JPH06290161A - Information processing system with combination limitation - Google Patents

Abstract

PURPOSE:To improve the processing speed of an information processing system using genetic algorithm by excluding an individual to be the cause of repeated evaluation from the object of operation. CONSTITUTION:In the case that a generation consisting of four individuals S1=1001, S2=1011, S3=0111, S4=0110 is considered there are 6 kinds (=4!/2) of the possible combinations of this population (group). If random combination is executed while no combination limitation is given, there is possibility that the pairs of (S1, S2), (S3, S4) are combined. But no new individual is generated entirely from the intersection of this pair, and the useless repeated evaluation comes to be executed. Then, breeding potential Pg is used, and if a condition that only the pair whose Pg (where Pg=Dh+Ld, Dh is Hamming distance of possible combination, Ld is difference length) is over 3 is combined is added to the combination limitation, the combinations of (S1, S2) and (S3, S4) not to generate entirely the new individual are omitted from genetic algorithm processing (GA), and useless repetition is not executed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention applies an genetic algorithm to optimize the cell layout of VLSI, optimize the number of intermediate layers of a three-layer neural network, optimize the schedule, etc. Regarding

[0002]

2. Description of the Related Art Genetic algorithms have been found in the process of modeling the process of biological evolution and conducting engineering simulations to elucidate the mechanism. In addition to research on the genetics of living organisms, it has now been found that this genetic algorithm can be effectively used in other fields such as industry for problems that were difficult to solve by conventional methods.

Genetic algorithm is Genetic Algo in English
Write rithm. Since the acronym is taken and is generally called “GA”, this name will be used in the following description. Although there is no direct relationship between the field in which the present invention is used and biology,
The idea is largely based on the theory from biology which is explained below on the genetic algorithm.

There are three aspects of the activity of the living body: substance, energy and information. A substance is a body forming a living body, and energy is a heat source (calorie) in which the living body operates. Information is data of internal and external communication systems for living organisms to live, and in higher organisms, highly developed brain and nervous systems process this. In addition, the genes that organisms pass on to their offspring are one of the information.

If parents having exactly the same gene bind to each other and transmit the genes to the progeny half by half, the organism should eventually form a population with certain characteristics. That process is the evolution of living things. Genetic information is DNA
It is written in, and it is transmitted to the descendants. Human DNA consists of about 3 billion nucleotide sequences, but the structure of the human DNA is currently less than 1%.

GA is one of the search methods for engineeringly simulating the mechanism of biological evolution, and usually consists of three operations: selection, crossover, and mutation. In the natural world, the principle of natural selection works, and organisms with strong genes that are suitable for the environment are selected and their offspring are left behind. A DNA molecule having genetic information is a double-stranded base molecule. When the parent replicates the offspring, the DNA helix is unwound and other DNA
To create a new individual. That is, a new individual is born by linking one gene with another gene. This is the crossover of genes.

On the other hand, the mutation means that a part of the gene is changed due to some cause. FIG. 1 conceptually shows the basic framework of GA. One cycle of the arrow represents one generation. For humans, one generation means 30 years. There are only ten generations of change in 300 years. Therefore, it takes a long time to unravel the evolutionary process, and it is a problem that cannot be solved easily. Therefore, it is required to clarify by an engineering method based on the genetic mechanism that has already been elucidated. One of the methods is GA.

When the evolution is to be elucidated by a computer using the GA method, genes are represented by bits, and three operations of selection, crossover and mutation are performed for optimization. This operation will be briefly described by taking the human blood type as an example.

There are four human blood types: A, B, AB, and O. This does not depend on where you live or your race. The blood type of a child born from an A-type father and a B-type mother is not limited to AB type, but may be A, B, or O type. If you get the genes half and half from your parents, AB
Only type children should be born, but not necessarily. From this, A type and A type
It turns out that there is a person who has an O-type gene.

However, A is the dominant gene for O because it shows only characteristics of type A blood on the surface. For B and O as well, B is the dominant gene. A and B
There is no superiority or inferiority, so it becomes another blood type, AB type. AA
Type B and BB type parents have only AB type, but AO type and BO type parents have A type, B type, A type
B type and O type may be born.

However, no other blood type is born.
In other words, it can be said that the evolution of human blood groups has converged. Currently, however, research on blood is progressing, and R
It is premature to conclude that evolution has ceased because it contains genes that are much more complex than we generally call blood groups, such as h (+) and Rh (-).

By computer processing using the GA method, the genes A, B and O are converted into bits. For example, A is 11, B is 10, and O is 00. On the surface, type A blood is also 1111 (A
A) and 1100 (AO) will be present. For blood type, if left and right, 1100 (AO) and 00
It can be treated as the same as 11 (OA).

