JPH04247556A - Search execution system - Google Patents

Abstract

PURPOSE:To accelerate search by executing the search to partial search depth by plural partial searching means provided at a search executing means and selectively outputting plural much better solutions according to the searched results. CONSTITUTION:A search advancement control means 301 instructs the search with a partial search space, which starts from a route node 202, as an object to a partial searcher S1. As soon as getting the searched results, the partial searcher S1 successively transmits those results to an order deciding means 303. The order deciding means 303 selects the much better result out of the received searched results and transmits it to the search advancement control means 301 and the search advancement control means 301 stops the search of the partial searcher S1.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to information processing technology, and particularly to a search execution method that is a basic technology of artificial intelligence (AI), operation research (OR), etc.

0002

[Prior Art] So-called search problems include route search problems (
There are eight puzzles, Rubik's cube, traveling salesman problem, job shop scheduling, theorem proving, etc.), games (chess, Othello, Go, etc.), and constraint satisfaction problems (eight queen, four color problem, etc.). A common method for handling these search problems is to describe the problem in a tree-structured search space in which a starting state is a root node and multiple states generated from the root node are represented as child nodes. In this method, even if the problem has a network structure, the state transition of the problem can be expressed as a tree structure, so the problem can be simplified and generalized, and it is convenient for theoretical handling. The A* algorithm, which has been proposed as a high-speed algorithm for finding the optimal path, and the αβ method, which is a high-speed algorithm for finding the optimal move in a game, are theories constructed to handle tree-structured search spaces.

In general, the search problem for finding an optimal solution requires an exponential amount of calculation, where D is the depth of the search space and b is the number of child nodes generated from a certain node. becomes. Such an event is called a combinatorial explosion, and it is a bottleneck in search problems. For example, with today's advanced computers, it is possible to find an optimal solution for 15 puzzles with a total of 1013 nodes in a reasonable amount of time, but it is almost impossible to find an optimal solution for 24 or more puzzles. be. Similarly, the number of nodes is 4x1
Today, it is impossible to solve the Rubik's Cube, which is 019, or the optimal solution for chess, which is 10120.

In search problems, in addition to cases in which finding an optimal solution is an important task, there are also many cases in which finding an approximate solution is more important. Most of the problems that exist in reality are like this. Rather, deriving the optimal solution requires a large amount of calculation as described above, so it can be said that it is almost powerless to solve actual problems. Therefore, the challenge for real search problems is to develop a method for finding an approximate solution as close to the optimal solution as quickly as possible. As a conventional technique from this point of view, there is a real-time search method used in games such as chess. This involves fixing the search depth to an appropriate value do, pruning using the αβ method, and finding the optimal solution Go.
Next, the search depth is increased by 1 as long as the time limit allows, and the optimal solutions G1, G2, G3, etc. in the cases of do +1, do +2, do +3, etc. are sequentially determined. The answer is Gi with the maximum i found within the time limit, thereby obtaining the most optimal solution within the limited time.

[0005] Such a method has been adopted in problems other than games, and R. E. Korf is used to solve route search problems using the A* algorithm (
R. E. Korf: “Real-Time Heuri
stic Search,”Artificial I
intelligence42, 99.189-211,
(see 1990). FIG. 3 is a diagram illustrating a search starting point gradual depth method, which is a method for this purpose. In FIG. 3, 101 is the entire search space, 102 is the root node (search starting point), 103 is the goal node (search end point), and 104, 105, and 106 are search depths d starting from search starting points 107, 108, and 109, respectively. subsearch space of, 111, 112, 113
represent the first stage of the optimal solution path in the partial search space of search depth d starting from search starting points 107, 108, and 109, respectively. Similarly, 110 is the first stage of the route from the next higher search starting point (not shown in the figure). In FIG. 3, the search proceeds as follows. First, fix the search depth to an appropriate value d,
A* Start searching for the optimal solution using the algorithm. Next, the search starting point is advanced by 1 in the depth direction along the path of the obtained optimal solution, and the search using the A* algorithm is repeated again at the search depth d. What is shown in FIG. 3 is the state after three iterations, where the first stage 111 of the route obtained by the optimal search in the partial search space 104 is selected, and the search is started. It shows how the first stage 112 of the route obtained by the optimal search of the partial search space 105 starting from the point 108 is selected. Such a process is repeated, and if the optimal search result of the partial search space reaches the goal node 103, the search ends at that point. There are several goal nodes other than those shown in the figure, and 103 indicates the one found first by Korf's search starting point gradual depth method. In this way, although there is no guarantee that an optimal solution will be obtained, a tentative answer can be obtained within a short time. According to a report by Korf, the number of moves required to solve the eight puzzle when the search depth d is 10 is 44 moves on average, which is worse than the average of 22 moves for the optimal solution, but the processing time is significantly reduced.

