CN101739602A - Multi-factor decision quantum variation method for quantum genetic algorithm - Google Patents

Abstract

The invention discloses a quantum variation method based on multi-factor decision, which comprises the following steps: after the population is updated by using quantum gates, carrying out the quantum variation process for computing a quantum variation probability which is most suitable for evolution of each individual in the contemporary population; codetermining the quantum variation of each individual by convergence factors, fitness factors and variation acceleration factors defined by the invention; and by computing the similarity difference between the observation state of the current generation and the optimum solution, the quality difference among individuals, the initial variation probability, the generation of which the current optimum solution is not changed and the maximum number of iterations of the evolution operation of the quantum genetic algorithm, acquiring the quantum variation probability of each individual of the current population. The invention can effectively improve the convergence rate and the global optimizing ability of the quantum genetic algorithm.

Description

A kind of multi-factor decision quantum variation method that is used for quantum genetic algorithm

Technical field

The present invention relates to a kind of quantum bit variation method that is used for quantum genetic algorithm, belong to the evolutionary computation technique field.

Background technology

Quantum genetic algorithm be a kind of with quantum calculation theoretical combine with evolution algorithm according to the probabilistic search optimization method.It utilizes quantum bit coded representation chromosome, and the consumption cervical orifice of uterus is more newly arrived and finished evolutionary search.Its great advantage is only to need small-scale population can realize effective search, and rate of convergence is fast.Because its thought is simple, be easy to the outstanding calculated performance that realizes and show, quantum genetic algorithm has won widely in each subject and field and has paid close attention to, and especially finds the solution at combinatorial optimization problem, fields such as adaptive control, Based Intelligent Control, pattern-recognition, manual search and machine learning.

In quantum genetic algorithm, chromosome is in the stack attitude or tangles attitude, and population is evolved to operate by the quantum revolving door and acts on quantum stack attitude and tangle attitude, thereby changes its phase place, and then changes the ground state of quantum bit.The quantum rotation door generally is expressed as:

$U\left(\mathrm{\θ}\right)=\left[\begin{array}{cc}\cos \left(\mathrm{\θ}\right)& -\sin \left(\mathrm{\θ}\right)\\ \sin \left(\mathrm{\θ}\right)& \cos \left(\mathrm{\θ}\right)\end{array}\right]$

Wherein θ is called rotation angle.

Quantum bit upgrades and is operating as:

$\left[\begin{array}{c}{\mathrm{\α}}^{*}\\ {\mathrm{\β}}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \left(\mathrm{\θ}\right)& -\sin \left(\mathrm{\θ}\right)\\ \sin \left(\mathrm{\θ}\right)& \cos \left(\mathrm{\θ}\right)\end{array}\right]\left[\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right]$

The evolution of quantum genetic algorithm operation at present is main adopts the quantum rotation door, so the algorithm performance quality depends primarily on the quality of revolving door.Though this algorithm is simple, but determining of rotation mode, rotation angle size and Orientation is not an easy thing, often need exploration many times just can find a proper rotation angle, and the versatility of revolving door is bad, and a revolving door often only adapts to one or a class problem.In rotary course, if rotation angle is excessive, will be easy to miss good solution space, and the too small meeting of rotation angle causes rate of convergence slow excessively, good chromosome slowly can't be updated to optimum solution.Simultaneously, the decision mechanism of revolving door makes individuality all evolve towards same direction, is easy to be absorbed in local optimal searching, and when search was absorbed in local optimal searching, this renewal operation can't provide better optimizing strategy to flee from this Local Search space, causes algorithm to be stagnated; When population converged near the optimum solution, this renewal operation can't provide adaptive low-angle precise search, to keep the stability of population in addition.

Summary of the invention

The objective of the invention is to the situation of asking problem scale bigger at waiting, on the basis that the quantum door upgrades, a kind of quantum bit variation method based on multi-factor decision is provided, can makes quantum genetic algorithm obtain algorithm convergence speed and global optimizing ability faster based on quantum door rotation angle step length mechanism and this multi-factor decision quantum bit variation method.