If one point is crossed under this condition, AO
(1100 or 0011) and BO (1000 or 0)
From a parent who has a gene of 010), 1111 (type A),
1100 or 0011 (A type), 1110 or 10
A child with 11 (AB type) and 0000 (OO) genes will be born. In GA, a gene in which a bit is expressed is called a genotype, and a number or a symbol is called a phenotype.

Mutations are expressed by inverting bits in GA. For example, suppose that the O-type gene is 00, but is converted to 01 by an external factor. This is A (1
Neither 1), B (10), nor O (00). Therefore, let's call this the C type. Generally, such mutations are lethal. Even if it is not lethal, it is culled in the natural world because it has a weak constitution and is different from those around it.

However, it is stronger than conventional genes,
If the gene is suitable for the natural environment, there is a possibility that the existing gene will be removed. GA is a method for simulating such a selection process and elucidating evolution.

When GA is used for selection, crossover, and mutation, it is common to randomly combine the selected individuals and perform crossover. However, when two linked individuals are similar, the offspring produced by crossover often have the same gene as the parent. As a result, some of the next-generation individuals will overlap with those of the current generation.

When such genetic information is subjected to function optimization using GA, what has already been evaluated will be evaluated again. This is called repeated evaluation. Repeated evaluation reduces the efficiency of the search. Therefore, when handling a group including a large number of individuals or a large amount of genetic information, it becomes an obstacle to computer processing, resulting in wasted processing time.

In the conventional processing technology, although the GA has a binding restriction for controlling the production of a lethal gene, no measures have been taken to reduce repeated evaluation. For this reason, it takes a lot of processing time by the computer, which becomes an obstacle in handling a large number of individuals and a large amount of genetic information.

[0019]

In addition to simulation of biological evolution and analysis of genetic information, GA is for optimization of cell layout of VLSI, optimization of the number of intermediate layers of three-layer neural network, optimization of schedule, etc. It is about to be used in various engineering applications.

On the other hand, there is a fundamental problem that the optimization process in GA takes time. Therefore, when GA is used for engineering applications, how to efficiently perform GA processing is a key point.
The present invention aims to create a system that solves this problem.

[0021]

[Means for Solving the Problems] GA advances generation alternation with selection, crossover, and mutation as one cycle. The selection is to select the object of the individual who optimizes the function. At this time, if the number of individuals to be processed can be reduced, the processing speed can be increased.

Conventionally, lethal individuals have been excluded as targets, and the absolute number of treated individuals has been narrowed down. However, no measures were taken against repeated evaluation. Therefore, in the present invention, in order to further narrow down the selection, the individual causing the repeated evaluation is excluded as the operation target. The present invention is intended to improve the processing speed by devising a selection condition (coupling restriction) for that purpose.

In the present invention, first, factors that influence the possibility that two individuals will cross each other to generate a new individual will be considered. After that, we propose the concept of reproductive potential as a measure of this possibility. As a result, only individuals with a reproductive potential above a given value are combined and the function is optimized.

First, consider crossover. When two individuals are similar, the child created by crossing them is often the same as the parent. For example, s ₁ = 10101
Let's do a one-point crossover for s ₂ = 10110.
In this case, five kinds of crossovers are possible, but a child different from the parent is generated only when the rightmost cut is selected as the crossover point.

All the children generated by the crossover of have different genes from the parent, but differ only by 1 bit.
It can be said that he is a child very similar to his parents. Therefore, it does not significantly affect evolution. For example, s ₁ ¹
, And s ₂ ² as a parent, the resulting child will be the same as the parent, or the same as the grandfather, grandmother (s ₁ , s ₂ ),
This is because it will be a closed system in evolution.

Since the same child as the parent is generated up to, it has not evolved at all. It is easy to imagine that parental connections with such genes are not so important in simulating evolution.

The number of different bits of the _two individuals s ₁ and s ₂ is called the Hamming distance. This is represented as D _h (s ₁ , s ₂ ).
When D _h (s ₁ , s ₂ ) = 0 and D _h (s ₁ , s ₂ ) = 1, s
The intersection of ₁ and s ₂ apparently does not produce new individuals, as we have seen in the example above. That is, the Hamming distance D _h serves as a guideline for easily generating a new individual.

However, the possibility of generating a new individual by crossover cannot be determined only by the Hamming distance. For example, two pairs (s ₁ , s ₂ ) = (1011,001
Consider 0) and (s ₁ ′, s ₂ ′) = (1011, 1101).

