JPH05173999A - Search system for solution of optimization problem - Google Patents

Abstract

PURPOSE:To automatically and efficiently search for such a solution that an evaluated value is maximum by correcting a method which selects a change position when a new symbol string is generated with the evaluated value given to the new symbol string. CONSTITUTION:A symbol string generation part 61 generates S symbol strings at random and a set of the S symbol strings is stored as an initial set in a symbol string set storage part 62. Then an evaluated value calculation part 64 calculates the evaluated values of the respective symbol strings included in the initial set and stores them in an evaluated value storage part 63 and a matrix correction part 67 performs normalization. Then a symbol string generation part 61 selects one (or two) symbol string at random from the symbol string set in the symbol string set storage part 62 and a matrix correction part 67 corrects the matrix in a matrix storage part 66 for symbol string generation and finds a symbol string which maximizes the evaluated value. Consequently, the possibility that a search is advanced in an improper direction is reduced when a search is made nearby an optimum solution and the solution which maximizes the evaluated value can automatically be searched for with efficiency.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a solution search method for an optimization problem for searching an optimum solution using a computer or the like.

[0002]

2. Description of the Related Art Conventionally, various methods have been proposed for searching an optimum solution for a given problem using a computer or the like.

For example, when there is a set of symbols and an index that gives an evaluation value to a symbol string created by arranging the symbols extracted from this set in a line, "find a symbol string that maximizes the evaluation value. When searching for a solution to the problem
The method of solving by a deterministic procedure requires a huge amount of calculation. Therefore, a non-deterministic element, that is, a solution search method incorporating a probabilistic method has been proposed.

[0004]

However, in the conventional search method for the solution of the optimization problem, which incorporates the probabilistic method as described above, the probability distribution is fixed,
When searching in the vicinity of the optimum solution, the search may proceed in an improper direction, and there is a problem in that many calculations may be required before reaching the optimum solution.

The present invention has been made in consideration of such a conventional situation, and is an optimum method capable of automatically and efficiently searching for a solution having the maximum evaluation value calculated by a given index. It is intended to provide a search method for a solution of the optimization problem.

[0006]

That is, a solution search method for an optimization problem according to the present invention is a method for automatically searching for a symbol string having a maximum evaluation value given to the symbol string based on a predetermined index. And a step of selecting one or a plurality of symbol strings with a probability according to the height of the evaluation value from a symbol string set composed of a plurality of symbol strings, and the selection based on a site selected by a predetermined method. Changing a part of the generated one or more symbol strings to create a new symbol string, changing the symbol string set according to the created new symbol string, and the created new symbol string. And a step of modifying a method of selecting a changed portion when the new symbol string is created, according to the evaluation value given to the.

[0007]

In the search method for the solution of the optimization problem of the present invention having the above-mentioned structure, the method of selecting the changed portion when creating a new symbol string is modified by the evaluation value given to the new symbol string.

Therefore, when searching in the vicinity of the optimum solution, it is possible to reduce the possibility that the search will proceed in an inappropriate direction, and to automatically and efficiently find the solution with the maximum evaluation value. You can explore.

[0009]

BEST MODE FOR CARRYING OUT THE INVENTION The details of a method for searching for a solution to an optimization problem according to the present invention will be described below with reference to the drawings.

In this embodiment, the present search method will be described by using an example of finding a route out of a maze as shown in FIG. That is, here, in the maze shown in FIG. 2, the purpose is to find the shortest route from the location S (coordinate (1,1)) to the location G (coordinate (5,5)).

(U, D, R, L) is prepared as a set of symbols. The meaning of each symbol is: U: move up. (When the current coordinate is (i, j) (i, j +
Move to 1). ) D: Move down. (When the current coordinate is (i, j) (i, j-
Move to 1). ) R: Move to the right. (When the current coordinate is (i, j) (i + 1,
Go to j). ) L: Move to the left. (When the current coordinate is (i, j) (i-1,
Go to j). ) Is. A symbol string in which these symbols are arranged corresponds to a route. For example, if the symbol string x is x = URUR, it means starting from S and moving to the upper right and the upper right, and the place reachable by x is in the dead end of the coordinate (3,3).

Furthermore, an index for assigning an evaluation value to an arbitrary symbol string is defined as follows. Evaluation value = 1 / (D * 4 + L) However, D: The distance between the destination finally reached by the symbol string and the destination point G.

