JPH06161980A - Fast processing method for genetic algorithm - Google Patents

Abstract

PURPOSE:To perform the fast processing of genetic algorithm by generating a gene string used in the genetic algorithm so as to be applied to computer architecture without imparting the property and information of the string. CONSTITUTION:When individual gene which comprises the gene string like an i-th gene GENE[i,k] (k=1, 2,...Lmax, where, Lmax: the number of genes which comprise the gene string) is arranged as shown in figure, no information other than that for the lowest-order bit on memory is required by expressing the gene string in a binary string. Therefore, the gene string is not defined in arrangement, and only the lowest-order bits are collected in one word, and it is used as a variable of integer type. In such a way, the genetic algorithm can be executed at high speed by comprising the gene string used in the genetic algorithm without impairing the property or information of the string, using the computer architecture, and efficiently using the resources of a computer.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for executing a genetic algorithm on a computer.

[0002]

2. Description of the Related Art Japanese Unexamined Patent Publication No. 2-236660 provides a genetic algorithm for solving an extended kind of problem, and restricts the size, shape or complexity of a target population. Without a genetic algorithm. In addition, JP-A-3-10366
The present invention relates to a method for learning and evaluating a neural network represented by a modified symbol string and repeating the modification of the symbol string to construct an optimal neural network.

[0003]

The genetic algorithm is a probabilistic search algorithm and takes time because it requires an iterative procedure. In the above-mentioned technique, the time required for processing the genetic algorithm is particularly mentioned. It has not been.

An object of the present invention is to provide a means for processing a genetic algorithm at high speed.

[0005]

In order to achieve the above object, in a computer having an input device, an output device, a memory, a CPU (central control unit) and other peripheral devices, a given problem and a computer architecture Generate symbol strings suitable for both and manipulate those symbol strings with pointer addresses. Further, the symbol string is arranged on the register and the gene sequence is converted by using the bit operation.

In describing the processing of the genetic algorithm, the above-mentioned symbol strings are called gene sequences, the individual symbols constituting the symbol strings are called genes, and the features are formed by the information of the gene sequences. Is generally called an individual, and hereinafter, these terms will be used in the present invention.

[0007]

The present invention configures a gene sequence used in a genetic algorithm without damaging its properties and information, utilizes a computer architecture, and efficiently uses the resources of the computer to speed up the genetic algorithm. Is what you want to do.

[0008]

【Example】

(Embodiment 1) FIG. 1 shows an embodiment of the present invention. Figure 1
It is a figure which shows the structure of the gene sequence at the time of performing the minimum value search of the nonlinear function of 1 input 1 output by a genetic algorithm.

FIG. 2 shows a hardware configuration for carrying out the present invention. In the figure, the central control unit CPU21 is 32
It has a register group 211 of bit length, and has an arithmetic unit 212 for performing logical operations such as a shift function for 32 bit operations and a bit operation function. In addition, the control unit 213 that executes an instruction based on the result decoded by the instruction decoder
have. In the data transfer between the random access memory RAM 221 included in the memory 22 and the CPU 21, the address bus 24 accesses each 32-bit word boundary, and the data is transferred to the CPU or the data bus 23.
It is exchanged with the RAM itself. A read-only memory ROM 222 included in 22 has a program written therein which is called first when the CPU starts the operation and performs the initial setting operation. The IO 27 is a data entrance / exit, through which the parameters used for processing are input from the input device 25, and the processing results are output to the output device 26. The above 32 bits are set according to the computer used in this embodiment, but the number of bits is not particularly limited.

A procedure for searching the minimum value of a given function using a genetic algorithm will be described below. (1) Generating a plurality of random numbers and expressing each in the form of a gene sequence, which is the initial state of the gene sequence. (2) These gene sequences are crossed over and changed according to the mutation. In addition, crossover is a process of exchanging a part of the gene sequence of an individual for a pair of individuals,
Mutation is a process that changes part of a gene sequence. (3) Each changed gene sequence is restored to each numerical value and input to the given function. And get the value of each function. (4) The entire evaluation is performed using all the obtained values of each function. The value of each function is evaluated according to the overall evaluation, and selection and multiplication are performed. In addition, selection is a process of eliminating an individual when the evaluation of the individual is low, and proliferation is a process of generating an individual having the same gene sequence when the evaluation of the individual is high. (5) Until the given end condition is satisfied (2) to (4)
The process of is repeated.