Considering an example in which possible crossovers are executed, (s
_The children generated by the crossover of ( ₁ , s ₂ ) are all individuals different from their parents. On the other hand, (s ₁ ′, s ₂ ′)
In the crossover, most of them are the same individuals as their parents. This is
The possibility of generating new individuals is influenced not only by the Hamming distance but also by the bit sequence of the parent gene.

Therefore, in the present invention, the distance (bit number) between the first one and the last one among the different bits of the individuals s ₁ and s ₂ is called the difference length, and the difference in length and the Hamming distance form the breeding potential. Introduce the concept.

[0031] When the difference in length denoted as _{L d (s 1, s 2} ), in the above example _{L d (s 1, s 2} ) = 3 L d (s 1 ', s 2') a = 1. Note that D _h (s ₁ , s ₂ ) = 0 and D _h (s ₁ , s ₂ ) =
For 1, L _d (s ₁ , s ₂ ) = 0.

The larger the Hamming distance, the greater the possibility that a new individual will be generated, and the greater the difference length, the greater the possibility. From this, P _g (s ₁ , s ₂ ), P _g (s ₁ , s ₂ ) -D _h (s ₁ , s ₂ ) + L _d (s ₁ , s ₂ )

It can be Especially, the maximum reproductive potential among individuals in the generation t is referred to as the maximum reproductive potential of the generation t, and is represented by PG (t).
That is, PG (t) to max {P _g (s _i ^t , s _j ^t ) | s _i ^t , s _j ^t are individuals of the generation t, and can be represented by a relational expression i ≠ j}.

In order to avoid repeated evaluation, in the present invention, only individuals s _i ^t and s _j ^t satisfying the relational expression P _g (s _i ^t , s _j ^t ) ≧ α are combined.
This is called a combined restriction MR.

Note that s _i ^t and s _j ^t are individuals of the generation t, and i ≠
j. Further, α is a threshold value given in advance.
When α <2, the combination limiting MR does not function and becomes a random combination. When α ≧ 3, the coupling limiting MR functions.

When incorporating the bond limiting MR into the GA, as a method of forming a pair satisfying the bond limiting MR, the generation t
The connection between the individuals can be performed as follows. The individual s ₁ ^t is taken out, and the reproductive potential P _g (s ₁ ^t , s _i ^t ) (i is an integer of 2 or more) when paired with another individual s _i ^t is calculated one by one.

If P _g (s ₁ ^t , s _i ^t ) ≧ α is found, s ₁ ^t and s _i ^t are combined as a pair and crossover is performed. If such s _i ^t cannot be found, s ₁ ^t is a single individual who does not satisfy the connection restriction MR. Repeat the same operation for the remaining individuals, except for paired individuals or single individuals.

GA incorporating the binding restriction MR consists of four operations: selection, binding, crossover and mutation. Crossovers and mutations are applied to the individuals paired by binding in the same manner as normal GA, but only mutations are applied to single individuals.

The GA process incorporating the connection limiting MR is terminated when t> maximum generation number or PG (t) ≦ β.

Here, t is the generation, PG (t) is the maximum breeding potential of the generation t, and β is a constant given in advance. It should be noted here that the latter end condition is not present in the conventional GA. This condition indicates that the reproductive potential declines with successive generations, making it difficult to generate new individuals. In other words, it means that evolution is nearing convergence.

As described above, the GA in which the coupling-limited MR is incorporated
2 and 3 are flowcharts of FIG.
For comparison, a conventional GA is put on FIG. In addition,
The meanings of the symbols are as follows. N _g : Maximum number of generations to be executed (number of trials) N _p : Number of individuals P _c : Crossover rate P _m : Mutation rate α: Threshold value of whether or not to combine β: Maximum reproductive potential termination condition constant s _i ^t : individual expressed by genotype. Here, i is an individual identifier and t is a generation.

[0042]

[Example] Now, four individuals s ₁ = 1001, s ₂ = 10
Consider a generation consisting of 11, s ₃ = 0111, s ₄ = 0110. The possible combinations of this population are 6 (=
4! / 2) There are streets. The Hamming distance D _h and the difference length L _d of the possible bonds are calculated as follows.

D _d (s ₁ , s ₂ ) = 1 L _d (s ₁ , s ₂ ) = 0 D _d (s ₁ , s ₃ ) = 3 L _d (s ₁ , s ₃ ) = 2 D _d ( s ₁ , s ₄ ) = 4 L _d (s ₁ , s ₄ ) = 3 D _d (s ₂ , s ₃ ) = 2 L _d (s ₂ , s ₃ ) = 1 D _d (s ₂ , s ₄ ) = 3 L _d (s ₂ , s ₄ ) = 3 D _d (s ₃ , s ₄ ) = 1 L _d (s ₃ , s ₄ ) = 0

If random coupling is performed without any coupling restriction, the pairs (s ₁ , s ₂ ) and (s ₃ , s ₄ ) may be coupled. However, no new individual is born from the crossover of this pair, and useless repeated evaluation is performed.