(The coordinates of the finally reached place are (i, j)
Then D = (5-i) + (5-j)) L: Length of symbol string (for example, x = RRRU length is 4.) If you hit a wall on the way, The position is decided as "the place where we could finally reach". For example, x = R
In the case of RUL, after moving twice to the right, there is a wall above it and it cannot move, so this position (coordinates (3, 1)) is taken as the “finally reachable place”.

Next, the procedure for generating a new symbol string will be described.

The upper limit of the length of the generated symbol string is N. Prepare three matrices with N + 1 rows and N + 1 columns.

[0016]

[Equation 1] Three procedures are prepared as a procedure for generating a symbol string.

(1) Procedure 1 (hereinafter referred to as Procedure C) Procedure C is a procedure for generating two new symbol strings from two symbol strings. Specifically, as shown in FIG. 3, the two original symbol strings are cut at a certain position in x and y (FIG. 3A), and these are replaced to create two new symbol strings x ′ and y ′.
(FIG. 3B). The lengths of x and y are m and n, respectively. Of course, m and n are N or less.

X = x ₁ x ₂ ………… x _i ………… x _m y = y ₁ y ₂ ………… y _j ……… y _n x, y The symbol string constituting each of them has a length of +1 You can add individual breaks. The x-division and the y-division are represented as follows.

[0019] _{x = □ 0 x 1 □ 1} x 2 □ 2 ...... □ i-1 x i □ i ...... □ m-1 x m □ m y = ○ 0 y 1 ○ 1 y 2 ○ 2 ...... ○ _j-1 y _j o _j ... o _n-1 y _n o _n Define a matrix for determining the part of x, y used to generate a new symbol string. This matrix is C (x, y)
= {Z _ij }. C (x, y) is a matrix of m + 1 rows and n + 1 columns in which the vertical represents the division of x and the horizontal represents the division of y.

(In z _ij , i = 0,1, ..., m, j = 0,1, ..., n
And ) Z _ij takes a value of 0 or 1. Then, whether z _ij takes 1 or 0 depends on the probability. The probability is determined by the following procedure using the matrix C of the equation.

(A) From the matrix C = {c _ij }, _0≤i≤m ,
Only the part of 0 ≦ j ≦ n is taken out and designated as C ′.

(B) Normalize C '. That is, Is calculated, and all the components of C'are divided by A to obtain C'again. When A = 0, all components of C'are 1 / (m · n)
And

(C) The value at the i-th row and the j-th column of the matrix _C'is z _ij =
The probability is 1.

By the above procedure, the matrix C (x, y)
Is determined stochastically. Two symbol strings x, y and C
A procedure for generating a new symbol string x ′, y ′ from (x, y) will be shown.

[0025] and x 'procedure to generate _{x' = x 'i x'} 2 ...... x 'k ...... x' m '.

Step 1: i ← 0, k ← 1, s ₁ ←
Let 0, s ₂ ← 0.

Step 2: Set j ← s ₂ .

Step 3: End if i> m.

Step 4: If j> n, go to Step 6.

Step 5: If z _ij = 1 then s ₁ ← i +
If it is 1, the process proceeds to step 7.

Otherwise, j ← j + 1 is set and the process returns to step 4.

Step 6: _x'k ← x _{i + 1} , i ← i +
Set 1, k ← k + 1 and return to step 2. Step 7: Set i ← s _i .

Step 8: If j> n, end.

Step 9: If i> m, go to Step 11.

Step 10: If z _ij = 1 then s ₂ ← j +
Return to step 2 as 1.

If not, i ← i + 1 is set and the process returns to step 9.

Step 11: _x'k ← y _{j + 1} , j ← j +
Set 1, k ← k + 1 and return to step 7. The procedure for generating y'is the same as the procedure for generating x ', and therefore its description is omitted.

(2) Procedure 2 (hereinafter referred to as Procedure M) Procedure M is a procedure for randomly changing a portion of one symbol string to generate a new symbol string. That is, FIG.
, A part of the original symbol string x (FIG. 4A) is replaced with another symbol to newly generate a symbol string x ′ (FIG. 4B). Note that the length of x is m. The length of the newly generated symbol string x'is also m. x = x ₁ x ₂
…… x _i …… x _m x '＝ x' _i x ' ₂ …… x' _j …… x ' _m x The symbol strings that make up x can have m + 1 delimiters.