The above processes (2) to (4) are called generations, and the number of repetitions is called the number of generations. In this way, the minimum value of the given function or a value close to the minimum can be obtained by repeating the generations. The specific detailed procedure will be described later (FIG. 7). The genetic algorithm is described in detail in the following documents. Goldberg, DE: Genetic Algorithms in Search, Opti
mization and Machine Learning, Addison-Wesley (198
9) Fig. 3 shows the procedure of the procedure for solving the problem using the genetic algorithm by PAD (Program Analysis).
is Diagram). The processing method of the present invention will be described by taking as an example the case where the minimum value of the following multimodal nonlinear function is obtained.

[0012]

[Equation 1]

However, the domain is 0 or more and less than 2 (0 ≦ x <
2). Then, priorities are given from the one with the smallest output value, and this order is used as the individual evaluation.

Regarding the setting of 31 gene strings, the conversion procedure from the set numerical value of the gene string to the gene string is used by using the PAD diagram of FIG. 5, and the conversion procedure of the gene string is converted by the PAD diagram of FIG. And explain each. The symbols used in FIGS. 5 and 6 have the following meanings. Gmax: total number of individuals di: i-th input value δi: integer part of a value obtained by multiplying di by η Lmax: number of genes constituting gene sequence Gene [i, k]: kth of i-th gene sequence In the value 52 of the gene of, the i-th input value di is multiplied by η and the integer part is set to δi.

Η is a constant, and its value is a variable η
The multiplied value is set so as to be included in 0 to 4294967295 (a value obtained by subtracting 1 from the 32nd power of 2). For example,
When 0 ≦ x <2, η = 2147483648 (3 of 2)
1). At 54, the remainder when δi is divided by 2,
That is, a value of 0 or 1 is obtained, and the quotient obtained by dividing δi by 2 at 55 is updated as δi. By repeating this at 53 up to the maximum length of the gene sequence, a binary sequence can be obtained. This binary string is a gene string. At 51, the input value of each function is converted into a gene sequence. In this method, the property of the input value having a large digit is represented by the left side (upper bit) of the gene, and the property of the input value having a smaller digit is represented by the right side (lower bit). As a result, the binary expression of δi is obtained.

For example, when η = 2147483648 (2 to the 31st power), when the input value d = 0.571875, δ = 1228092.
211, and the gene sequence is {010010010011001100110011
00110011}.

Further, after converting the information of the gene sequence into numerical values in 63 and 64 of FIG. 6, it is divided by η in 65 and returned to the input value of the function. Reference numeral 61 controls to apply the above processing to all gene sequences. For example, the gene sequence is {001011100001011101011101.
10111000}, δ = 739728568, and the input value is 0.
It becomes 6889259.

Next, a method of constructing a gene array will be described with reference to FIG. In this example, since the gene sequence is represented by a binary sequence, the i-th gene sequence GENE
[I, k] (k = 1, 2, ..., Lmax, where Lm
ax is the number of genes that make up the gene sequence), and the individual genes that make up the gene sequence are arranged as shown in FIG.
On the memory, information other than the least significant bit is unnecessary. Therefore, the gene sequence is not defined by an array, and only the least significant bit is collected in one word and used as one integer type variable.
For example, {001011010001011101011101
A gene sequence composed of 32 binary-valued genes such as 10111000} can be represented by a single decimal number 7397728568.

In the parameter setting 32 shown in FIG. 3, an arbitrary number of individuals and the crossover rate, selection multiplication rate, and mutation rate corresponding thereto are set. These are values in the range of 0 to 100 [%]. In addition, the number of times to terminate the repetition is set appropriately. In this example, the number of individuals is 100 and the gene length is 3
2, 80% crossover rate, 10% selection growth rate, 5 mutation rate
%, The number of censored generations was set to 200, but the number is not limited to this value.

