CN102915407B - Prediction method for three-dimensional structure of protein based on chaos ant colony algorithm - Google Patents

Abstract

The present invention relates to a kind of prediction method for three-dimensional structure of protein based on chaos ant colony algorithm, protein three-dimensional structure is abstracted into the position of food source in chaos ant colony algorithm by the method, then uses chaos ant colony algorithm to carry out protein three-dimensional structure prediction: first this algorithm randomly generates<i>sN</i>the food source of individual scale, searches again for all food sources and produces new food source, and calculate its energy value, retain more excellent food source, then produce new food source according to the algorithm of tournament selection outstanding food source of decision search part, according to the size of energy value, retain outstanding food source.When food source does not update in the searching times set, then obtain New food source by Chaos Search and replace former food source.During search globally optimal solution, while more New food source every time, update current optimal solution and energy value thereof.The method not only has preferable estimated performance and precision of prediction, and it is short to run the time, and operational efficiency is high.

Description

Prediction method for three-dimensional structure of protein based on chaos ant colony algorithm

Technical field

The present invention relates to protein three-dimensional structure electric powder prediction, a kind of prediction method for three-dimensional structure of protein based on chaos ant colony algorithm.

Background technology

Protein Structure Prediction Problem is also referred to as protein folding.The shape of protein folding structure determines its biological function to a great extent, and the structural information grasping protein has great importance for the function and effect studying protein.Therefore, protein three-dimensional structure prediction has become important one of the studying a question of bioinformatics.

At present, the determination techniques of protein structure mainly has X-ray crystallography (X-raydiffraction), nuclear magnetic resonance technique (nuclearmagneticresonance, NMR).Although protein structure determination technology has had the most significantly being in progress, but determine that the process of protein structure is the most extremely complex by experimental technique, cost is higher.Therefore, occur in that the method that many utilizes computer forecast protein structure, specifically include that homology method (homologymodeling), Folding recognition (foldingrecognition), ab initio prediction method (abinitiomethod) etc..

Thermodynamics hypothesis based on the native protein conformation correspondence minimum energy that Anfinesen etc. proposed in 1973, uses theoretical calculation method to be possibly realized from the natural structure of aminoacid sequence predicted protein matter.Protein folding prediction problem is converted into two key issues: one is the mathematical model proposing preferably to reflect amino acid residue interphase interaction and environment etc.；Two is to assume to develop efficient searching method according to thermodynamics, searches for global minimum in the multiple local minimums from the potential surface of protein.Along with the increase of protein sequence length, the amount of calculation of search volume is exponentially increased.Therefore, it is necessary to set up a native conformation that can distinguish protein and the coarse grain model of non-native conformation.Be widely used at present is the non-lattice model of AB, it considers that topmost power is hydrophobic interaction in protein structure forming process, by abstract for aminoacid for hydrophobicity (Hydrophobic) with hydrophilic (Hydrophilic).On the basis of the non-lattice model of AB, design an optimized algorithm and search for best native protein conformation and become the key of protein three-dimensional structure forecasting problem.But, even if applying the model of simplification, protein structure prediction is still that a NP difficult problem.

Between in the past few decades, scholars propose many algorithms in predicted protein matter three dimensional structure problem and solve to search for globally optimal solution problem.Such as, the method that genetic algorithm combines with simulated annealing, than other method more high efficiency；The tabu search algorithm improved, it is to avoid the roundabout search of algorithm, improves search performance and the robustness of algorithm；Tabu search algorithm is applied in genetic algorithm, searches the structure of protein rapidly and accurately, lower than the minimum energy that other algorithms are tried to achieve.But, these methods combine many algorithms, and long operational time, efficiency are low, have certain limitation.

Summary of the invention

It is an object of the invention to provide a kind of prediction method for three-dimensional structure of protein based on chaos ant colony algorithm, the method not only has preferable estimated performance and precision of prediction, and it is short to run the time, and operational efficiency is high.

