CN103020709A - Optimization calculation method based on artificial bee colony algorithm and quantum-behaved particle swarm optimization algorithm - Google Patents

Abstract

The invention discloses an optimization calculation method based on artificial bee colony algorithm and quantum-behaved particle swarm optimization algorithm, which comprises the following main steps: (1) forming an objective function to be optimized according to an practical problem; (2) inputting universal operation parameters including population number, number of iterations, variable dimension number, variable value range and objective function to be optimized of algorithms; (3) calculating by one or more calculation methods selected from ABC (artificial bee colony), QPSO (quantum-behaved particle swarm optimization), QPSO+ABC and ABC+QPSO; step (4) directly judging whether the result meets the optimization requirement when only one method is used, and comprehensively comparing the calculation results and evaluating whether the optimal result meets the optimization requirement of this time if more than one calculation methods are used; (5) stopping calculating when the requirement is met, and outputting the calculation result and the iteration curve; and (6) correcting the input parameters of the algorithms when the requirement is not met, calculating again, outputting the calculation result and the iteration curve after the parameters are adjusted, and obtaining the final optimization result.

Description

A kind of optimized calculation method based on artificial bee colony algorithm and quanta particle swarm optimization

Technical field

The present invention relates to the optimization application in artificial intelligence, the Management Science and Engineering, relate in particular to a kind of optimized calculation method based on artificial bee colony algorithm and quanta particle swarm optimization.

Background technology

Optimization problem is present in the real world in a large number, and in scientific research and engineering application, the effect of optimum theory and technology becomes more and more important especially.In addition, optimisation technique also has widely purposes in the industry-by-industry of national economy.Find the solution the needs of the optimization problem of the features such as extensive, combination, non-linear, discreteness, randomness, multiple goal, promoting the development of mathematic programming methods and intelligent optimization algorithm.The colony intelligence optimized algorithm is one of them study hotspot in recent years.

The artificial bee colony algorithm is a kind of efficient Swarm Intelligence Algorithm, and it imitates the gathering honey behavior of honeybee and searches for.Honeybee carries out different activities according to separately the division of labor, and realizes sharing and exchanging of bee colony information, thereby finds the optimum solution of problem.Show that by numerical function optimization and multimodal function optimization the ABC algorithm has better Optimal performance than genetic algorithm, differential evolution algorithm and Particle Swarm Optimization.

Quanta particle swarm optimization is that quantum theory is incorporated in the basic particle group algorithm, deficiency for the basic particle group algorithm optimizing, from quantum-mechanical angle, utilize the quantum uncertainty principle to describe the motion state of particle, basic particle group algorithm is improved.It is seen as a kind of new, one of probabilistic algorithm that can exert an influence to the basic particle group algorithm future thrust.Use through polytype and to show: the method have travelling speed soon, stronger optimizing performance.

Above-mentioned two kinds of algorithms respectively have advantage, often need to adopt above-mentioned two kinds of algorithms to be optimized computing in production practices.Can adopt a kind of method wherein to calculate the result, also can compare two kinds of arithmetic result, decide what to use; In addition, for further improving ability of searching optimum, also can adopt the mixed method (QPSO+ABC and ABC+QPSO) of these two kinds of methods to carry out the optimizing intensive treatment, in order to obtain better optimum results.

Summary of the invention

The technical problem to be solved in the present invention provides a kind of optimized calculation method based on artificial bee colony algorithm and quanta particle swarm optimization.

In order to solve the problems of the technologies described above, the technical solution used in the present invention is: based on the optimized calculation method of artificial bee colony algorithm and quanta particle swarm optimization, the artificial bee colony algorithm is called ABC in the following text, and quanta particle swarm optimization is called QPSO in the following text, may further comprise the steps:

Step 1: analyze practical problems, work out objective function to be optimized;

Step 2: the operational factor of input ABC or QPSO, described operational factor is population number, iterations, dimension, variable-value scope, objective function to be optimized;

Step 3: according to the optimization demand, can select a kind of two or three in the following algorithm or four kind to calculate:

(a) select the ABC algorithm;

(b) select the QPSO algorithm;

(c) selecting sequence is QPSO+ABC and the hybrid algorithm that is connected with cascaded structure;

(d) selecting sequence is ABC+QPSO and the hybrid algorithm that is connected with cascaded structure;

Step 4: only adopt a kind of in the above-mentioned algorithm if calculate, directly to export result of calculation, to turn to step 5; If obtain better optimum results or carry out between algorithms of different Optimal performance relatively, can select two or three in above-mentioned four kinds of methods or four kind to carry out comparison of computational results, turn to step 6;

Step 5: whether the optimum results of judging this single algorithm satisfies this suboptimization requirement, turns to step 7;

Step 6: the result of calculation of comprehensive several algorithms of more above-mentioned selection, filter out optimal result according to the quality of target function value, estimate this optimal result and whether satisfy the requirement that this suboptimization is calculated;

Step 7: if meet the demands, computing finishes; Otherwise the operational factor of modification algorithm increases population number and iterations, recomputates, and result of calculation and iterativecurve after the output operational factor is adjusted obtain the final optimization pass result.

