Computers in Chess: Solving Inexact Search Problems

169 Pages·1984·3.757 MB·English

by  M. M. Botvinnik (auth.)

SYMBOLIC COMPUTATION
Managing Editors: J. Encarnayao P. Hayes
Artificial Intelligence
Editors: L. Bole A. Bundy J. Siekmann
Springer Series
in Symbolic Computation
Editors
Computer Graphics: J. Encarnac;:ao; K. Bib, J.D. Foley, R. Guedj,
J.W. ten Hagen, F.RA Hopgood, M. Hosaka, M. Lucas, A.G. Requicha
Artificial Intelligence: P. Hayes; L. Bole, A. Bundy, J. Siekmann
Computer Aided Design
J. Encarna~io, E.G. Schlechtendahl
1983. ix, approx. 350 pages. 183 figures
Augmented Transition Networks
L. Bolc
1983. xi, 214 pages. 72 figures.
Automation of Reasoning 1
Classical Papers on Computational Logic 1957·1966
J. Slekmann, G. Wrightson
1983. xii, 525 pages. 37 figures
Automation of Reasoning 2
Classical Papers on Computational Logic 1967·1970
J. Siekmann, G. Wrightson
1983. xii, 637 pages. 39 figures
Computers in Chess
Solving Inexact Search Problems
M.M. Botvinnik
1984. xiv, 158 pages. 48 figures
M. M. Botvinnik
Computers in Chess
Solving Inexact
Search Problems
Translated by Arthur A. Brown
With Contributions by A. I. Reznitsky, B. M. Stilman,
M. A. Tsfasman, and A. D. Yudin
With 48 Illustrations
Springer-Verlag
New York Berlin Heidelberg Tokyo
M. M. Botvinnik Arthur A. Brown (Translator)
c/o VAAP-Copyright lO709 Weymouth Street
Agency of the U.S.S.R. Garrett Park, MD 20896
B. Bronnaya 6a U.S.A.
Moscow lO3lO4
U.S.S.R.
Library of Congress Cataloging in Publication Data
Botvinnik, M. M. (Mikhail Moiseevich), 1911-
Computers in chess.
(Symbolic computation. Artificial intelligence)
Translation of: 0 reshenii netochnykh perebornykh
zadach.
Bibliography: p.
Includes index.
1. Chess-Data processing. 2. Search theory.
I. Title. II. Series.
GVI447.B67513 1983 001.4'24 83-10571
Original Russian edition: 0 Reshenii netochnukh perebornykh zadach. Moscow:
Nauka, 1978.
© 1984 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 18t edition 1984
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Typeset by Science Typographers, Medford, NY.
987654321
ISBN-l3: 978-1-4612-9736-9 e-ISBN-13: 978-1-4612-5204-7
DOl: 10.1 007/978-1-4612-5204-7
Preface to the English Edition
Much water has flowed over the dam since this book went to press in
Moscow. One might expect that PIONEER would have made substantial
advances-unfortunately it has not. There are reasons: the difficulty of the
problem, the disenchantment of the mathematicians (because of the delays
and drawing out of the work), and principally the insufficiency and some
times complete lack of machine time.
The general method used by PIONEER to solve complex multidimen
sional search problems had already been formulated at that time. It was
supposed that the successful completion of the chess program PIONEER-l
would provide a sufficient validation for the method. We did not succeed in
completing it. But, unexpectedly, PIONEER's method obtained a different
kind of validation.
Since our group of mathematicians works at the Institute for Electroen
ergy, we were invited to solve some energy-related problems and were
assigned the task of constructing a program that would plan the recondi
tioning of the equipment in power stations-initially for one month. Until
then, the technicians had been preparing such plans without the aid of
computers.
Although the chess program was not complete even after ten years, the
program PIONEER-2 for computing the monthly repair schedule for the
Interconnected Power System of Russian Central was completed in a few
months. In mid-October of 1980 a medium-speed computer constructed the
plan in 40 seconds. When, at the end of the month, the mathematician A.
Reznitsky turned over the results to the Central Dispatch Control (CDC) of
the power system, he was treated with disbelief, since the plan already
prepared by the technicians differed from the computed plan. In a day or
v
vi Preface to the English Edition
so, however, things were cleared up. PIONEER-2 turned out to be more
competent than the humans. Using the methods of the chess master, the
computer very quickly found a high priority variation in the plan, tested the
possibility of improving it, and produced the results. PIONEER-2 was at
once adopted by the CDC for implementation.
In the following year, PIONEER-3 was developed to produce the annual
plan for all power stations in the USSR. The plan for 1982 was produced in
3 minutes 19 seconds. If one notes that the monthly plan dealt with 200
units for 30 days, and the annual plan with 600 units for 365 days, one must
be amazed; the dimension of the full-width search tree for the annual plan is
essentially infinite. The truth of the matter is that by using the chess
master's method, the search problem is reduced to one of analysis, and
therefore the solution depends only weakly on the dimensions of the search.
In 1982 the program was updated. It not only produces the plan, but if
necessary minimizes the increase in the reserve power that must be dedi
cated to offset the output of the units in repair. The technicians like this
very much, since now they can only approximate the amount of reserve
power needed for maintenance; the computer itself made the value of the
reserve more precise. However, the program was more complex and the
1983 plan consumed 12 minutes 6 seconds.
Why should the maintenance planning present a simpler problem than
chess? The answer is not hard to find. Let us look at two schemes for solving
an enumerative problem.
Scheme (a) corresponds to a solution of the problem by a full-width
search. It is a simple scheme, but suitable only for the case in which the
branching factor during the search is small; only then can we obtain a deep
solution. For a branching factor appreciably greater than unity we can in
general obtain only a weak and superficial solution because of the
catastrophic growth of the search tree. Moreover, and this is the essential
point, since the full-width search is not connected with the essence of the
problem we are trying to solve, a good positional estimate is excluded;
without it we cannot find a good solution.
The chess master uses Scheme (b). He processes his initial information,
establishes a goal for the inexact game, establishes a multi-level system, sets
priorities for the inclusion of moves for consideration, and constructs a
positional estimate. After this, the game of chess-a search task of very high
dimension-reduces to a problem in analysis; the branching factor remains