It is an object of the invention to by following technical scheme realization: present invention prediction method for three-dimensional structure of protein based on chaos ant colony algorithm, for the protein containing n residue, point protein three-dimensional structure being abstracted in 2n-5 dimension space, the i.e. position of food source in chaos ant colony algorithm, then uses chaos ant colony algorithm to carry out protein three-dimensional structure prediction as follows:

(1) initiation parameter: food source scale SN, algorithm maximum cycle Maxloop, searching times limit, Chaos Search maximum iteration time C_max, population minimum energy value E_minWith optimum individual h_min, algorithm current iteration number of times loopcount=0, food source search counter c are set_i=0(i=1,2,...,SN)；

(2) SN food source is randomly generated；

(3) formula is usedCalculate the energy value of all food sources, obtain optimal energy E₀And optimal solution h of correspondence₀, update current optimal solution h_min=h₀With current optimal energy E_min=E₀；

(4) calculating of a step (3) is often completed, then current iteration number of times loopcount adds 1, and judges that current iteration number of times loopcount, whether less than maximum cycle Maxloop, is to go to step (5), otherwise termination algorithm, exports globally optimal solution h_minWith global optimum's ENERGY E_min；

(5) formula is pressedThe field searching for all food sources solves, and calculates its energy value, if the energy value of New food source is less than the energy value of former food source, then replaces former food source with New food source, otherwise retains former food source, and search counter c of correspondence adds 1；

(6) use algorithm of tournament selection policy selection part food source to carry out a field again and solve search, calculate its energy value, retain the food source that energy value is low；

(7) judging whether the food source not updated in the searching times limit set, if it is present utilize Logistic equation Chaos Search one New food source of generation to replace it, corresponding search counter c resets；

(8) formula is usedCalculate the energy value of each food source, if E₀<E_min, then current optimal solution h is updated_min=h₀With current optimal energy E_min=E₀, go to step (4).

The invention has the beneficial effects as follows for protein three-dimensional structure forecasting problem, chaos ant colony algorithm is used on the basis of the non-lattice model of AB, artificial bee colony algorithm introduces the thought of chaos optimization, when certain solution is absorbed in local optimum, the randomness and the ergodic that utilize Chaos Variable make it jump out locally optimal solution, not only combine the ability of artificial bee colony algorithm global search and Local Search, and utilize Chaos Search to avoid Premature Convergence, be absorbed in the problems such as locally optimal solution, realize global optimization, thus obtain estimated performance more more preferable than other algorithms and precision of prediction.Additionally, the algorithm that the present invention uses is simple, running the time short, operational efficiency is high, has wide application space.

Accompanying drawing explanation

Fig. 1 is present protein three dimensional structure schematic diagram.

Fig. 2 is the flow chart of the present invention used chaos ant colony algorithm.

Detailed description of the invention

Present invention prediction method for three-dimensional structure of protein based on chaos ant colony algorithm, for the protein containing n residue, point protein three-dimensional structure being abstracted in 2n-5 dimension space, the i.e. position of food source in chaos ant colony algorithm, then uses chaos ant colony algorithm to carry out protein three-dimensional structure prediction as follows:

(1) initiation parameter: food source scale SN, algorithm maximum cycle Maxloop, searching times limit, Chaos Search maximum iteration time C_max, population minimum energy value E_minWith optimum individual h_min, algorithm current iteration number of times loopcount=0, food source search counter c are set_i=0(i=1,2,...,SN)；

(2) SN food source is randomly generated；

(3) calculate the energy value of all food sources, obtain optimal energy E₀And optimal solution h of correspondence₀, update current optimal solution h_min=h₀With current optimal energy E_min=E₀；

(4) calculating of a step (3) is often completed, then current iteration number of times loopcount adds 1, and judges that current iteration number of times loopcount, whether less than maximum cycle Maxloop, is to go to step (5), otherwise termination algorithm, exports globally optimal solution h_minWith global optimum's ENERGY E_min；

(5) field searching for all food sources solves, and calculates its energy value, if the energy value of New food source is less than the energy value of former food source, then replaces former food source with New food source, otherwise retains former food source, and search counter c of correspondence adds 1；

(6) use algorithm of tournament selection policy selection part food source to carry out a field again and solve search, calculate its energy value, retain the food source that energy value is low；

(7) judging whether the food source not updated in the searching times limit set, if it is present utilize Logistic equation Chaos Search one New food source of generation to replace it, corresponding search counter c resets；

(8) energy value of each food source is calculated, if E₀<E_min, then current optimal solution h is updated_min=h₀With current optimal energy E_min=E₀, go to step (4).