As preferably, objective function to be optimized refers to that a class can be converted into the function of asking extreme value, the error between the calculated value that calculates such as the measured value of experiment gained and according to theory.

As preferably, computing method adopt the MATLAB Programming with Pascal Language.

As preferably, the calculation procedure of artificial bee colony algorithm is as follows:

(1) carries out respectively initialization according to self span of each variable according to population number, carry out subsequently dimension and merge, form bee colony initial population x _Ij, i=1 ..., SN, j=1 ... D, wherein SN represents the quantity of food source, D is the dimension of variable;

(2) calculate the function fitness value of population, and estimate population;

(3) gathering honey honeybee (x _Ij) by formula (1) produces new explanation v near its neighborhood in the food source neighborhood _Ij:

v _ij＝x _ij+φ _ij(x _ij-x _kj) (1)

Wherein, x _kExcept x _iOutside a solution choosing at random, φ _IjBe a variation range in the random number of interval [a, a], a gets 1 usually, then, uses greedy selection algorithm and determines v _iAnd x _iQuality;

(4) according to formula (2), according to fitness value (fit _i) calculate and separate x _iProbable value p _i:

$p_i={\mathrm{fit}}_i/\left(\underset{i=1}{\overset{\mathrm{SN}}{\mathrm{\Σ}}}{\mathrm{fit}}_i\right)---\left(2\right)$

Wherein, for minimization problem, the calculating of fitness value by formula (3) is calculated:

${\mathrm{fit}}_i=\left\{\begin{array}{ccc}1/(1+f_i)& \mathrm{if}& f_i\&GreaterEqual;0\\ 1+\mathrm{abs}\left(f_i\right)& \mathrm{if}& f_i<0\end{array}\right\}---\left(3\right)$

Wherein, f _iBe target function value;

(5) for observing honeybee, in the neighborhood of its selected food source, produce new explanation, adopt relatively v of greedy selection algorithm _iAnd x _iQuality;

(6) determine the solution x that abandons _i, a new explanation adopting formula (4) to produce at random

Replace it, with it as search bee:

x ^/ _ij＝xmin _j+rand(0，1)*(xmax _j-xmin _j) (4)

Wherein, xmin _jThe span lower limit of parameter j, xmax _jThe span upper limit for parameter j;

(7) the present best solution of memory, if satisfy the ending standard requirement, algorithm stops, output result of calculation; Otherwise, forward step (2) to and continue iteration.

As preferably, the new explanation that obtains in the calculation procedure 3 of artificial bee colony algorithm and the step 5 will be carried out respectively range check to each variable range, the interval that makes it not exceed himself and change.

The invention has the beneficial effects as follows:

Choose these two kinds colony intelligence optimized algorithms that the required input parameter is few, Optimal performance is strong of artificial bee colony algorithm and quanta particle swarm optimization and be integrated into a universal computing platform, it has the following advantages:

(1) the parameter input is simple, easy to operate; (2) user can solve the actual optimization problem that it runs into easily by the objective function to be optimized of establishment oneself, is with a wide range of applications and practical value; (3) user can observe this algorithm parameter variation to the rule that affects of Optimal performance by changing the parameters of certain algorithm; (4) for same optimization problem, can adopt the various combination account form to calculate, relatively Optimal performance situation and the quality of result of calculation, thus select optimum result of calculation for; Particularly two kinds are mixed account forms (QPSO+ABC and ABC+QPSO), adopt in the initial population of will the optimum results of front a kind of method directly implanting subsequent algorithm and participate in successive iterations calculating, have strengthened the Optimal performance of algorithm.

Description of drawings

The present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

Fig. 1 is the process flow diagram that the present invention is based on the optimized calculation method embodiment of artificial bee colony algorithm and quanta particle swarm optimization.

Fig. 2 is the iterativecurve figure that the present invention is based on the optimized calculation method embodiment A BC of artificial bee colony algorithm and quanta particle swarm optimization.