close to unity, and nothing prevents reaching a deep solution.
We can now see why maintenance planning is easier than chess. In the
planning problem, the initial information fed to the computer scarcely needs
processing; it is already in a form suitable for analysis. In chess, on the
other hand, the data destined for analysis is deeply hidden in the initial
data. The principal task consists in transforming the initial data to a form
suitable for analysis. Herein lies one of the reasons for our delay in finishing
PIONEER-I.
Preface to the English Edition vii
Nevertheless, the chess program has made some progress. Where before
we looked on chess as a three-level system (attack trajectories with attacking
and attacked pieces, fields of play, the ensemble of fields) we now model the
game of chess as a four-level system. A field of play has a somewhat abstract
nature; on the basis of the field we have now formed a real chain of
trajectories (this is the third level) and an ensemble of such chains (the
fourth level) which is a genuine mathematical model of a position.
We had already developed the concept of the compound field, composed
of a number of simple fields, but we did not know how to analyze it. The
priority for inclusion of moves in the search was based on the "practicabil
ity" of the several trajectories, and such a priority did not yield good results.
We now base the priority on the practicability of a chain of trajectories,
which we call a compound field. To a first approximation we may say that
the trajectories in a chain belong to two fields. A chain must have its own
basic attack trajectory and, of course, the target of attack. As we noted
above, an ensemble of chains constitutes the mathematical model.
The positional estimate is now based not only on material values but also
on the situational value of the pieces. The concept of the situational value
had already been introduced in the author's earlier book Computers, Chess,
and Long-range Planning, but it was not formalized. We have now suc
ceeded in doing that. The greater the value of a chain (of trajectories) with
which a piece is connected, the higher the situational value of that piece.
This was tested on a position in a game by Botvinnik-Capablanca. We
succeeded for the first time in increasing the positional estimate in the
course of a sacrificial combination. We are currently sharpening some new
developments, after which PIONEER will be suggested for the analysis of
quiescent positions.
Few people believe in the success of our work. Nevertheless, I had not
expected Ken Thompson to be skeptical; so far as I know, Claude Shannon
is also skeptical. This is most curious, since in the historical development of
an artificial chess master there have been only two major events: the
fundamental work by Shannon (1949), and the construction of BELLE, a
high-speed specialized computer by Thompson (1980). BELLE has attained
national master rating and is World Champion among chess-playing com
puters. However, BELLE uses the brute force method, and this is hardly
capable of further progress. It is the computer's turn to adopt a more
fruitful method-perhaps PIONEER. And if PIONEER is unsuccessful, we
must believe that some other method will be found. The problem must and
will be solved.
Note: Recently the solution to the maintenance planning problem has
again been advanced. The program PIONEER-5 will be completed in
December. It will deal with a whole set of resources expended in the
maintenance process, instead of with one resource only. Since these re
sources are in part local and in part centralized, PIONEER will begin with
local preliminary plans, for orientation, and then proceed to the second and
viii Preface to the English Edition
higher levels. It will then reverse the process and return finally to the lower
levels, where priority will be given to the general interests of the integrated
energy system; the local plans will then be optimal.
After PIONEER-5 has successfully completed its trials, one may assume
that, to a first approximation, it will be capable of planning any branch of
the economy.
As for PIONEER-I, there remains the completion of the positional
estimate, and then further progress can be made.
Moscow M. M. BOTVINNIK
June, 1982
Preface to the Russian Edition
This book gives an account of the theory needed for the solution of inexact
enumeration problems; the theory as expounded here is to some extent
based on hypothesis, since our experience does not yet fully support our
theoretical position. When our chess program PIONEER begins to play at
master strength, we may say that the theory has a solid basis.
The (unfinished) history of the development of strong chess programs is
connected with a struggle between two different trends. The prevailing
opinion, for a long time, was that the computer should not imitate a chess
master's thought processes, and that the method for play by a machine
should be based on an exhaustive search for possible moves. Since the first
successes of PIONEER, the position has changed to some extent; from now
on, computer programs will increasingly tend to imitate humans.
The first part of the book contains a general statement of the method
that, in our opinion, should be used for the solution of inexact enumerative
control problems; we use the game of chess as an example to show how the
general theory can be successfully applied. A detailed exposition of the
algorithmic basis is given in the appendices, which were written by mathe
maticians who took part in the development of PIONEER. They should be
of interest to program designers and should aid in the practical application
of the principles set forth in this book.
ix
Contents
CHAPTER I
The General Statement
Definition of an Inexact Task 1
Inexact Tasks and Control Systems 2
Two Methods for Solving Inexact Problems 2
The Goal of the Game and the Scoring Function 6
Goal and Prognosis (The Optimal Variation) 7
Multi-level Control Systems 8
Types of Multi-level Systems 9
Advantages of the General Goal 11
The Method for Connecting the Optimal Variations of the Components for
Types C and E Regimes 12
Computer Programs and Humans 13
The Expansion of Artifical Intelligence 14
CHAPTER 2
Methods for Limiting the Search Tree 15
Truncation 15
The Goal of an Inexact Game 16
The Scoring Function 16
Breaking Off a Variation 17
The Pruning of Branches 17
The Horizon 17
Two Trees: The Mathematical Model (MM) 18
The Stratification of the System 19
Three General Limitation Principles 20
Improving the Results of a Search 21
xi