In step (3) and step (8), the energy value of food source is calculated as follows:

In formula, preceding paragraph is backbone twist potential energy, unrelated with sequence self, only relevant by the bond angle between adjacent key；Consequent for the gravitational potential energy between non-conterminous residue, it changes along with the change of sequence, and i.e. on main chain key, the change of any pair non-conterminous residue all will cause it to change, wherein:

Here,Represent the classification of amino acid residue, if it belongs to A, then；If it belongs to B, then。

In step (5), the field searching for all food sources as follows solves, and calculates its energy value:

New food sourceBy former food sourceJth dimension update；Wherein, k, j, r are random number,And,,。

In step (7), Logistic equation Chaos Search one New food source of generation by following:

By initial valueIteration goes out a time series；WhereinIt is the control parameter of chaos state,Take 4, so that Logistic equation is completely into chaos state.

Below in conjunction with specific embodiment, the present invention is further illustrated.

The present invention uses domestic and international widely used fibonacci sequence as the protein sequence of simulation, and it is defined as:, wherein, "" representing concatenation operator, former sequences are.It is therefore found that hydrophobic amino acid A is always isolated in the sequence；And hydrophilic amino acid B may occur in pairs, it is also possible to individually occur.Carrying out coding under Matlab2008 environment to realize, each parameter is provided that population number is set to(n is protein sequence length), maximum iteration time is 1000n, in limit=200, Logistic chaos sequence,, each equal random walk of protein sequence algorithm seeks its meansigma methods 50 times.

1. the three-dimensional non-lattice model of AB

The non-lattice model of three-dimensional AB that Stillinger et al. proposes is to develop on the basis of the two dimension non-lattice model of AB, think that the main cause of protein folding is hydrophobic interaction, and amino acid residue is divided into hydrophobicity (A) and hydrophilic (B) two class, therefore, protein sequence is conceptualized as the sequence that A and B is formed.The three-dimensional non-lattice model of AB mainly has a three below advantage: first, can determine the structured data of protein according to the residue sequence of polypeptide chain completely, not affected by the imperfection of Protein Data Bank information；They are two years old, it is possible to the principal character of real simulated albumin matter structure；Its three, model describe use neutral net concept, be the basis studying protein folding structure further.

In three dimensions, being bonded to be connected into and do not have the polymer in direction by unit length successively of the monomer on aminoacid sequence, connecting the bond angle that two key-likes of three adjacent monomers become can arbitrarily change.During the model that the non-lattice model of AB is predicted as three dimensional structure, in addition to considering the bond angle between adjacent key, in addition it is also necessary to consider 2 interplanar torsion angles that adjacent 3 key vectors are constituted, as shown in accompanying drawing Fig. 1.For the protein being made up of n amino acid residue, b_i(i=1,2 ..., n) representing i-th amino acid monomer, its three-D space structure is by 2 bond angle θ of n₁,θ₂,…,θ_n-2Angle beta is reversed with n 3₁,β₂,…,β_n-3Determine, here θ_i、β_iScope be respectively。θ_i、β_iIt is positive angle when turning clockwise, is negative angle when rotating counterclockwise.

In the non-lattice model of AB, the energy of protein folding is made up of the gravitational potential energy of the Lennard-Jones form between backbone twist potential energy and non-conterminous residue.One protein sequence containing n amino acid residue, its potential-energy function E is expressed as:

Preceding paragraph is backbone twist potential energy, unrelated with sequence self, only relevant by the bond angle between adjacent key；Consequent for the gravitational potential energy between non-conterminous residue, it changes along with the change of sequence, and i.e. on main chain key, the change of any pair non-conterminous residue all will cause it to change.Wherein:

Here,Represent the classification of amino acid residue, if it belongs to A, then；If it belongs to B, then.Understanding from formula, residue has stronger gravitation to AA, and residue has more weak gravitation to BB, and residue then has more weak repulsion to AB.Reflecting the characteristic of authentic protein to a certain extent, i.e. during protein folding, because there being bigger captivation between hydrophobic residue, and form hydrophobic inner core, hydrophilic residue is then ostracised outside.Represent the space length between non-conterminous residue, by bond angle θ_iWith torsion angle beta_iDetermine.