Fig. 3 is the iterativecurve figure that the present invention is based on the optimized calculation method embodiment QPSO of artificial bee colony algorithm and quanta particle swarm optimization.

Fig. 4 is the iterativecurve figure that the present invention is based on the optimized calculation method embodiment A BC+QPSO of artificial bee colony algorithm and quanta particle swarm optimization.

Fig. 5 is the iterativecurve figure that the present invention is based on the optimized calculation method embodiment QPSO+ABC of artificial bee colony algorithm and quanta particle swarm optimization.

Embodiment

Present embodiment is the application example of a water quality parameter identification, and Fig. 1 is its process flow diagram.

Analyze river water mass tracing experiment data, at definite Longitudinal Dispersion D _LDuring with mean velocity in section v, the analytic solution of describing the one-dimensional river water mass tracing experiment under the instantaneous input tracer agent condition that adopt more:

$c=(M_0/\left(A\sqrt{4*\mathrm{pi}*D_L*t}\right))*\exp (-{(x-\mathrm{vt})}^2/\left(4D_{L}t\right));$

In the formula: c is the tracer agent mass concentration, M ₀Quality for instantaneous input tracer agent; A is the river cross section area; D _LBe longitudinal dispersion coefficient of river; X is the distance between sampled point and release position; T is the time; V is the cross section of river mean flow rate, and pi represents π, gets 3.14 during calculating and gets final product.

Objective function is:

$\min f\left(\mathrm{\&theta;}\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{(c_i-c_j)}^2$

In the formula: c _iBe the actual tracer agent mass concentration value that constantly observes at i; c _jBe the i tracer agent mass concentration value constantly of utilizing following formula to calculate; θ is parameters of river water quality vector to be estimated, i be tracer concentration observation time sequence number (i=1,2 ..., n).Choose suitable parameter value θ so that the sum of squares of deviations of concentration calculated value and concentration observed reading reaches minimum, this moment corresponding parameters of river water quality value to be problem required.

Known M ₀=10kg, x=500m has provided parameter true value θ ₁=D _L=3000m ²/ mir, θ ₂=v=30m/min and θ ₃=A=20m ²The time, the corresponding raw data c of different time _i, specifically see Table 1.

Table 1:c _i～t _iThe corresponding table of raw data

t i/min	6	10	12	14	16	20	24	36
									c i/(mg.L -1)	0.254	0.583	0.649	0.663	0.642	0.552	0.444	0.197

It is 30 that population number is set, and the iteration total degree is that the variation range of 300, three parameters is respectively: [0,300000], and [0,3000], [0,2000], objective function is shuizhicanshu, result of calculation is as follows:

Adopt the result of calculation of ABC: target function value is 9.230009e-007, and variable result to be optimized is followed successively by 3001.46,30.0082,20.0009, and the iterativecurve of output as shown in Figure 2.

Adopt the result of calculation of QPSO: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 3.

Adopt the result of calculation of ABC+QPSO: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 4.

Adopt the result of calculation of QPSO+ABC: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 5.

Observation and comparison to the concrete iterativecurve of above-mentioned four kinds of methods is as follows:

By observing Fig. 2 and Fig. 3, can find out that QPSO is being better than ABC aspect speed of convergence and the optimum results;

Fig. 4 has reflected and sequentially has been the mixed running effect of two kinds of algorithms of ABC+QPSO, shows that QPSO has had certain improvement finding the solution on the basis of ABC to the result again, has obtained more excellent result; Fig. 5 has reflected and sequentially has been the mixed running effect of two kinds of algorithms of QPSO+ABC, show that QPS0 has obtained good result, and not finding the solution of ABC improves to some extent to the above results.

In the present embodiment, the variable of artificial bee colony algorithm (ABC) is not to search for by identical interval, but searches for according to the interval of self, like this can convergence speedup speed and enhancing optimizing effect.

Be convenient and use, in present embodiment uses, an interactive interface close friend's the optimization computing platform that adopted MATLAB GUI technological development.This platform is made of three parts: (1) load module part, for the bound scope and the objective function to be optimized that receive population number, dimension, variable-value; (2) output module: the optimal objective function value that output is calculated and corresponding variable-value; (3) iterativecurve display module: can demonstrate real-time dynamicly the target function value of certain algorithm with the evolution process of iterations.Its interactive interface is made of 2 panels, 9 static text frames, 8 Edit Text frames, 1 coordinate axis control and 1 drop-down menu.Optimize computing platform by this, the user just can solve the complicated optimum problem that runs in the reality as long as be aided with simple operations at the interface.