X used to generate a new symbol sequence
Define a matrix to determine the part of. This matrix is M
(X) = {z _ij } will be written. M (x) is a square matrix of m + 1 columns that represents the division of x in the vertical and horizontal directions. (In z _ij , i, j = 0,1, ..., m). Z _ij takes either a value of 0 or 1. In the case of i> j, z _ij = 0. Only in the case of i ≦ j, whether z _ij takes 1 or 0 is determined by the probability. The probability is the procedure C using the matrix M of the formula.
Make the same decision as in.

Now, assume that the matrix M (x) is stochastically determined. A procedure for generating a new symbol string x ′ from the symbol string x and M (x) will be shown.

Procedure for generating x ′ Step 1: For 0 ≦ i ≦ m, let x ′ _i ← x _i .

(Copy x to x '.) Step 2: Set i ← 0 and j ← 0.

Step 3: If j> m, i ← i + 1,
Let j ← i.

Step 4: If i> m, end.

Step 5: If z _ij = 1 then _{x'i + 1} ,
..., each value of x _'j, replacing {U, D, R, L } in symbols chosen lanthanum among.

Step 6: Set j ← j + 1 and return to Step 3.

(3) Procedure 3 (hereinafter referred to as Procedure I) The procedure is that, as shown in FIG. 5, the original symbol string x is rearranged in the reverse order to create a new symbol string. This is a procedure to generate x '. Note that the length of x is m. Also, the length of the newly generated symbol string is m.

X = x _i x ₂ ...... x _i ...... x _m x '= x' _i x ' ₂ ...... x' _j ...... x ' _m x The symbol string forming x has m + 1 divisions. Can be turned on.

X used to generate a new symbol sequence
Define a matrix to determine the part of. This matrix is I
(X) = {z _ij } will be written. I (x) is a square matrix of m + 1 rows and m + 1 columns that represents the division of x in the vertical and horizontal directions.
(In _{z ij i, j = 0,1,} ......, and m) z _ij takes a value of either 0 or 1. When i> j, z _ij = 0, and i ≦ j
Only in the case of, the probability determines whether z _ij takes 1 or 0. The probability is determined using the matrix I of the formula as in the case of the procedure C.

Now, assume that the matrix I (x) is determined stochastically. A procedure for generating a new symbol string x ′ from the symbol string x and I (x) will be shown.

Procedure for generating x ′ Step 1: For 0 ≦ i ≦ m, let x ′ _i ← x _i .

(Copy x to x '.) Step 2: Set i ← 0 and j ← 0.

Step 3: If j> m, i ← i + 1,
Let j ← i.

Step 4: If i> m, end.

Step 5: If z _ij = 1 then _{x'i + 1} ,
......, 'each of the values of _j, x' x _j, rearranged so as to be in reverse order and ...... x _{'i + 1.}

Step 6: Set j ← j + 1 and return to Step 3.

Next, the adaptive modification of the generation method will be described.

The generation method is modified by modifying the matrices C, M, I of the equation. The matrix is modified based on the evaluation value given to the newly generated symbol string. Let e be the evaluation value of the newly generated symbol string. When there are a plurality of generated symbol strings, the maximum value is e. The matrix correction method at this time is shown below.

(1) Matrix C Matrix C (x, y) = {zj used when a new symbol string is generated
i} (0≤i≤m, 0≤j≤n).

C ← C + eΔC where ΔC = {wij} (0 ≤ i ≤ N, 0 ≤ j ≤ N)
Is _{ wij = zij (0 ≤ i ≤ m, 0 ≤ j ≤ n) wij =
0 (other cases).

(2) Matrix M Matrix M (x) = {z used when generating a new symbol string
ij} (0≤i≤m, 0≤j≤m).

M ← M + eΔM where ΔM = {wij} (0 ≤i ≤N, 0 ≤j ≤N)
Is _{ wij = zij (0≤i≤m, 0≤j≤m) wij =
0 (other cases).

(3) Matrix I Matrix M (I) = {z used when generating a new symbol string
ij} (0≤i≤m, 0≤j≤m).

I ← I + eΔI where ΔI = {wij} (0 ≤ i ≤ N, 0 ≤ j ≤ N)
Is _{ wij = zij (0≤i≤m, 0≤j≤m) wij =
0 (other cases).