Under the non-lattice model of AB, it was predicted that the three dimensional structure of the protein containing n monomer, it is simply that n-2 bond angle θ to be found out₁,θ₂,…,θ_n-2Angle beta is reversed with n-3₁,β₂,…,β_n-3So that the value of potential-energy function formula is minimum.So prediction three dimensional structure problem translates into the constraint minimum problem solving object function E:

2. chaos bee colony optimized algorithm

2.1 artificial bee colony algorithm

Artificial bee colony (ArtificialBeeColony, ABC) algorithm is that DervisKaraboga proposed in 2005.Artificial bee colony comprises three kinds of individualities: gathering honey honeybee, follow honeybee and investigation honeybee.Each gathering honey honeybee has a food source determined, and scans for the neighborhood of food source in iteration, and after search every time, the information of food source is fed back to by gathering honey honeybee follows honeybee, follows honeybee and will be selected in food source to carry out a field search again.If there is no more preferable food source in the searching times limit set, then will abandon this food source, investigation honeybee starts the New food source that random search is feasible simultaneously.In an iterative process, bee colony follows following rule for the search of food source: the neighborhood solution that search target is the solution that last time obtains that gathering honey honeybee is each；Information is shared by gathering honey honeybee with following honeybee, follows honeybee and selects one of them food source, and scans in its neighborhood；Food source and gathering honey honeybee are that relation, i.e. gathering honey honeybee number and food source number are equal one to one.In ABC algorithm, a feasible solution of the position correspondence optimization problem of food source, the fitness function of the income degree correspondence problem of food source.

2.2 Chaos Search

Chaos be nature be widely present non-linear linearly, there is the features such as randomness, ergodic and regularity, can not repeatedly travel through all states by the rule of himself within the specific limits.It is exactly a typical chaos system that conventional Logistic maps, and it is according to following formula: Produce chaos sequence.By initial valueIteration can go out a time series.WhereinIt is the control parameter of chaos state, whenTime Logistic equation completely into chaos state, therefore in the present inventionTake 4.

2.3 based on CABC algorithm predicts protein structure

Chaos ant colony algorithm (CABC) combines ABC algorithm and chaos optimization searching method, in the global search of ABC algorithm and the characteristic of Local Search, introduce the thought of Chaos Search, it is to avoid algorithm is absorbed in local optimum, accelerate Algorithm Convergence, it is possible to predicted protein matter structure effectively.Method based on CABC algorithm predicts protein three-dimensional structure is as follows:

2.3.1 encoding scheme

The present invention is using Gauss coordinate as the coded system of food source in CABC algorithm.For the protein containing n residue, can be shown as with 2n-5 argument table, this embodies 2 bond angles of n and 3 torsion angles of n in protein three-dimensional structure.The Gauss coordinate of the i-th amino acid residue of so individual h can be expressed as:

According to above formula, first three aminoacid space coordinates of protein is followed successively by (0,0,0), (0,1,0) and (cos (θ₁),sine(θ₁), 0), the amino acid residue coordinate of postorder all calculates on the basis of its previous residue coordinate.

2.3.2 initial food source

The point three dimensional structure of protein can being abstracted in 2n-5 dimension space according to above-mentioned encoding scheme, i.e. the position of food source in CABC algorithm.Algorithm SN food source of initial random generation, each food source is represented by.The scale in initial food source is very big on algorithm impact, and there is limitation too small hunting zone, is easily absorbed in local optimum, excessive, is easily caused amount of calculation too big, and convergence rate is slack-off.Therefore, initial population size SN is set to 3 times of residue of protein number n, i.e. SN=(2n 5) × 3 by the present invention.

2.3.3 the gathering honey honeybee search phase

First gathering honey honeybee carries out field search to food source, and each food source is assigned to corresponding gathering honey honeybee.Gathering honey honeybee is according to following formula search field food source:

In formula, New food sourceIt is by former food sourceJth dimension update.Wherein, k, j, r are random number,And,,.From above formula, x_ijWith x_kjDifference the least, the variable quantity of food source is the least.Therefore, when all of food source is close to optimal solution, its step-size in search reduces the most accordingly.

In CABC algorithm, gathering honey honeybee uses greedy principle at New food sourceWith former food sourceBetween accept or reject, if the adaptive value of the New food source searched is better than former food source, then replaces the position of former food source with new food source position, otherwise keep former food source invariant position.If food sourceIt is not updated to merit, then corresponding search counterAdd 1, otherwiseReset.

