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Increasing Efficiency and Quality in the Automatic Composition of Three-Move Mate Problems

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In this article, we demonstrate the use of composing ‘experience’ in the form of piece location probability values derived from a database of mate-in-3 chess problems. This approach was compared against a ‘random’ one. Comparisons were made using ‘experiences’ derived from three different databases, i.e. problems by human composers (HC), computer-generated compositions that used the HC experience (CG), and mating ‘combinations’ taken from tournament games between humans (TG). Each showed a reasonable and statistically significant increase in efficiency compared to the random one but not each other. Aesthetically, the HC and CG were better than the others. The results suggest that composing efficiency and quality can be improved using simple probability information derived from human compositions, and unexpectedly even from the computer-generated compositions that result. Additionally, these improvements come at a very low computational cost. They can be used to further aid and entertain human players and composers.
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Increasing Efficiency and Quality in the Automatic
Composition of Three-Move Mate Problems
Azlan Iqbal1
1 College of Information Technology, Universiti Tenaga Nasional, Kampus Putrajaya,
Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
azlan@uniten.edu.my
Abstract. In this article, we demonstrate the use of composing ‘experience’ in
the form of piece location probability values derived from a database of mate-
in-3 chess problems. This approach was compared against a ‘random’ one.
Comparisons were made using ‘experiences’ derived from three different
databases, i.e. problems by human composers (HC), computer-generated
compositions that used the HC experience (CG), and mating ‘combinations’
taken from tournament games between humans (TG). Each showed a
reasonable and statistically significant increase in efficiency compared to the
random one but not each other. Aesthetically, the HC and CG were better than
the others. The results suggest that composing efficiency and quality can be
improved using simple probability information derived from human
compositions, and unexpectedly even from the computer-generated
compositions that result. Additionally, these improvements come at a very low
computational cost. They can be used to further aid and entertain human players
and composers.
Keywords: Artificial intelligence, chess, composition, probability, experience,
efficiency, aesthetics.
1 Introduction
A chess problem or ‘composition’ is a type of puzzle typically created by a human
composer using a chess set. It presents potential solvers with a stipulation, e.g. White
to play and mate in 3 moves, and is usually composed with aesthetics or beauty in
mind. Compositions often adhere to certain composition conventions as well, e.g. no
‘check’ in the key (i.e. first) move. One of the earliest books on chess problems, using
an early Indian form of the game, is from the 9th century AD [1]. Composition
tournaments are at present held all over the world and attract competitors from diverse
backgrounds [2].
The automatic composition of chess problems – pertaining to Western or
international chess, in particular – is relatively uninvestigated. Especially in contrast
to chess playing which was “once seen as a really hard thing humans could do and
computers couldn’t” [3] but is now losing emphasis in the artificial intelligence (AI)
community in favor of ‘more complex’ games like go and Arimaa [4-6]. Perhaps a
The final publication is available at link.springer.com
http://www.springer.com/computer/hci/book/978-3-642-24499-5
better reason than the emphasis on chess playing for much of AI history, automatic
chess problem composition may have suffered because ‘creativity’, the essential
component that is usually mirrored in aesthetics, is not well defined [7].
Chess problems actually provide a convenient domain of investigation for
creativity or aesthetics – more so than say, music [8] or paintings [9] – since there is a
clear and distinctly measureable contrast between problems by human composers and
otherwise-identical move sequences or ‘combinations’ that typically take place in real
games between humans [10, 11]. Advances in this area can be of immediate benefit to
human composers and players in terms of educational and entertainment value since
there is virtually no limit to the potential output of a machine.
Section 2 reviews briefly related and relevant previous work. Section 3 details the
steps involved in the composing approaches tested. Section 4 explains the
experimental setup and results. Section 5 presents a discussion of the results. Section
6 summarizes the main points with some thoughts on future work.
2 Previous Work
Schlosser presented an effective ‘basic’ method of automatically composing chess
problems [12, 13]. It consists essentially of: 1) constructing a complete database of
chess endgames, 2) eliminating positions that do not have a unique and optimal move
sequence, and 3) selecting the ‘true’ chess problems with the help of a human expert.
The method is therefore limited to the number of pieces which endgame databases or
‘tablebases’ support, e.g. presently 6 pieces including kings [14], and also depends on
human expert intervention. This inherently limits the ‘automatically’ generated
compositions in terms of scope and output potential.
