim.Or rather, as claims below reflect, all features of disclosed single embodiment before inventive aspect is to be less than.Therefore, the claims following embodiment are incorporated to this embodiment thus clearly, and wherein each claim itself is as independent embodiment of the present invention.

Those skilled in the art are appreciated that and adaptively can change the module in the equipment in embodiment and they are arranged in one or more equipment different from this embodiment.Module in embodiment or unit or assembly can be combined into a module or unit or assembly, and multiple submodule or subelement or sub-component can be put them in addition.Except at least some in such feature and/or process or unit be mutually repel except, any combination can be adopted to combine all processes of all features disclosed in this instructions (comprising adjoint claim, summary and accompanying drawing) and so disclosed any method or equipment or unit.Unless expressly stated otherwise, each feature disclosed in this instructions (comprising adjoint claim, summary and accompanying drawing) can by providing identical, alternative features that is equivalent or similar object replaces.

All parts embodiment of the present invention with hardware implementing, or can realize with the software module run on one or more processor, or realizes with their combination.It will be understood by those of skill in the art that the some or all functions that microprocessor or digital signal processor (DSP) can be used in practice to realize according to the some or all parts in the document protection equipment of the embodiment of the present invention.The present invention can also be embodied as part or all equipment for performing method as described herein or device program (such as, computer program and computer program).Realizing program of the present invention and can store on a computer-readable medium like this, or the form of one or more signal can be had.Such signal can be downloaded from internet website and obtain, or provides on carrier signal, or provides with any other form.

The present invention will be described instead of limit the invention to it should be noted above-described embodiment, and those skilled in the art can design alternative embodiment when not departing from the scope of claims.In the claims, any reference symbol between bracket should be configured to limitations on claims.Word " comprises " not to be got rid of existence and does not arrange element in the claims or step.Word "a" or "an" before being positioned at element is not got rid of and be there is multiple such element.The present invention can by means of including the hardware of some different elements and realizing by means of the computing machine of suitably programming.In the unit claim listing some devices, several in these devices can be carry out imbody by same hardware branch.Word first, second and third-class use do not represent any order.Can be title by these word explanations.

Claims (10)

1. solve a method for Nonlinear programming Model based on cuckoo searching algorithm, be suitable for running in computing equipment, and comprise the steps:

A, a stochastic generation m Bird's Nest calculate the fitness of each Bird's Nest, each Bird's Nest represents a solution of Nonlinear programming Model;

B, from m Bird's Nest Stochastic choice Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest;

C, from m Bird's Nest Stochastic choice m × P _aindividual Bird's Nest, produces m × P by performing the flight of row dimension _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein 0 < P _a< 1;

The Bird's Nest that in D, acquisition m Bird's Nest, fitness is the highest, if the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, is then stored as current optimum Bird's Nest by this Bird's Nest; And

E, judge whether iterations reaches predetermined threshold value, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, return step B.

2. the row dimension flight the method for claim 1, wherein performed in step C is the row dimension flight based on sinusoidal carrier.

3. method as claimed in claim 2, wherein, in the row dimension based on sinusoidal carrier in-flight, determine the step-length y that flies in the following manner:

According to row dimension stochastic distribution determination arbitrary width t;

Change arbitrary width t according to sine function y=Asin (ω t)+b, obtain the step-length y that flies, wherein A is the amplitude of sine function, and ω is the angular frequency of sine function, and b is the offset distance of sine function.

4. method as claimed in claim 3, wherein, determine A and b according to following formula:

$\left\{\begin{array}{c}b+A=L_{\max }\\ b-A=L_{\min }\end{array}\right.$

L _maxfor the upper limit of control variable value in Nonlinear programming Model, L _minfor the lower limit of control variable value in Nonlinear programming Model.

5. method as claimed in claim 3, wherein, in step D, when the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, also perform step C and step D pre-determined number according to new sine function, wherein said new sine function is y=Asin (ω ' t+ θ)+b, ω '=ω/α, α > 1 t _nfor the arbitrary width of previous generation.

6. solve a device for Nonlinear programming Model based on cuckoo searching algorithm, reside in computing equipment, and comprise:

Initialization module, be suitable for a stochastic generation m Bird's Nest and calculate the fitness of each Bird's Nest, each Bird's Nest represents a solution of Nonlinear programming Model;

First row dimension flight module, is suitable for Stochastic choice Bird's Nest from m Bird's Nest, by performing row dimension flight generation new Bird's Nest, and calculating the fitness of new Bird's Nest, if the fitness of new Bird's Nest is greater than the fitness of former Bird's Nest, then replacing former Bird's Nest with new Bird's Nest;

Secondary series dimension flight module, is suitable for Stochastic choice m × P from m Bird's Nest _aindividual Bird's Nest, produces m × P by performing the flight of row dimension _aindividual new Bird's Nest, calculates the fitness of new Bird's Nest, and replaces former Bird's Nest with new Bird's Nest, wherein 0 < P _a< 1;

Update module, is suitable for obtaining the Bird's Nest that in m Bird's Nest, fitness is the highest, if the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, then this Bird's Nest is stored as current optimum Bird's Nest; And

Judge module, is suitable for judging whether iterations reaches predetermined threshold value, if so, the optimum solution of current optimum Bird's Nest as Nonlinear programming Model is exported, otherwise, trigger secondary series dimension flight module and update module.

7. device as claimed in claim 6, wherein, the row dimension flight that secondary series dimension flight module performs is the row dimension flight based on sinusoidal carrier.

8. device as claimed in claim 7, wherein, secondary series dimension flight module in the row dimension based on sinusoidal carrier in-flight, determines the step-length y that flies in the following manner:

According to row dimension stochastic distribution determination arbitrary width t;

Change arbitrary width t according to sine function y=Asin (ω t)+b, obtain the step-length y that flies, wherein A is the amplitude of sine function, and ω is the angular frequency of sine function, and b is the offset distance of sine function, and determines A and b according to following formula:

$\left\{\begin{array}{c}b+A=L_{\max }\\ b-A=L_{\min }\end{array}\right.$

L _maxfor the upper limit of control variable value in Nonlinear programming Model, L _minfor the lower limit of control variable value in Nonlinear programming Model.

9. device as claimed in claim 8, wherein, when update module determines that the fitness of this Bird's Nest is greater than the fitness of current optimum Bird's Nest, secondary series dimension flight module and update module are also according to the process of new sine function pre-determined number, and wherein said new sine function is y=Asin (ω ^'t+ θ)+b, ω '=ω/α, α > 1, t _nfor the arbitrary width of previous generation.

10. a computing equipment, resident just like the device solving Nonlinear programming Model based on cuckoo searching algorithm according to any one of claim 6 to 9 in this computing equipment.