For realizing above-mentioned goal of the invention, the present invention adopts following technical scheme:

Following steps mainly illustrate the quantum mutation process, omit the detailed description of the quantum door being upgraded operation, are that example is described algorithm to find the solution maximal value below.

Step 1, the maximum evolutionary generation of initialization population, the population size, initialization quantum door upgrades operating parameter; Initialization quantum variation parameter: set initial variation probability and the constant algebraically of the current optimum solution of population;

Step 2 is carried out the quantum door and is upgraded;

Step 3 is calculated the fitness value that each quantum bit chromosome of current population is observed attitude, obtains the optimum chromosome that evolves to current population;

Step 4 is calculated each the chromosome observation attitude of current population and the similarity of optimum chromosome observation attitude, and is write down maximum similarity, minimum similarity and similarity mean value, utilizes similarity to calculate converging factor;

Step 5 is obtained maximum adaptation degree value and the minimum fitness value of current population, and calculates the fitness factor;

Step 6 according to the situation of change of optimum solution, is calculated the variation speedup factor of current population;

Step 7, according to the converging factor of each chromosome observation attitude, the fitness factor and variation speedup factor are determined this chromosomal quantum variation probability;

Step 8, operation quantum bit mutation operation, and write down current evolutionary generation;

Step 9 judges whether current evolutionary generation is maximum evolutionary generation; If the current evolutionary generation of quantum genetic algorithm then returns step 2 less than maximum evolutionary generation; If the current evolutionary generation of quantum genetic algorithm equals maximum evolutionary generation, then execution in step 10;

Step 10 is based on the quantum genetic algorithm termination of quantum door rotation angle step length mechanism and multi-factor decision quantum bit variation method;

Wherein, in the described step 1, the maximum evolutionary generation max_gen of initialization population is a constant, and population scale is N, and Probability p initially makes a variation ₀With the current algebraically λ that do not change that separates all are constants, set according to concrete problem oneself;

In the described step 2, carry out quantum bit according to the quantum door rotation table of setting and upgrade;

In the described step 3, each individual fitness value in the population after the calculated amount cervical orifice of uterus upgrades, and record evolves to current on behalf of the optimum individual that ends;

In the described step 4, be example with the binary coding, similarity can be described with the interchromosomal Hamming distance, and converging factor s computing formula is:

$s=\frac{\stackrel{\‾}{d}-d_{\min }}{d_{\max }-d_{\min }}$

In the following formula

Represent average Hamming distance, promptly average similarity, d _MaxAnd d _MinRepresent maximum Hamming distance and smallest hamming distance respectively, promptly minimum similarity and maximum similarity;

In the described step 5, the computing formula of fitness factor f is:

$f=\frac{f_{\max }-f_j}{f_{\max }-f_{\min }}$

F in the formula _jRepresent j individual fitness value;

In the described step 6, variation speedup factor h (n) is a variable, and n is current evolutionary generation, and its computing formula is:

In the following formula, f _Max(n) be the n maximum adaptation degree value in generation, α is a constant;

In the described step 7, quantum variation probability calculation formula is

$p_m^j=\left\{\begin{array}{cc}{p}_0\·s\·f+h\left(n\right),& f_{\max }\≠f_{\min }\\ p_0,& f_{\max }=f_{\min }\end{array}\right.$

P in the formula _m ^jRepresent j individual quantum variation probability;

In the described step 8, the not gate variation is adopted in the quantum variation, i.e. the probability amplitude of exchange variation position;