[0006]

However, the search starting point gradual depth method proposed by Korf has a major problem regarding its reliability as a search method, as described below. In other words, in the case of the eight puzzle, it was safe to say that the search would be successful as long as the number of steps required to arrive at the solution was not considered, but this cannot be said in general; There can be any number of problems for which space does not contain a solution. In such a case, the goal that could originally be reached by searching the entire search space at once cannot be reached using the search starting point gradual depth method, which is a major drawback of this search method. This drawback is not noticeable when there are many paths leading to the goal, such as the eight puzzle that Korf uses as an example, but the search starting point gradual depth method is generally a search method that lacks certainty. It can be said.

The present invention has been made in view of the above, and
The purpose is to provide a search execution method that reduces search uncertainty, which is a drawback of the search starting point gradual depth method, and achieves faster search.

[0008]

[Means for Solving the Problems] In order to achieve the above object, the search execution method of the present invention is a search execution method that searches a tree-structured search space of a certain search depth, which is not deeper than the search depth. A search execution means having a plurality of partial search means for searching to a partial search depth, a ranking determination means for selecting and outputting a plurality of better solutions from the search results output by the search execution means, and overall control of the search execution process. The gist is to have a search progress control means.

[0009]

[Operation] In the search execution method of the present invention, a plurality of partial search means provided in the search execution means searches to a partial search depth, and a plurality of better solutions are selected and output from the search results.

0010

DESCRIPTION OF THE PREFERRED EMBODIMENTS Examples of the present invention will be described below with reference to the drawings.

The most important feature of the search execution method of this embodiment is that it executes a search in a plurality of mutually independent partial search spaces using the search starting point gradual depth method, and that it mutually compares and evaluates the search results obtained. The method is to select a plurality of best routes from among them, gradually deepen the search, and repeat the same search again.

First, the basic principle will be explained using FIG. In FIG. 1, 201 is the entire search space, 202 is the root node (search starting point), and 203 is the goal node (search end point).
, 204-212 are partial search spaces with a search depth d, and 215-217, 219-221 are the first optimal solution paths in the partial search spaces with a search depth d starting from the respective search starting points. The stage 218 represents the first stage of the second optimal solution path in the partial search space of search depth d starting from the search starting point. Note that 213 and 214 are similarly the first stage of the route from the next higher search starting point (not shown in the figure). In Figure 1, the search starting point is omitted to avoid complexity.
Similar to FIG. 3, the vertices of the triangle correspond to it. Further, FIG. 1 corresponds to a case where the multiplicity k that appears in the following explanation is 2.

In FIG. 1, the search proceeds as follows. First, at the root node, the search depth is fixed to an appropriate value d and a search in the partial search space is started. The search starting point is advanced by 1 in the depth direction along the path of the first to kth optimal solutions obtained thereby to generate k partial search spaces. Search depth d for these subsearch spaces independently
Execute the search. Next, the search results of each partial search space are collected and evaluated, and k different routes are selected in descending order of the search results. Then, the search starting point is advanced by 1 in the depth direction along these k optimal solution paths, k partial search spaces of the next layer are generated, and the same process is repeated.

What is shown in FIG. 1 is the state after the search at the root node and the subsequent search have been performed twice (however, as already mentioned, the multiplicity k=
2). If the search starting point is advanced in the depth direction along the first stage 213 of the optimal search path obtained by searching the second layer partial search space and the first stage 214 of another optimal search path, the next Partial search spaces 204 and 205 are obtained. In FIG. 1, 214 is marked with ■ and 213 is marked with ■, and the circled numbers indicate the optimal ranking based on a comprehensive view of all search results up to the second layer.

In the third layer, the partial search space 204,
205 are searched independently, and the first stage 215, 216 of each optimal search path is obtained. Here, 215
There are circled numbers such as ■ and 216, but 3
A comprehensive look at all search results up to the layer shows that the optimal ranking is in this order. When comparing the full search results up to the second layer and the full search results up to the third layer, the way in which the circled numbers are assigned is reversed.