Above-described embodiment of the present invention does not consist of the restriction to protection domain of the present invention.Any modification of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., all should be included within the claim protection domain of the present invention.

Claims (5)

1. based on the optimized calculation method of artificial bee colony algorithm and quanta particle swarm optimization, described artificial bee colony algorithm is called ABC in the following text, and described quanta particle swarm optimization is called QPSO in the following text, may further comprise the steps:

Step 1: analyze practical problems, work out objective function to be optimized;

Step 2: the operational factor of input swarm intelligence algorithm, described operational factor is population number, iterations, dimension, variable-value scope, objective function to be optimized;

Step 3: according to the optimization demand, can select one or both or three kinds or four kinds in the following algorithm to calculate:

(a) select the ABC algorithm;

(b) select the QPSO algorithm;

(c) selecting sequence is QPSO+ABC and the hybrid algorithm that is connected with cascaded structure;

(d) selecting sequence is ABC+QPSO and the hybrid algorithm that is connected with cascaded structure;

Step 4: only adopt a kind of in the above-mentioned algorithm if calculate, directly to export result of calculation, to turn to step 5; If obtain better optimum results or carry out between algorithms of different Optimal performance relatively, can select two or three in above-mentioned four kinds of methods or four kind to carry out comparison of computational results, turn to step 6;

Step 5: whether the optimum results of judging this single algorithm satisfies this suboptimization requirement, turns to step 7;

Step 6: the result of calculation of comprehensive several algorithms of more above-mentioned selection, filter out optimal result according to the quality of target function value, estimate this optimal result and whether satisfy the requirement that this suboptimization is calculated;

Step 7: if meet the demands, computing finishes; Otherwise the operational factor of modification algorithm increases population number and iterations, recomputates, and result of calculation and iterativecurve after the output operational factor is adjusted obtain the final optimization pass result.

2. optimized calculation method according to claim 1 is characterized in that: described optimized calculation method employing MATLAB Programming with Pascal Language.

3. optimized calculation method according to claim 1, it is characterized in that: objective function to be optimized described in the step 1 refers to that a class can be converted into the function of asking extreme value.

4. optimized calculation method according to claim 1, it is characterized in that: the calculation procedure of described artificial bee colony algorithm is as follows:

(1) carries out respectively initialization according to self span of each variable according to population number, carry out subsequently dimension and merge, form bee colony initial population x _Ij, i=1 ..., SN, j=1 ... D, wherein SN represents the quantity of food source, D is the dimension of variable;

(2) calculate the function fitness value of population, and estimate population;

(3) gathering honey honeybee (x _Ij) by formula (1) produces new explanation v near its neighborhood in the food source neighborhood _Ij:

v _ij＝x _ij+φ _ij(x _ij-x _kj) (1)

Wherein, x _kExcept x _iOutside a solution choosing at random, φ _IjBe a variation range in the random number of interval [a, a], a gets 1 usually, then, uses greedy selection algorithm and determines v _iAnd x _iQuality;

(4) according to formula (2), according to fitness value (fit _i) calculate and separate x _iProbable value p _i:

$p_i={\mathrm{fit}}_i/\left(\underset{i=1}{\overset{\mathrm{SN}}{\mathrm{\&Sigma;}}}{\mathrm{fit}}_i\right)---\left(2\right)$

Wherein, for minimization problem, the calculating of fitness value by formula (3) is calculated:

${\mathrm{fit}}_i=\left\{\begin{array}{ccc}1/(1+f_i)& \mathrm{if}& f_i\&GreaterEqual;0\\ 1+\mathrm{abs}\left(f_i\right)& \mathrm{if}& f_i<0\end{array}\right\}---\left(3\right)$

Wherein, f _iBe target function value;

(5) for observing honeybee, in the neighborhood of its selected food source, produce new explanation, adopt relatively v of greedy selection algorithm _iAnd x _iQuality;

(6) determine the solution x that abandons _i, a new explanation adopting formula (4) to produce at random Replace it, with it as search bee:

x ^/ _ij＝xmin _j+rand(0，1)*(xmax _j-xmin _j) (4)

Wherein, xmin _jThe span lower limit of parameter j, xmax _jThe span upper limit for parameter j;

(7) the present best solution of memory, if satisfy the ending standard requirement, algorithm stops, output result of calculation; Otherwise, forward step (2) to and continue iteration.

5. optimized calculation method according to claim 4 is characterized in that: the new explanation that obtains in the calculation procedure 3 of described artificial bee colony algorithm and the step 5, carry out respectively range check to each variable range, the interval that makes it not exceed himself and change.

Images