Noshita explained how – for Tsume-Shogi (Japanese chess mating problems) – a
board position can be randomly-generated and then ‘transformed’ by removing or
adding pieces through certain operations [15]; a principle equally applicable to
international chess. A game-solving engine can then be used to determine the
solution, if any. The majority of such positions end up having no solution. Some
improvements, e.g. generating compositions with more pieces, can be obtained by
‘reversing’ moves one at a time from a given mate position with the aid of a solving
engine to test if the problem is ‘complete’, i.e. it has a unique solution [16].
Several criteria for determining the artistic value of the compositions can be
automatically tested for but these tend to rely on confirmation by human experts, in
any case [16]. The reason is likely because these criteria and their automatic
evaluation techniques may not have been experimentally-validated. ‘Optimization’ or
the removal of unnecessary pieces can be performed so long as it does not invalidate
the solution. Pieces may also be added at particular points in the process [17]. Within
a restricted scope, a ‘reverse’ method without the need for a time-consuming solving
engine is possible [18], but this typically comes at the cost of more memory.
Chess problems, e.g. two-movers, can also be ‘improved’ a fair amount using a
computer. Domain experts are first consulted in order to formalize the knowledge
required to assess the ‘quality’ of compositions. This results in simple formulas (e.g.
first move pins a white piece = 3 × piece’s value) or specific weights for certain
detectable maneuvers and features (e.g. Grimshaw theme = 45). Pieces can then be
deleted, added or replaced to improve the position [19]. Composing efficiency and
quality here can be improved but mainly via somewhat computationally-intensive
‘search’ enhancements [20, 21].
In summary, the two main issues in this area relate to computational efficiency
(processing power, memory) and quality functions (aesthetics). The first is
reminiscent of the problem the AI community faced with regard to early chess playing
programs, but eventually ‘solved’ thanks in large part to powerful hardware that
became available. Former world chess champion Garry Kasparov’s loss to IBM’s
supercomputer Deep Blue in 1997 being the prime example. That, in retrospect, is not
seen as much of an achievement in AI. It is therefore preferable not to fall into the
same predicament with compositions. The output of automatic composers, relative to
the time they take, should be increased at minimal computational cost; this can be
seen as making them ‘cleverer’.
The second issue is likely due to the lack of experimental validation when it comes
to quality functions and aesthetics models, and an over-reliance on expert opinion
which tends to be inconsistent [11, 22, 23]. There is likely no consistent
‘methodology’ pertaining to how the best human composers compose problems. They
tend to take their time, abide by a number of ‘accepted’ composition conventions, and
leave the rest to personal style, experience and creativity [24]. This may be why it is
difficult for computers to compose original chess problems like they do, and to do so
on demand or within a stipulated time frame. In any case, aesthetics or quality in
chess can, in fact, now be assessed computationally to a reasonable degree within the
scope of three-move mate problems using an experimentally-validated model [10, 11,
25]. This minimizes or removes altogether the need for human expert intervention for
chess problems of that type, and makes the process of aesthetic assessment more
consistent, reliable and affordable; especially for research purposes. That model will
therefore be used in lieu of chess experts, perhaps for the first time, to assess the
quality of our automatically generated compositions. More details about it are in
section 4. The ability to generate more efficiently compositions that ‘work’ is good in
itself but that they are, on average, of higher quality is even better.
3 The Composing Methodology
This research was limited to orthodox mate-in-3 problems (#3) in standard
international chess. The ‘composing’ feature was incorporated into a computer
program. Two automatic composing approaches were compared, i.e. ‘experience’ and
‘random’. The main difference between them is that the first uses an ‘experience
table’, explained below, after step 4. The process as follows applies to both.
1. Place the two kings on random squares on the board. Accept them so far as
the resulting position is legal; otherwise, repeat the process.
2. Alternating between White (first) and then Black, determine whether the
next selection will be an actual piece or a ‘blank’, i.e. nothing. The
probability of choosing a blank for White was set to 16.67% (1 in 6 chance,
given the other five piece types) whereas for Black, it was set to 33.34%
(twice as likely) to give White a better chance of checkmating ; compositions
are generally seen from the standpoint of White winning.
3. If a ‘blank’, return to step 2 with the side in question having lost its ‘turn’.
4. If an actual piece is to be selected, choose one of the five remaining piece
types at random (equal odds) and place it on a random square that is
unoccupied. Keep trying until one is found.