The following documents describe the above parameter values in detail. Goldberg, DE: Genetic Algorithms in Search, Opti
mization and MachineLearning, pp.70-74, Addison-Wes
ley (1989) The PAD diagram shows the processing procedure of the genetic algorithm of this embodiment. Outbreak of 71, from 0 to 429496729
A random number of an integer value up to 5 (a value obtained by subtracting 1 from 2 32), which is the same as the number of individuals, is generated and placed on the memory. These random numbers become the initial state of each gene sequence. In order to speed up the process, an address table that stores the start address where each gene sequence is stored is prepared and the pointer address is moved without moving the substance of the gene sequence. Further, the random numbers used in the procedure after the generation 71 of the group are 1 to the number of individuals (100),
A random sequence of integer values up to the gene length (32) is used, so a random sequence of integer values is generated for each generation and used in each process.

Reference numeral 72 is a termination decision, and the process is repeated after 200 generations. In the evaluation 73 of each individual, the gene sequence represented by each integer value is converted into the input value of the given function using the procedure of FIG. 4 described above, and the output value of the function is obtained from each gene sequence. Among all the individuals, the ones with the smallest output value are sorted in order, and this rank is used as the evaluation value of the individuals. However, the entity of the gene sequence is not moved in the memory, and the pointer address of the gene sequence is manipulated to point the gene sequence in ascending order.

In the overall evaluation 74, it is determined whether or not the average value of the evaluations of the individual solutions performed in the evaluation 73 of each solution has become smaller than an appropriate threshold value. When it is judged to be small, it is considered that a satisfactory solution has been obtained, the result is displayed, and the processing is stopped. The selection and multiplication 75 replaces a gene sequence having a low evaluation with a gene sequence having a high evaluation from the individuals rearranged in ascending order according to the evaluation obtained in the evaluation 73 of each individual. As a result, the number of individuals with a high rating increases, and the number of individuals with a low rating disappears. In the present example, in the gene sequence of the top 10 individuals, which corresponds to the selection growth rate of 10% of 100 solutions,
Replace the gene sequence of the bottom 10 individuals.

The processing of the crossover 76 will be described with reference to FIGS. 8 and 9. 80% out of 100 at first
0 sets of 2 genes are selected by 40 pairs each without duplication.
However, in the present embodiment, the duplicate selection is not made, but a method that allows duplication may be used. In this embodiment, as a method of avoiding duplication, a random number permutation of numbers from 1 to 100 is created and stored in an array, and gene sequences are extracted according to the order. Next, from the group of gene sequences arranged in the gene sequence data 81, the two gene sequences Gene [i], G indicated by the pointer address 82 extracted by using the random number permutation described above.
ene [j] is stored in the register x and the register y of the register group 83, respectively.

Next, a random number is used to randomly determine the crossover bit k of the gene sequence. All the mask patterns 84, which are integer type variables for masking the crossing bits k to LSB (least significant bit), are arranged in advance in the memory, and a mask pattern mask for masking from k bits to LSB is masked.
[K] is loaded into the register z of the register group 83. FIG. 9 shows the crossover procedure of the gene sequences arranged in the register. (Step 1) Gene [i], Gene [j] and m
The ask [k] is stored in the registers x, y, and z, respectively. (Step 2) Register x, register z, register y
The result of the bitwise AND of the register z and the register z is stored in the register a and the register b, respectively.

(Step 3) The bit of the register z is inverted. (Step 4) Register x, register z, and register y
And the result of the bitwise AND of the register z is stored in the register x and the register y, respectively. (Step 5) Bit-OR the registers x and b, and the registers y and a, and return them to the memory of the original address where Gene [i] and Gene [j] existed.

Thus, the crossover of the gene sequence from k bits to LSB is completed. In this way, the gene sequence for which crossover has been completed is returned to the original memory, and 40 sets or 80
Until the processing of each gene sequence is completed, a pair of gene sequences are sequentially extracted according to a list in which the array of integer values is randomly replaced, and the above procedure is repeated.

The processing of the mutation 77 is shown in FIGS.
Will be explained. First, as shown in FIG.
A sequence of 5 genes, which is 5%, is selected from 0 genes. As a method of avoiding this duplication, the random number permutation described above is used. A pointer address group 10 selected by using a list in which the sequence of integer values is randomly replaced.
One gene sequence Gene [i] pointed to by one of the two
Are stored in the register x of the register group 103, respectively. Next, a random number is used to randomly determine the mutation start bit k1 and the mutation end bit k2 of the gene sequence.