Furthermore, in the fourth layer, the partial search space 206
, 207 are performed independently, and the first stage 217, 219 of each optimal search path is obtained. However, when looking comprehensively at all search results up to the fourth layer, as shown by the circled numbers, the overall optimal ranking for 219 is ■, and the second optimal search obtained from the partial search space 206 The first stage 218 of the route has a higher rating ■. At this point, the subsequent search is performed using the partial search space 20
The partial search spaces 208 and 209 subsequent to 6 are executed, and the search in the partial search space 210 is truncated.

[0017] Such a process is repeated, and if the optimal search result of any partial search space reaches the goal node 203, the search ends at that point. There are several goal nodes other than those shown in the figure, and 203 indicates the one found first by this search method.

Compared with FIG. 3, the search results in FIG. 1 can be said to show more appropriate results. This is because, as is clear from the comparison between the two figures, at the fourth layer search stage, route 112, which was the optimal candidate in Figure 3, becomes the third candidate (219) from the overall perspective as shown in Figure 1. This is because it is too much. According to this search execution method, although there is no absolute guarantee that an optimal solution will be obtained, a better-quality approximate solution can be found in a short time, and there is a risk of ending up without finding the solution that was supposed to be found. will decrease.

According to this search execution method, the amount of calculation required for the search is k times smaller than that of the prior art Korf's search starting point progressive depth method. This is because the present search execution method searches the entire search space in k ways in parallel, and ends the search when one of the routes reaches one of several goal nodes, whereas the conventional method This is because the search is continued until a specific route reaches the goal node, so the search depth to the goal node by this search execution method is equal to or smaller than that of the conventional technique. Simply put, this search execution method is able to find a more optimal route than the prior art, but this fact means that the depth of search to reach a solution is smaller. If by chance the conventional technique obtains the same solution as the solution of the present search execution method, the amount of calculation of the present search execution method will be k times that of the conventional technique, but the search depth will generally be smaller. The amount of calculation is reduced by a corresponding amount.

Next, an embodiment of the present invention will be described with reference to FIG. In FIG. 2, 301 is a search progress control means, 302 is a search execution means, 303 is a search result ranking determination means, and 304 to 306 are partial searchers S1, S2...,
It is Sk.

The search execution method shown in FIG. 2 operates under the overall control of the search signal control means 301, and its operation will be explained below.

The search progress control means 301 first initializes the whole, and then continues to initialize the partial searcher S1 (304
) to search the partial search space starting from the root node 202. Partial searcher S1 (30
4), as soon as the search results are obtained, they are sequentially sent to the ranking determining means 303. The ranking determining means 303 selects k better results from the received search results. for example,
If the search algorithm of the partial searcher is a method of finding solutions in order from the best to the best, then the first k received corresponds to that. If the best solution is not found in order, the quality of the results is compared and evaluated. however,
In either case, if the first stage of the optimal solution path is the same, it must be counted as one. Ranking determining means 30
3, when it has finished finding k better search results, it notifies the search progress control means 301, and the search progress control means 30
1 stops the search of the partial searcher S1 (304). The result obtained in this way may be less than k if the number of child nodes generated from the root node is small. In such a case, the search by the partial searcher S1 (304) progresses to the end, so the search by the partial searcher S1 (304) proceeds to the end.
4) transmits it to the search progress control means 301. This completes the search using the root node as the search starting point.