This is where the two approaches diverge. In the random approach, no position
transformation occurs and we skip to just after step 7. In the experience approach, the
experience table is used for that purpose. The table is created (beforehand) based on
the rapid, automatic analysis of a chess problem database. Three databases (see
section 4 for details) were used in experimentation to derive three different experience
tables. Fig. 1 shows, in two columns, how the probability information may be stored
in a text file.
Sq: 36
0: 65.33
1: 4.8
2: 4.33
3: 1.78
4: 1.72
5: 0.66
6: 0.52…
Fig. 1. Contents of an ‘experience table’.
The first line indicates the square (0-63) – upper left to lower right of the board –
followed by the piece types (0-12) and their associated probabilities (% occurrence)
as follows: blank, (white) pawn, knight, bishop, rook, queen, king, (black) pawn,
knight etc. For instance, in this example it was determined that, in the initial positions,
a white bishop occupied one of the central squares (e4, in the algebraic chess
notation) only 1.78% of the time.
5. Based on the probability information, examine the squares immediately
around the one chosen in step 4 for potentially better placement.
6. If there is a king on one of those squares, skip it. If a square is blank but has
a higher associated probability value for the random piece selected in step 4,
shift the random piece there.
7. If there is a piece in a surrounding square but that square has a higher
associated probability value for the random piece than the one currently on
it, replace it with the random one. In order to increase the likelihood of
White being able to force mate, black pieces cannot replace white ones.
At this point, the two approaches converge. The ‘final’ generated position was set to
have at least two black pieces to avoid ‘lone king’ mates, a minimum total of four
pieces and a maximum total of sixteen pieces.
8. If a minimum piece requirement is not satisfied, return to step 2.
9. If the maximum piece limit is exceeded, discard the position thus far and
return to step 1.
The following are some possible ‘violations’ in the composing process.
a. Exceeding the original piece set, e.g. having three rooks of the same color.
b. Having two bishops in an army occupying squares of the same color.
c. Having a pawn occupying the eighth rank.
The first two are not actually illegal but they are somewhat unconventional in
compositions. In such cases, the ‘offending’ piece is removed and the process returns
to step 4; this therefore does not count as a further transformation of the position but
simply a ‘mistake’ to be corrected. The possibility of castling was given a ‘neutral’
50% random probability of being legal, assuming a king and one of its rooks happen
to be on the right squares. Determination of legality based on retrograde analysis was
considered unnecessary for the purposes of this research [26, 27]. En passant captures,
if plausible, default to illegal. ‘Officially’, in compositions, castling in the key move
is legal unless it can be proved otherwise whereas en passant is legal only if it can be
proved the last move by the opponent permitted it [28].
10. If an illegal position results, remove the random piece from its square and
return to step 2.
11. A mate-solver is used to determine if the tentatively acceptable position
generated has a forced mate-in-3 solution to it. If not, do not remove the
random piece, and return to step 2.
12. If there is such a solution, the position is optimized as shown in the code
below. This makes the composition more economical in form [29].
FOR every square
IF not occupied by a king and not empty THEN
Remove piece
IF forced mate-in-3 can still be found THEN
Proceed
ELSE
Return piece to its original location
END IF
END IF
NEXT
To be thorough, optimization is performed three times, starting from the upper left to
the lower right of the board; white pieces first, then black, and then white again.
Fewer passes proved to be insufficient in certain positions. Optimization generally
increases the aesthetic quality of a composition by removing unnecessary or passive
pieces and should apply equally to both the random and experience approaches to
make the comparisons more meaningful.
13. If the position can be optimized, test it as in step 8. Satisfying that, consider
the composing attempt successful.
The number of transformations or iterations per composing attempt was limited to 21,
after which a new composing attempt begins regardless (step 1). Scant positions
would result given too few iterations, and the opposite given too many. There was no
implementation of particular composition conventions, e.g. no captures in the key
move, no ‘duals’ (see section 5 for more on this). The process as described in this
section may seem more complicated than necessary. For instance, why not just draw
the pieces from a fixed set and place them on the squares based on their associated
probabilities in the experience table? The reason is that doing so results in less
creative variation and very similar-looking, if not identical, generated compositions.