The procedure of mutation will be described with reference to FIG. (Step 1) Gene sequence Gene to be mutated
[I] in the register x and mask pattern mask [k
1] to mask [k2] in registers y and z, respectively.
To load. (Step 2) Bit-exclusive OR calculation of the registers y and z is performed, and the result is stored in the register y. (Step 3) The bit XOR calculation of the register x and the register y is performed, the result is stored in the register x, and the result is returned to the memory of the original address where the Gene [i] was located.

In this way, after inverting all the bit values from the k1 bit to the k2 bit on the register x, the operation of returning to the original address memory is performed again. Thus k
The mutation of the gene sequence from 1 bit to k2 bits is completed.

The gene sequence thus mutated is returned to the original memory, and the next gene sequence is extracted according to the random number permutation until the processing of all five gene sequences is completed, and the above procedure is performed. repeat. Table 1 shows the results of comparison of the processing speed between this method and the conventional method.

The conventional method differs from the present method in the following points. -Gene sequence configuration Symbol string of integer type one-dimensional array-Gene sequence transfer method Do not use pointer address. The speed is compared by the number of clock cycles.

[0032]

[Table 1]

However, in the item of comparison of gene generation processing, random numbers using addition, multiplication, and division are used in the conventional method, but this method uses a list in which the sequence of integer values is randomly replaced. Is shown. In addition, regarding the items of comparison of processing after that, both the conventional method and the proposed method,
This method is used.

(Embodiment 2) An embodiment in which the present invention is applied to the maximum value search of a 2-input 1-output non-linear function will be described in detail. The hardware configuration of the computer that executes the genetic algorithm is the same as in FIG. 2 of (Embodiment 1), and the procedure of the problem solving method is the same as that of FIG. 3 in (Embodiment 1).

The problem given is the following multimodal nonlinear function.

[0036]

[Equation 2]

However, the domain of the two input values is both 0 and less than 1 (0≤x <1, 0≤y <1). Further, it is assumed that it is known that the output value range is 0 or more and less than 1 (0 ≦ z <1).

The output value of the above function is evaluated by the following evaluation function.

[0039]

[Equation 3]

However, yi is the output value of the i-th nonlinear function, and zi is the value of the evaluation function of that output value.

The gene sequence setting 31 is the same as (Example 1) except that two input values are expressed by two genes. In the parameter setting 32, an arbitrary number of individuals, and a crossover rate and a mutation rate for them are set. These are arbitrary values of 0 to 100 [%], and the number of times the repetition is terminated is set appropriately. In this example, the number of individuals is 500, the gene length is 32, and the crossover rate is 80.
%, The mutation rate is 5%, and the number of censored generations is 200, but it is not particularly limited to these values.

Further, regarding the selection multiplication, the number thereof is determined by using the following formula.

[0043]

[Equation 4]

[0044]

[Equation 5]

Here, zi is the evaluation value of the i-th output value calculated in (Equation 3), Gmax is the number of individuals, and ci is the number of surviving i-th gene sequences in the next generation. Also, integer (x) in (Equation 5) is a function for calculating the maximum integer that is not greater than x.

The execution procedure of the genetic algorithm (Example 1) is the same as the PAD diagram of FIG. In the generation 71 of the group, two random numbers of integer values are set for each individual, that is, 200
Generate. In the following, the same processing as (Example 1) is performed. In the abortion determination 72, the 200 generations are repeated and the processing is ended. The method of crossover 76 for performing the same processing as in (Example 1) for the evaluation 73 of each individual, the overall evaluation 74, the selection and the multiplication 75 will be specifically described below. Gene sequence Gene1 which is two sets of four integer type variables pointed to by pointer addresses extracted using a random number permutation from the gene sequence group arranged in the gene sequence data
[I], Gene2 [i], Gene1 [j], Gen
e2 [j] are respectively assigned to registers x1, x2,
Store in y1 and y2. Gene1 is generated using the mask pattern mask [k1] of the gene sequence randomly selected.
[I] and Gene1 [j] are crossed over. Similarly, using the mask pattern mask [k2], Gene2
[I] and Gene2 [j] are crossed. The procedure of the crossover method is the same as that shown in FIG. 9 (Example 1).