Therefore, using the breeding potential P _g of the present invention, P _g
If the condition that (P _g = D _h + L _d ) only joins pairs of 3 or more is added to the binding constraint, no new individuals are generated (s ₁ , s ₂ ) and (s ₃ , s ₄ ). The combination is omitted from the GA process and no useless repeated evaluation is done.

The maximum reproductive potential PG is (s ₁ ,
Since a pair of _{s 4), (s 1,} s 4) and (s _2, s ₃₎
When the crossover is performed with the combination of, there is a high possibility that a new individual will occur.

Next, let us numerically show the effectiveness of GA incorporating the coupling-limited MR. For that, Simple G
A (SGA) and SGA are GAs with combined MR
Compare (SGA '). Next two-dimensional six-hump
Consider the minimization of the camera-back function SHC. ^{_{f (x) = x 1 6}} /3-2.1x 1 4 + 4x 1 2 + x 1 x 2 -4
x ₂ ² +4 x ₂ ⁴ −2 ≦ x _i ≦ 2 where i = 1, 2

There are six local minimum solutions to this problem,
Two of them are global minimum solutions. The minimum value is -1.0
31. The following parameters are adopted in SGA and SGA '. Maximum number of generations N _g = 50, number of individuals N _p
= 20, the crossover rate P _c = 0.95, mutation rate P _m = 0.0
05, the variables x ₁ and x ₂ are both represented by a 12-bit binary integer, and the generation N _g is generated, and then the process ends.

Under the above conditions, while changing the seed of random numbers, SGA and SGA 'were used to perform 50 calculation trials. FIG. 5 shows how the average objective function values for each generation in SGA and SGA ′ when α = 5 converge.

FIG. 6 shows how the minimum objective function values converge. Note that these are average values for each generation in 50 calculation trials. From these figures, the average objective function value and the minimum objective function value are both SGA 'and SGA'.
It can be confirmed that the convergence is faster than that.

FIG. 7 is a statistical result of the minimum objective function value obtained in each calculation trial. This chart shows the number of calculation trials in the interval that is the minimum objective function value and the average value of the minimum objective function values in 50 calculation trials. From the table,
SGA 'when α = 3, 4, 5, 6 is SG
It can be seen that the result is better than A.

From FIG. 7, it can be seen that when α is set to a large value such as α = 20, SGA 'has a worse result than SGA. This is because if α is too large, the individuals that are likely to generate new individuals by crossover cannot be combined, and as a result, new individuals cannot be generated much.
That is, it is shown that when incorporating the coupling restriction MR, care must be taken not to take α too large.

FIG. 8 is a flowchart of SGA 'used to obtain the results of FIGS. This flow is
It is basically the same as that of FIG. 2, but does not include the termination condition based on the maximum potential PG (t). In the flow chart,
I is a table for storing unprocessed individuals. When pairing is performed, another individual is preempted, so that individual is deleted from I to prevent double processing.

[0054]

The information processing system of the present invention is a VLSI.
There is an effect that the GA processing can be efficiently performed with respect to the optimization of the cell arrangement, the optimization of the number of intermediate layers of the three-layer neural network, and the optimization of the schedule.

[Brief description of drawings]

FIG. 1 is a conceptual diagram of a genetic algorithm (GA).

FIG. 2 is a flow chart of a GA incorporating a limited-coupling MR of the present invention.

FIG. 3 is a flow chart of a GA incorporating a combination-limited MR according to the present invention.

FIG. 4 is a flowchart of a conventional GA.

FIG. 5 is a graph showing the convergence status of the average objective function value for each generation in SGA and SGA ′ when α = 5.

FIG. 6 is a graph showing the state of convergence of the minimum average objective function value for each generation in SGA ′ when SGA and α = 5.

FIG. 7 is a chart showing statistical results of minimum objective function values obtained in each calculation trial.

FIG. 8: SGA ′ used to obtain the results of FIGS.
It is a flowchart of.

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[Procedure amendment]

[Submission date] April 8, 1993

[Procedure Amendment 1]

[Document name to be corrected] Drawing

[Name of item to be corrected] Drawing 8

[Correction method] Change

[Correction content]

[Figure 8]

Claims (1)

[Claims] 1. An information processing system using a genetic algorithm, comprising means for combining only individuals having a reproductive potential that is equal to or greater than a given value, which indicates the degree of possibility that two individuals will cross each other to generate a new individual. An information processing system characterized in that