4 The Experimental Setup
For every comparison made, automatic composition was attempted 100 times for 40
‘cycles’. The composing efficiency (i.e. successes/attempts) for each cycle was
calculated, and the mean used as a basis of comparison. For comparisons within the
experience approach, i.e. between different experience tables, the databases included:
29,453 (mostly published) problems by human composers1 (HC), 1,500 computer-
generated compositions that used the experience table derived from the HC (CG), and
3,688 forced mate-in-3 combinations taken from tournament games between at least
club-level human players, i.e. rated at least 1600 Elo points (TG). From this point,
mention of any of these databases in the context of composing efficiency will refer to
the experience table that was derived from it. For statistical purposes, usage of the
two sample t-test assuming equal (TTEV) or unequal (TTUV) variances – to establish
if a difference in means was significant – was determined by first running a two
sample F-test for variances on the samples (which were assumed to have a normal
distribution). T-tests were all two-tailed, and at a significance level of 5%. Table 1
shows the results. The standard deviation is given in brackets.
Table 1. Mean composing efficiency.
Random Experience
HC CG TG
23.70%
(3.69)
28.03%
(4.45)
28.38%
(4.49)
27.25%
(3.94)
The differences in mean efficiency were not statistically significant between any of
the experience approaches. However, they were all different to a statistically
significant degree when compared to the random approach as follows.
HC vs. Random: TTEV; t(78) = 4.735, P<0.01
CG vs. Random: TTEV; t(78) = 5.087, P<0.01
TG vs. Random: TTEV; t(78) = 4.160, P<0.01
Even though the improvements may not look very large in terms of raw percentage,
they actually translate to quite a few more successful compositions than the random
1 Sourced from Meson Chess Problem Database (http://www.bstephen.me.uk/); courtesy of
Brian Stephenson.
approach. For instance, after 10,000 composing attempts, the CG approach would
have 433 more compositions than the random one. This is enough to fill two small
books on chess problems.
Every automatically generated composition was assessed using the chess aesthetics
program, CHESTHETICA that incorporates Iqbal’s mate-in-3 chess aesthetics model
[10, 11, 25]. The model is too complex to be sufficiently explained here but all the
necessary information pertaining to its workings are available in the resources just
cited. We are not attempting to further debate or justify its merits here but simply
consider it validated and are applying it to this research. In principle, the model uses
17 aesthetic features (e.g. pin, skewer, fork, economy, sparsity, material sacrifice)
common to real games and compositions, and can discriminate effectively between
these domains but not within them. To give the reader some idea how the features are
evaluated, one of the evaluation functions is shown in equation 1 where T1 represents
the aesthetic value of the fork theme, if detected, after a piece moves; v() denotes the
standard Shannon value of the piece, d() the Chebyshev distance between two pieces
and r() the ‘power’ of the piece. These concepts are fully explained in [10, 11, 25].
T1 = fc × [(v(fpn) + n + (d(fk, fpn) × r(fk)-1)) - k] . (1)
fc = fork constant, fp = forked piece, fk = forking piece,
k = number of possible ‘check’ moves by fp
The results also correlate well with mean human-player aesthetic ratings and agree
with the typical selections of experts. It is a more consistent, reliable and cost-
effective alternative to the traditional approach of using one or two human experts.
This is something that was not possible before due to a lack of experimentally-
validated aesthetic assessment technology. Given the sheer number of compositions to
be assessed, human experts would not have been a viable option here in any case. A
higher score implies that the combination is more likely to be considered beautiful by
the majority of human chess players of reasonable competence in the game. The
model is used to evaluate beauty in the game, and therefore does not explicitly
account for some of the composition conventions – that may have little to do with
beauty or creativity per se – typically adhered to by composers. Table 2 shows the
mean aesthetic scores. The standard deviation is given in brackets.
Table 2. Mean composition aesthetic scores.
Random Experience
HC CG TG
2.104
(0.44)
2.168
(0.46)
2.178
(0.46)
2.088
(0.46)
The differences in means were not statistically significant between the HC and CG
approaches, and TG and random, but were in all other cases as follows.
HC vs. Random: TTEV; t(2067) = 3.259, P<0.01
CG vs. Random: TTEV; t(2081) = 3.743, P<0.01
HC vs. TG: TTEV; t(2209) = 4.121, P<0.01
CG vs. TG: TTEV; t(2223) = 4.619, P<0.01
Even though the difference between say, the CG and random approaches is small, i.e.