The method of applying the mutation 77 will be specifically described. Either of the set of gene sequences which are two integer type variables pointed to by one of the pointer address groups selected by using the random sequence from the group of gene sequences arranged in the gene sequence data. Are respectively stored in the registers of the register group. Next, the mutation start bit k1 and the mutation end bit k2 of the gene sequence are randomly determined. The mutation procedure is (Example 1) in the same manner as shown in FIG. FIG. 12 shows a solution search process in this embodiment.

(Embodiment 3) The present invention is applied to the traveling Salesman problem.
lem, hereinafter simply referred to as “TSP”). Normally, when solving a TSP with a genetic algorithm, if the array of cities is simply expressed as a gene sequence, a large number of individuals will overlap the cities that go around when performing crossover or mutation, and the population will die. . As a method for solving this duplication problem, Refens
There is a method considered by Tette et al. The outline is described below (references will be described later).

With the city names as A, B, C, D, ..., A list is created in which the city names are arranged in the order of traveling cities. The city name A is counted from the left of this standard list, and the number is recorded. And from the standard list A
Get rid of. Next, the same process is performed for city name B, and the number that appears is recorded to the right of the number that was recorded earlier. In the same way, continue like C, D, ... until you run out of city names, and you'll have a list of numbers on the circuit.

The gene sequences of the tour routes of the five cities thus expressed and the crossover mechanism by the gene sequences are shown. An example in which the third digit of the crossover is crossed is shown. Before crossover BCAED → 22121 → 22 + (121) DAECB → 41321 → 41 + (321) After crossover 22+ (321) → 22321 → BCEDA 41+ (121) → 41121 → DABEC The gene sequence converted by the above method is the highest order. It can be seen that the digits have numbers 1 to 5 and the lowest digit has only 1. In addition, this method is described in detail in the following documents. Grefenstette, JJet al.:"Genetic algorithms for th
e traveling salesman problem ", Proc. of an Intern
ational Conference on Genetic Algorithms and Thei
r Applications, pp. 160-168 (1985) A method of creating a gene sequence by the method of Grefenstette will be described with reference to FIG. The k-th digit of this gene sequence has a number from 1 to k. To express the value of the k-th digit, at most, a fractional part of log (k) / log (2) is rounded up. It can be expressed if there is a bit string of numerical values. The lowest digit is always 1, and need not be expressed. In this way, the information on the traveling city is compressed and treated as one-word information.

FIG. 14 shows a method of crossing gene sequences. The crossover is performed by the same procedure as that of the crossover 76 in FIG. 8 of (Example 1), but as shown in FIG. 15, the mask pattern is set at a fixed position so that the information of each city is not damaged. Create to come.

Regarding the mutation, the same procedure as that of the mutation 77 shown in FIG. This procedure is shown in Figure 1.
This will be described in detail using 6. The case where a mutation is performed at the k-th digit of a gene sequence will be described below. (Step 1) Gene [i] is loaded into the register x from the gene sequence group, and mask [k-1] and mask [k] are loaded into the register y and the register z from the mask pattern group. (Step 2) A bit logical product of register y and register z is calculated, and the result is stored in register y. (Step 3) Bit-exclusive OR calculation of register x and register y is performed, bit negation calculation is further performed, and the result is stored in register x. (Step 4) One pattern corresponding to the kth digit is randomly selected from the mutation pattern group and loaded into the register y. (Step 5) After performing bit OR calculation of register x and register y and storing the result in register x,
This result is returned to Gene [i].

Since only the numbers 1 to k can be entered in the k-th digit of the gene sequence, all the bit patterns of the mutation pattern group are prepared in advance. In this embodiment, since the number of traveling cities is 11,
A total of 2 to 11 and 65 patterns are required.

[0054]

INDUSTRIAL APPLICABILITY The present invention creates a gene sequence used in a genetic algorithm so as to be suitable for a computer architecture without damaging its properties and information. This saves memory. In addition, it is possible to reduce the frequency of loading and storing between memory and registers. As a result, high speed processing of the genetic algorithm becomes possible.