The search progress control means 301 controls the partial searchers S1, S2,..., Sk for searching all the layers except the root node, that is, the partial search space from the first layer onwards.
(304 to 306) are executed concurrently. In the following, the operation of FIG. 2 in this case will be explained. First, the search progress control means 301 gradually deepens the search starting point based on the k better search results obtained by the ranking determination means 303, and the partial searchers S1, S2,...,Sk (30
4 to 306), allocate a new partial search space. This assignment may be performed simply, but search results up to the previous layer may also be used in some cases. For example, the partial searcher S2 (305) is in the partial search space 204 in FIG.
, the results up to the depth d-1 of the partial search space 206 should remain in the partial searcher S2 (305). Therefore, the partial searcher S2 (305
) to search the partial search space 206, the amount of search is reduced compared to the case where it is assigned to completely unrelated partial searchers. Now, the partial searchers S1, S2,..., Sk
(304 to 306) sequentially obtain search results and send them to the ranking determining means 303, as in the case of a search using the root node as the search starting point. The ranking determining means 303 selects k better results from the received search results. if,
If the search algorithm of the partial searchers is a method of finding solutions in order from the best one, each partial searcher S1, S2
,...,Sk (304-306) search results sent from γ11, γ12,..., γ1n1, γ21, γ2
2,..., γ2n2 ,..., γk1, γk2,..., γkn
k, at least γ1n1, γ2n2,
..., γknk is not included in the k items. However, in a special case where all k solutions are biased toward partial searcher j with good search results, n1 , n2 , ..., nj-1 , nj+1 ,
..., after confirming that nk is 1 or more, γj1
, γj2,..., γjk are selected. This is a means for selecting the more optimal k search results after confirming that at least the last search result obtained from each partial searcher has a rank worse overall than the k-th search result. It has become. This processing process is different from the case where the root node is used as the search starting point, but by doing so, the optimal k items can be found by comprehensively looking at the search results of a certain hierarchy. If the search algorithm of the partial searcher is not a method of finding solutions in order from the best one, the quality of the results is compared and evaluated, and k better results are left. In either case, if the first stage of the optimal solution route is the same, it must be counted as one, as in the case where the root node is used as the search starting point. Ranking determining means 3
When 03 has finished obtaining k better search results, it transmits it to the search progress control means 301, and the search progress control means 3
01 is the partial searcher S1, S2,...,Sk (304
to 306) is stopped. The result obtained in this way may be less than k if the number of generated child nodes is small. In such a case, the search by the partial searcher progresses to the end, and the search progress control means 301 is notified of this. If all the partial searchers complete the search, the search progress control means 301 notifies the ranking determining means 303 of this, and terminates the ranking determining process. This concludes the explanation of the search operation when a node other than the root node is used as the search starting point.

In FIG. 2, when a goal node is obtained as a result of the search, the partial searcher that found it informs the search progress control means 301, and the search progress control means 301
performs search termination processing. Alternatively, instead of terminating immediately, the process may wait for the search results for the defective goal node to arrive before moving on to the terminating process. This makes it possible to deal with ties (tie-breaks) that often appear in searches.

Although this search execution method does not obtain a complete solution, the relationship between search depth and processing time is on the linear order (O(
D)), which prevents combinatorial explosion due to exponential order O(bD), and can be considered to be of practical value.

Note that the internal search algorithm of the partial searcher is not limited to any system, but the A* algorithm (P
．． E. Hart et al. ：”A Formal
Basis for the Heuristic D
termination of Minimum C
ost Paths,”IEEE Trans.of
Systems Science and Cyber
netics, vol. SSC-4, No. 2, pp.
100-107, 1968), IDA* algorithm (REKorf: “Depth-first
iterative-deeping: An opt
imal admissible tree search
h,”Artificial Intellegenc.
e 27, pp. 97-109, 1985), or an algorithm that preferentially searches for the best solution or a solution that is considered to be the best, such as the long-existing best-first search algorithm or the hill-climbing method.

[0027]

[Effects of the Invention] As explained above, according to the present invention,
This method has the effect of being able to obtain a higher quality approximate solution than the prior art, and reducing the risk that a solution that should originally have been obtained will not be obtained. In addition, the amount of calculation required for the search is k due to the small search depth.
Since it is smaller than twice as much, providing k partial searchers has the effect of reducing the search processing time.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram for explaining the principle of a search execution method of the present invention.

FIG. 2 is a configuration diagram of a search execution method according to an embodiment of the present invention.

FIG. 3 is an explanatory diagram of a conventional search starting point gradual deepening method.

[Explanation of symbols]

301 Search progress control means 302 Search execution means 303 Ranking determining means 304-306 Partial searcher

Claims (2)

[Claims] 1. A search execution method for searching a tree-structured search space with a certain search depth, comprising a plurality of partial search means for searching to a partial search depth that is not deeper than the search depth; ranking determining means for selecting and outputting a plurality of better solutions from the search results output by the search execution means;
1. A search execution method comprising: a search progress control means that controls search execution processing as a whole. 2. The plurality of partial search means each send search results to the ranking determination means in order from the best solution,
Either at least one of the solutions output from each partial search means is not included in the plurality of outputs of the ranking determining means, or all of the plurality of solutions output from one of the partial searching means are included in the plurality of outputs of the ranking determining means. Claim 1 characterized in that it is included in a plurality of outputs and the remaining outputs of the partial search means are not zero.
The search execution method described.