2.3.4 follow the honeybee search phase

After all of gathering honey honeybee completes search, pass to follow honeybee by the information of food source.Following honeybee and select food source according to the information obtained, the probability that the food source that fitness is the highest is followed honeybee selection is the biggest.In the CABC algorithm of the present invention, follow honeybee and select to use algorithm of tournament selection strategy (TournamentSelection) during food source.Algorithm of tournament selection strategy is selection course based on local competition, and its main thought is to select k individuality to compare at random in colony, and the individuality that adaptive value is big is chosen, and wherein k is contest scale.Therefore, all food sources are divided into one group (i.e. k=2) by two-by-two, according to above-mentioned formula:

Comparing the energy value of the two, the food source selecting energy value little carries out field search.Such selection mode makes adaptive value, and good food source has bigger choice, and poor food source also has an opportunity to be chosen.Different from other selection strategyes, algorithm of tournament selection strategy only using the relative value of adaptive value as the standard selected, and positive and negative to adaptive value does not require such that it is able to avoid the excellent individual impact on algorithm, prevent the phenomenon that algorithm is precocious and stagnates to a certain extent.

2.3.5 Chaos Search New food source

In CABC algorithm, if certain food source search for limit time continuously after still without obtaining more preferable food source, show that this food source is absorbed in local optimum, investigation honeybee then finds New food source to replace it.The present invention utilizes Chaos Search to produce chaos sequence based on current locally optimal solution, and the optimal solution in chaos sequence is replaced original solution.Make the solution stagnated continue to evolve by Chaos Search, improve convergence of algorithm speed and precision.Assume that the solution that search is stagnated is, we are with above-mentioned Logistic equation

As iterative formula.The step of chaos optimization is as follows:

(1)It is mapped in the definition territory [0,1] of Logistic equation:, wherein:(,)；

(2) Chaos Variable sequence is produced with Logistic Equation Iterative,It it is the maximum iteration time of Chaos Search；

(3) Chaos Variable is passed through inverse mappingReturn to former solution space,, calculate its adaptive value；

(4) optimal solution Chaos Search obtained replaces original solution.

2.4 arthmetic statement

The chaos ant colony algorithm flow process based on the non-lattice model of AB that the present invention relates to is as shown in Figure 2.First algorithm initializes parameters, randomly generate the food source of SN scale, then gathering honey honeybee is searched for all food sources and produces new food source, and calculate its energy value, retain more excellent food source, then by gathering honey honeybee feedack, follow honeybee and produce new food source according to the algorithm of tournament selection outstanding food source of decision search part, according to the size of energy value, retain outstanding food source.When food source does not update in the searching times limit set, investigation honeybee then obtains New food source by Chaos Search and replaces former food source.During search globally optimal solution, gathering honey honeybee, follow honeybee and investigation honeybee acts on food source in turn, and update current optimum individual while more New food source every timeAnd energy value.Arthmetic statement is as follows:

(1) initiation parameter: food source scale SN, algorithm maximum cycle Maxloop, searching times limit, Chaos Search maximum iteration time C_max, population minimum energy valueAnd optimum individual, algorithm current iteration number of times loopcount=0, food source search counter c are set_i=0(i=1,2,...,SN)；

(2) SN food source is randomly generated；

(3) formula is usedCalculate the energy value of all food sources, obtain optimal energyAnd the optimal solution of correspondence, update current optimal solutionAnd optimal energy；

(4) current iteration number of times loopcount=loopcount+1, if loopcount < Maxloop, then turns (5), otherwise termination algorithm, exports globally optimal solutionAnd energy；

(5) according to formulaThe field searching for all food sources solves, and calculates its energy value, if the energy value of New food source is less than former food source energy value, then New food source is replaced former food source, otherwise retains former food source, and search counter c of correspondence adds 1；

(6) use algorithm of tournament selection policy selection part food source to carry out a field again and solve search, calculate its energy value, retain the food source that energy is low；

(7) food source (i.e. c=limit) that search does not updates for limit time is determined whether, if it is present utilize formulaChaos Search produces a New food source and replaces it, and corresponding search counter c resets；

(8) formula is usedCalculate the energy value of each food source, if, then current optimal solution and optimal energy are updated,, turn (4).

It is above presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, when produced function is without departing from the scope of technical solution of the present invention, belong to protection scope of the present invention.