The calculating of quantum variation probability is to be made a strategic decision jointly by converging factor, the fitness factor and variation speedup factor in the quantum genetic algorithm provided by the present invention, wherein converging factor s hour, illustrate this moment population converged to optimum solution near, the probability that makes a variation this moment will diminish along with diminishing of converging factor, can keep population stability, otherwise the variation probability will become big; The introducing of the fitness factor mainly is to consider from the difference between individuality, the individuality that fitness is big, i.e. and defect individual variation probability is little, the individuality that fitness is little, be that relatively poor individual variation probability is big, help the individuality of keeping on top like this, strengthen the evolution amplitude of of inferior quality individuality simultaneously; The ability that the introducing energy enhancement algorithms of variation speedup factor is fled from the local optimal searching interval, from its definition as can be known, when algorithm continues λ generation and its optimum solution when still not changing, increase the variation probability by the variation speedup factor, the variation speedup factor is in the process that increases, population evolution initial stage amplitude is bigger, and the later stage is less, can accelerate the search rate of optimum solution.

Quantum variation method by converging factor, the fitness factor and three factor Shared Decision Making of variation speedup factor can remedy the deficiency of being brought by the renewal of quantum door separately, the converging factor and the fitness factor stability of population of keeping on top on the one hand, when population is restrained, converging factor can provide the ability of precise search, and the fitness factor then fully takes into account difference individual between population and is convenient to defect individual towards more excellent direction evolution; Consider that on the other hand the quantum rotation door upgrades operation algorithm is absorbed in the situation processing power deficiency of local optimal searching, introduce the variation speedup factor, the main effect of this factor is the global optimizing ability of enhancement algorithms.

Description of drawings

Below in conjunction with accompanying drawing algorithm provided by the present invention is further elaborated.

Fig. 1 describes the process of multi-factor decision quantum variation.

Fig. 2 is the quantum genetic algorithm process flow diagram based on the quantum rotation door upgrades and the multi-factor decision quantum makes a variation.

Embodiment

As shown in Figure 2, algorithm begins the first step need be separated problem coding schedule and be shown as quantum bit chromosome, needs in the initialization procedure maximum evolutionary generation, and the correlation parameter that quantum upgrades door and the variation of multi-factor decision quantum carries out initialization; The observation attitude of obtaining initial population is finished in initialization, and it is carried out the fitness assessment, obtains the optimum individual of current population, judges then whether population evolves to maximum evolutionary generation, if, the output optimum solution, otherwise the algorithm end enters iterative process; 7 to 10 steps of algorithm are that quantum upgrades the door process, do not do detailed description herein; The quantum door is reappraised to new population after upgrading and finishing, obtain the parameters of quantum variation, calculate converging factor, the fitness factor and variation speedup factor, calculate quantum variation probability at last and carry out the quantum mutation operation, obtain the population of a new generation thus, this process is 11 to 15 steps of algorithm; In algorithm 16 step, turning back to for the 6th step after population algebraically upgrades continues judge whether population evolves to maximum algebraically, if words output optimum solution, algorithm end, otherwise algorithm enters iterative process.

Above the quantum variation method based on multi-factor decision of the present invention is had been described in detail, but specific implementation form of the present invention is not limited thereto.For the those skilled in the art in present technique field, the various conspicuous change of under the situation of spirit that does not deviate from the method for the invention and claim scope it being carried out is all within protection scope of the present invention.

 

Claims (2)

1. multi-factor decision quantum variation method that is used for quantum genetic algorithm is characterized in that:

Described quantum variation method based on multi-factor decision;

Wherein, in the described algorithm, the quantum bit chromosomal variation is determined jointly by defined converging factor, the fitness factor and variation speedup factor among the present invention;

In described the same generation population, each chromosome all obtains a quantum variation probability of serving for the evolution of oneself specially;

2. quantum bit chromosomal variation as claimed in claim 1 is determined jointly by defined converging factor, the fitness factor and variation speedup factor among the present invention, be it is characterized in that:

Described each chromosomal quantum variation probability by the similarity difference when between former generation observation attitude and optimum solution, between individuality good and bad degree, initially the evolve maximum iteration time of operation of algebraically that probability, current optimum solution do not change and quantum genetic algorithm that makes a variation is determined jointly;

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