0.074 – and therefore probably difficult for humans to perceive – it is nevertheless an
improvement over the random approach, and no worse than it despite the reasonable
increase in efficiency (see Table 1). An aesthetic difference of approximately 0.5 or
more would be more obvious to humans [25]. Mate-in-3 compositions by humans
average approximately 2.1 aesthetically whereas analogous combinations from
tournament games average about 1.7 [25]. The latter, in their ‘original’ form, are not
optimized in any way, e.g. step 12 in section 3. The aesthetic score for a combination
from either of these domains typically ranges from 0.5 to 5.0; in rare cases slightly
lower or higher. Overall, these results suggest that the experience approach, using a
table of piece-placement probability values derived from any of the databases is
reasonably better than the random approach in terms of composing efficiency, and to
a small but significant degree also aesthetics (given the HC and CG).
5 Discussion
The experimental results show that simple piece-placement probability values derived
from a database of compositions – when used in the composing process as explained
in section 3 – improves composing efficiency compared to an approach that does not
benefit from that information. In two of the three experience approaches (HC and
CG), a small improvement in terms of aesthetics was also detectable. The CG
approach was actually included to see if the computer could also ‘learn’ from its own
composing experience but this does not appear to be the case. The computational cost
for these improvements is minimal, especially in contrast to any approach that
involves game-tree searching [30] beyond confirming if a solution exists, i.e. the use
of a solving engine.
Previous work in the area (see section 2) may not have explored this idea to
improve efficiency and aesthetics because sizeable databases of human compositions
are generally difficult to come by. Without the appropriate sort of piece placement
and position transformation process (see section 3), the approach may also have
seemed likely to converge toward a ‘local maximum’, i.e. the high probability of
certain pieces on certain squares and subsequently similar compositions generated. In
any case, until the idea is actually tested as was done here, we cannot be sure what the
results would look like. For instance, without experimentation it would have been
difficult to predict that ‘experience’ gained from a TG database would improve
composing efficiency (though not aesthetics), or that compositions generated by a
computer based on experience derived from human compositions would be just as
effective as a source of experience.
Even though the generated compositions benefited from the probability values
derived from a database of problems by human composers (HC), that database
henceforth becomes unnecessary given the (smaller but equally effective) computer-
generated one it helped produce (CG). The reason for this may be because there is a
lot of personal style, taste and convention in human compositions that do not
necessarily aid the strict process of composing problems that ‘work’ or even relate to
beauty per se [11]. This ‘information’ may be mostly stripped away in the
automatically generated compositions that result. It is important to remember that a
winning composition is not necessarily among the most beautiful. Sometimes, though
not often, the elegance of a simpler composition or an analogous combination that
occurs in an actual game can be considered more beautiful by the majority of
reasonably competent players than a ‘difficult’ composition with hundreds, if not
thousands, of variations that only the most experienced composers can appreciate.
Fig. 2 shows an example of this contrast; one is a 1st prize winning composition by a
human composer (rather complicated) and the other occurred in a game between two
chess engines in a simulated match (simple and elegant).
1. Qf8 exd6+ 2. Qe7 Nd7 3. Qxd6# 1. Bd6 Kc8 2. a8=Q+ Kd7 3. f8=N#
Alfreds A Dombrovskis,
1st Prize, Schakend Nederland
1973
Rybka 3 vs. Fritz 8
2010
Fig. 2. The aesthetics of a human composition vs. chess engine match combination.
This does not mean, however, that the automatic composer can currently compete
with the best human composers. Composition tournaments, and their judges, often
have requirements and conventions that are not necessarily associated with beauty in
the game but typically conflated with it. Such requirements or conventions (e.g. no
key move that restricts the enemy king’s movement) can be added as additional filters,
if so desired, but these will likely significantly lower the number of successfully
generated compositions. Like human composers, the automatic composer needs to be
made ‘aware’ of these rules or it stands to have most of its compositions rejected.
The improvements obtained mainly in efficiency and somewhat in aesthetics using
an experience table can be used to automatically generate more compositions that
‘work’ (or the same number in less time), and possibly more of reasonable quality.
This can be of value in terms of entertaining players and perhaps even aiding human
composers (both amateurs and experts) by providing ideas they can further develop
for their particular needs. Fig. 3 shows two comparable high-scoring examples of the
automatically generated compositions from the pool of those generated by the HC and
CG experience approaches; both the HC and CG are considered to be equivalent
based on the experimental results shown in section 4. The main line is shown in bold
whereas notable variations are shown in brackets. An experienced FIDE composition
judge and solver, Michael McDowell, provided a detailed analysis of these two
compositions – without being told they were composed by a computer or provided
with the solutions – and was of the opinion that: “In summary, to the experienced
solver B has better content than A, but both score poorly for beauty and neither is of
sufficiently high quality to be published in a reputable chess problem magazine.