Claims (1)

1. a prediction method for three-dimensional structure of protein based on chaos ant colony algorithm, it is characterized in that: for the protein containing n residue, point protein three-dimensional structure being abstracted in 2n-5 dimension space, the i.e. position of food source in chaos ant colony algorithm, then uses chaos ant colony algorithm to carry out protein three-dimensional structure prediction as follows:

(1) initiation parameter: food source scale SN, algorithm maximum cycle Maxloop, searching times limit, Chaos Search maximum iteration time C_max, population minimum energy value E_minWith optimum individual h_min, algorithm current iteration number of times loopcount=0, food source search counter c are set_i=0, i=1,2 ..., SN；

(2) SN food source h (θ is randomly generated₁, θ₂..., θ_n-2, β₁, β₂..., β_n-3)；For the protein being made up of n amino acid residue, the three-D space structure of i-th amino acid monomer is by 2 bond angle θ of n₁,θ₂,…,θ_n-2Angle beta is reversed with n 3₁,β₂,…,β_n-3Determine, θ_i、β_iScope be respectively-π≤θ_i,β_i≤ π, θ_i、β_iIt is positive angle when turning clockwise, is negative angle when rotating counterclockwise；

(3) calculate the energy value of all food sources, obtain optimal energy E₀And optimal solution h of correspondence₀, update current optimal solution h_min=h₀With current optimal energy E_min=E₀；

(4) current iteration number of times loopcount adds 1, and judges that current iteration number of times loopcount, whether less than maximum cycle Maxloop, is to go to step (5), otherwise termination algorithm, exports globally optimal solution h_minWith global optimum's ENERGY E_min；

(5) field searching for all food sources solves, and calculates its energy value, if the energy value of New food source is less than the energy value of former food source, then replaces former food source with New food source, otherwise retains former food source, and search counter c of correspondence_iAdd 1；

(6) use algorithm of tournament selection policy selection part food source to carry out a field again and solve search, calculate its energy value, retain the food source that energy value is low；

(7) food source that do not updates in the searching times limit set is judged whether, if it is present utilize Logistic equation Chaos Search to produce a New food source to replace it, corresponding search counter c_iReset；

(8) energy value of each food source is calculated, if E₀<E_min, then current optimal solution h is updated_min=h₀With current optimal energy E_min=E₀, go to step (4)；

In step (3) and step (8), the energy value of food source is calculated as follows:

$E=\underset{i=1}{\overset{n-2}{\&Sigma;}}\frac{1}{4}(1-{\mathrm{cos\&theta;}}_i)+\underset{i=1}{\overset{n-2}{\&Sigma;}}\underset{j=i+2}{\overset{n}{\&Sigma;}}4\&lsqb;r_{ij}^{-12}-C({\mathrm{\&xi;}}_i,{\mathrm{\&xi;}}_j)r_{ij}^{-6}\&rsqb;$

In formula, r_ijRepresent the space length between non-conterminous residue, by bond angle θ_iWith torsion angle beta_iDetermining, preceding paragraph is backbone twist potential energy, unrelated with sequence self, only relevant by the bond angle between adjacent key；Consequent for the gravitational potential energy between non-conterminous residue, it changes along with the change of sequence, and i.e. on main chain key, the change of any pair non-conterminous residue all will cause it to change, wherein:

$C({\mathrm{\&xi;}}_i,{\mathrm{\&xi;}}_j)=\left\{\begin{array}{cc}+1,& {\mathrm{\&xi;}}_i={\mathrm{\&xi;}}_j=1\\ +0.5,& {\mathrm{\&xi;}}_i={\mathrm{\&xi;}}_j=-1\\ -0.5,& {\mathrm{\&xi;}}_i\&NotEqual;{\mathrm{\&xi;}}_j\end{array}\right.$

Here, ξ_iRepresent the classification of amino acid residue, if it belongs to A, then ξ_i=1；If it belongs to B, then ξ_i=-1；A is hydrophobicity one class, and B is hydrophilic one class；

In step (5), the field searching for all food sources as follows solves, and calculates its energy value:

y_ij=x_ij+r(x_ij-x_kj)

x_i、x_kRepresent i-th respectively, k food source, x_ij、x_kjRepresent the jth dimension of the jth dimension of i-th food source, kth food source, New food source y respectively_iBy former food source x_iJth dimension according to above-mentioned formula update, be designated as y_ij；Wherein, k, j, r are random number, k ∈ 1,2 ..., SN} and k ≠ i, j ∈ 1,2 ..., 2n-5}, r ∈ [-1,1]；

In step (7), Logistic equation Chaos Search one New food source of generation by following:

Z_p+1=μ Z_p(1-Z_n) p=0,1,2 ...

By initial value Z₀∈ [0,1] iteration goes out time series Z₀, Z₁, Z₂...；Wherein μ is the control parameter of chaos state, so that Logistic equation is completely into chaos state.