Further, in the present invention, the above-mentioned crossover / mutation of the gene sequence is performed by bit operation in the register. As a result, processing in the register is possible without performing memory access. As a result, high speed processing of the genetic algorithm becomes possible. Further, in the above-mentioned gene sequence, each of the places where the genes are arranged has information indicating the characteristics of the individual. Therefore, the arrangement positions of the genes showing the characteristics of the individuals close to each other are made to approach each other. by this,
The gene sequence can be processed while maintaining the characteristics of the individuals of the previous generation.

[Brief description of drawings]

FIG. 1 is an image diagram of conversion of (gene sequence → gene sequence) used in Example 1.

FIG. 2 is a hardware configuration diagram.

FIG. 3 PAD of genetic algorithm modeling procedure
It is a figure.

FIG. 4 is a one-input / one-output nonlinear function used in the first embodiment.

FIG. 5 is a PAD diagram showing the procedure of (numerical value → gene sequence) conversion used in Example 1.

FIG. 6 is a PAD diagram showing the procedure of (gene sequence → numerical value) conversion used in Example 1.

7 is a PAD of the genetic algorithm used in Example 1. FIG.
It is a figure.

FIG. 8 is a hardware configuration diagram for performing a crossover process of the genetic algorithm used in the first embodiment.

FIG. 9 is a register configuration diagram for performing a crossover process of the genetic algorithm used in the first embodiment.

FIG. 10 is a hardware configuration diagram for performing mutation processing of the genetic algorithm used in the first embodiment.

FIG. 11 is a register diagram showing mutation processing of the genetic algorithm used in Example 1;

FIG. 12 is a diagram showing a process of solution search of the genetic algorithm performed in the second embodiment.

FIG. 13 is a diagram showing gene sequences used in Example 3.

FIG. 14 is a diagram showing a process of crossover of gene sequences used in Example 3;

FIG. 15 shows a mask pattern used for processing of crossover of gene sequences used in Example 3.

FIG. 16 is a diagram showing processing of mutation of a gene sequence used in Example 3.

[Explanation of symbols]

111 register unit 112 arithmetic unit 12 memory 121 RAM 13 data bus 14 data bus 22 GA gene sequence setting in modeling procedure 81 gene sequence data arranged on memory 82 address pointer 83 arranged on memory Permanent register group 84 Mask data arranged on memory 101 Gene sequence data arranged on memory 102 Address pointer 103 arranged on memory Register group permanently arranged on CPU

Claims (4)

[Claims] 1. When a value of an evaluation function defined on a metric space is minimized, a domain is mapped to a symbol string set,
The number of symbol strings is extinguished by the value of the evaluation function, the number of symbol strings is increased by the value of the evaluation function, the symbols in multiple symbol strings are partially exchanged, and the symbols in the string are arbitrary. In the processing method of changing one or a plurality of symbols in the above and repeating the above-mentioned means to search for a symbol string that obtains an optimal solution, the above-mentioned mapping is a continuous mapping, and the length of the symbol string is The number of bits of the computer, the register length, without compromising the properties and information that the structure of the symbol string has.
A high-speed processing method of a genetic algorithm, characterized by converting to a form suitable for the memory length, the number of registers, the number of memories, the number of arithmetic units, etc. to efficiently use the resources of a computer. 2. The processing method according to claim 1, wherein after the symbol string is loaded into a register on the central controller, the symbol string is processed without being saved from the register to the memory during the above-mentioned crossover and mutation processing. A high-speed processing method of a genetic algorithm characterized by: 3. A method for evaluating each symbol string in the symbol string group according to claim 1, wherein in order to perform processing such as multiplication and selection by arranging the symbol strings in descending order of evaluation value, the actual arrangement of the symbol strings is performed. A high-speed processing method for a genetic algorithm, which is characterized by speeding up by manipulating a pointer address of a symbol string as a method of retaining only the order without performing reversion. 4. A high-speed processing method of a genetic algorithm, characterized in that, in the processing method according to claim 1, the processing method according to claim 2 and the processing method according to claim 3 are used in combination.