(A) White to play and mate in 3 moves (B) White to play and mate in 3 moves
1. Qg7 Ba7+ (d5/Bc7, Rh6#) 2. d4
Bxd4+ (Bb8, d5#; d5/Bb6/Bc5, Rh6#)
3. Nxd4#
1. Ke6 Nf7 (Na6/Nc6, Qxh8#; Kd8,
Qa7, Nf7, Rxb8#; Kf8, Rxb8#) 2.
Qh8+ Nxh8 3. Rxb8#
Aesthetic score: 3.95 Aesthetic score: 4.03
Fig. 3. Examples of the computer generated compositions using the experience approach.
The experience approach – suitably adapted – is also, in principle, applicable to other
variants of the game like fairy chess and even Shogi. The only caveat is perhaps the
requirement of a sizeable collection of human compositions of that type to gain
‘experience’ from; we would assume at least 1,000 combinations. The approach can
be combined with other methods as described in section 2, possibly with improved
results. Automatically composing longer problems (e.g. four or five-movers) –
relatively rare in international chess – would likely be constrained by the strength and
speed of the solving engine, and would require a suitably adapted aesthetics model.
6 Conclusion
Composing high quality chess problems requires considerable experience, knowledge,
effort and time by human composers. Doing so computationally is therefore a
challenge. Nevertheless, it is certainly possible to strictly compose problems – in
principle, for any complex board game like chess – using a particular combination of
techniques and technologies. Even so, many of them are computationally-intensive
and therefore limit performance.
In this article, we have shown through experimentation that a simple ‘experience
table’ can – at a very low computational cost – improve the automatic composition of
chess problems in terms of efficiency and in some cases to a small degree, aesthetics
as well. In order to do so, one first needs a sizeable database of compositions by
humans in order to derive the piece-placement probability values; but beyond that, the
compositions generated by the computer are sufficient as a source of ‘experience’. A
proper piece placement and position transformation strategy is also necessary to avoid
convergence upon very similar-looking compositions. This idea, to the best of our
knowledge, has never been tested before in the automatic composition of chess
problems, but has now been shown to be a viable option. The output and
entertainment potential of this technology can be considered reasonably significant.
Future work in this area would include, 1) looking at the effects of combining the
various approaches of composing as described in section 2 and in this research to find
the ‘perfect mix’ that provides the best compromise between efficiency and quality, 2)
finding a way to apply the aesthetics model used at the ‘knowledge level’ so the
automatic composer places pieces on the board with aesthetics in mind instead of just
focusing on compositions that ‘work’, and 3) factoring in various composition
conventions, in such a way that does not significantly compromise composing
efficiency or beauty, in order to be able to compete with the best human composers.
Ultimately, the idea of a continuous feedback loop of ‘experience’ should be explored
to see if a computer can learn and grow from its own composing experience.