Next, the overall procedure will be described. The search is executed as shown in the flowchart of FIG. 1 using the procedure for generating a new symbol string and the adaptive correction procedure of the generating method described above. Further, FIG. 6 shows a schematic configuration of an apparatus for performing such a search.

In FIG. 6, reference numeral 61 is a symbol string creating unit for creating a symbol string, 62 is a symbol string group accommodating unit for accommodating the created symbol string group, and 63 is an evaluation for accommodating the evaluation value of the symbol string. The value accommodating section 64 is an evaluation value calculating section for calculating the evaluation value of the symbol string by the above-described index, and 65 is a procedure accommodating section for accommodating the procedure C, the procedure M, and the procedure I for generating the symbol string. Further, 66 is a matrix accommodating portion for accommodating a symbol string for accommodating a matrix C, a matrix M, and a matrix I for determining a portion used for generating a new symbol string, and 67 is a accommodating portion 66 for symbol string preparation. Matrix C, matrix M, matrix I in
Is a matrix modification unit that modifies by the method described above.

With the apparatus thus configured, first,
The symbol string creating unit 61 randomly creates S symbol strings, and stores the S symbol string sets in the symbol string set accommodating unit 62 as an initial set (step 1).

Next, the evaluation value calculation unit 64 calculates the evaluation value of each symbol string included in the initial set according to the index described above, and stores it in the evaluation value storage unit 63 (step 2).

After that, the matrix modifying unit 67 sets all the components of the matrices C, M and I to 1 / N ² for normalization (step 3).

After that, the symbol string creating unit 61 selects two symbol strings x and y from the symbol string set in the symbol string set accommodating unit 62 with a probability proportional to the size of the evaluation value (step 4). Next, the symbol string creating unit 61 randomly selects one of the procedures C, M, and I from the procedure accommodating unit 65 (step 5).

The symbol string creating unit 61 refers to the matrix C, the matrix M, and the matrix I of the symbol string creating matrix accommodating unit 66,
Generate a new symbol string x '(and y') using the method described above, using both x and y if procedure C is selected, and using x if procedure M or procedure I is selected. (Step 6).

Next, the evaluation value calculation unit 64 calculates the evaluation value of x '(and y') according to the index described above, and stores it in the evaluation value storage unit 63 (step 7).

After that, the symbol string creating unit 61 randomly selects one (or two) symbol strings from the symbol string set in the symbol string set accommodating unit 62 and replaces it with x '(and y'). (Step 8).

Then, the matrix correction unit 67 causes the matrix (C, C, in the symbol string creation matrix accommodating unit 66 corresponding to the procedure selected in step 5 according to the evaluation value of x '(and y').
M, I) is corrected by the above-mentioned formula (step 9).

By repeating the process from step 4 above, the symbol string that maximizes the evaluation value is found. The determination of the end is made, for example, by comparing the highest evaluation value with the set value (if the value is smaller than the set value, repeat the process) (step 10).

As described above, according to the present embodiment, the method of creating a new symbol string from an old symbol string is adaptively modified according to past cases, so that the target symbol string can be obtained with a smaller amount of calculation. It can be generated, and the symbol string that maximizes the evaluation value can be efficiently found.

[0077]

As described above, according to the solution search method of the optimization problem of the present invention, a solution that maximizes the evaluation value calculated by a given index is automatically and efficiently selected. You can explore.

[Brief description of drawings]

FIG. 1 is a view for explaining a process of one embodiment of the present invention.

FIG. 2 is a diagram for explaining a maze in an example.

FIG. 3 is a diagram for explaining a procedure C.

FIG. 4 is a diagram for explaining a procedure M.

FIG. 5 is a diagram for explaining a procedure I.

FIG. 6 is a diagram showing a schematic configuration of an apparatus for realizing an embodiment of the present invention.

Claims (1)

[Claims] 1. A method for automatically searching for a symbol string having the maximum evaluation value given to a symbol string based on a predetermined index, wherein the evaluation value is calculated from a symbol string set consisting of a plurality of symbol strings. A step of selecting one or a plurality of symbol strings with a probability according to the height, and changing a part of the selected one or a plurality of symbol strings based on the site selected by a predetermined method, and a new symbol string Creating the new symbol string, changing the symbol string set according to the created new symbol string, and changing when creating the new symbol string by the evaluation value given to the created new symbol string. A method for searching for a solution to an optimization problem, comprising the step of modifying a method for selecting a part.