References
1. Sezgin, F.: (ed.) Book on Chess (Kitab al-shatranj): Selected Texts from al-‘Adli, Abu Bakr
al-Suli and Others. Institute for the History of Arabic-Islamic Science, Johann Wolfgang
Goethe University, Frankfurt am Main (1986)
2. Giddins, S.: Problems, Problems, Problems. ChessBase News, 16 April,
http://www.chessbase.com/newsdetail.asp? newsid=6261 (2010)
3. Horvitz, E., Getoor, L., Guestrin, C., Hendler, J., Konstan, J., Subramanian, D., Wellman,
M., Kautz, H.: AI Theory and Practice: A Discussion on Hard Challenges and
Opportunities Ahead. AI Magazine 31(3), 103--144. (2010)
4. Hsu, F-H.: Cracking Go. IEEE Spectrum 44(10), 50--55 (2007)
5. Ekbia, H.R.: Artificial Dreams: The Quest for Nonbiological Intelligence. Cambridge
University Press, Cambridge, UK (2008)
6. Hartmann, D.: Human Superiority Restored. ICGA Journal 33(3), 150 (2010)
7. Boden, M.A.: Computer Models of Creativity. AI Magazine 30(3), 23--34 (2009)
8. Manaris, B., Roos, P., Penousal, M., Krehbiel, D., Pellicoro, L., Romero, J.: A Corpus-
Based Hybrid Approach to Music Analysis and Composition. In: The 22nd Conference on
Artificial Intelligence (AAAI-07), pp. 839--845. AAAI Press, Vancouver, BC (2007)
9. Rigau, J., Feixas, M., Sbert, M.: Conceptualizing Birkhoff's Aesthetic Measure Using
Shannon Entropy and Kolmogorov Complexity. In: The Eurographics Workshop on
Computational Aesthetics in Graphics, Visualization and Imaging, pp. 105--112,
Eurographics Assoc., Banff, AB, Canada (2007)
10. Iqbal, M.A.M.: A Discrete Computational Aesthetics Model for a Zero-sum Perfect
Information Game. Ph.D. thesis. Faculty of Computer Science and Information
Technology, University of Malaya, Kuala Lumpur, Malaysia, http://metalab.uniten.edu.my/
~azlan/Research/pdfs/phd_thesis_azlan.pdf (2008)
11. Iqbal, A.: Aesthetics in Mate-in-3 Combinations, Part I: Combinatorics and Weights. ICGA
Journal 33(3), 140--148 (2010)
12. Schlosser, M.: Computers and Chess Problem Composition, ICCA Journal, 11(4), pp. 151--
155 (1988)
13. Schlosser, M.: Can a Computer Compose Chess Problems? In: Beal, D. F. (ed.) Advances
in Computer Chess 6, pp 117--131. Ellis Horwood Ltd., Chichester, UK (1991)
14. Haworth, G.M.: Chess Endgame Knowledge Advances. ICGA Journal 33(3), 149 (2010)
15. Noshita, K.N.: A Note on Algorithmic Generation of Tsume-Shogi Problems. In: The
Game Programming Workshop '96, pp. 27--33. Kanagawa, Japan (1996)
16. Hirose, M., Matsubara, H., Itoh, T.: The Composition of Tsume-Shogi Problems. In:
Advances in Computer Chess 8, pp. 299--318. Universiteit Maastricht, the Netherlands
(1996)
17. Watanabe, H., Iida, H., Uiterwijk, J.W.H.M.: Automatic Composition of Shogi Mating
Problems. In: Games in AI Research, pp. 109--123. Universiteit Maastricht, the
Netherlands (2000)
18. Horiyama, T., Ito, H., Iwama, K., Kawahara, J.: Enumeration of Tsume-Shogi Diagrams by
the Reverse Method. In: The International Conference on Informatics Education and
Research for Knowledge-Circulating Society, pp. 193--196. Kyoto, Japan (2008)
19. HaCohen-Kerner, Y., Cohen, N., Shasha, E.: An Improver of Chess Problems. Cybernetics
and Systems 30(5), 441--465 (1999)
20. Fainshtein, F., HaCohen-Kerner, Y.: A Chess Composer of Two-Move Mate Problems.
ICGA Journal 29(1), 32--39 (2006)
21. Fainshtein, F., HaCohen-Kerner, Y.: A Deep Improver of Two-move Chess Mate
Problems. Cybernetics and Systems, 37(5), 443--462 (2006)
22. Bilalić, M., McLeod, P., Gobet, F.: Inflexibility of Experts – Reality or Myth? Quantifying
the Einstellung Effect in Chess Masters. Cognitive Psychology 56(2), 73--102 (2008)
23. Walls, B.P.: Beautiful Mates: Applying Principles of Beauty to Computer Chess Heuristics.
M.Sc. dissertation. University of Sussex, UK (1997)
24. Albrecht, H. How Should the Role of a (Chess) Tourney Judge Be Interpreted? The
Problemist, 7, 21--218 (2000)
25. Iqbal, A.: Aesthetics in Mate-in-3 Combinations, Part II: Normality. ICGA Journal 33(4),
202--211 (2010)
26. Thomson, K.: Retrograde Analysis of Certain Endgames. ICCA Journal 9(3), 131--139
(1986)
27. Smullyan, R.: Chess Mysteries of Sherlock Holmes: Fifty Tantalizing Problems of Chess
Detection. Random House Puzzles, New York (1994)
28. Lipton, M., Matthews, R.C.O., Rice, J.: Chess Problems: Introduction to an Art. Citadel
Press, New York (1965)
29. Iqbal, A.: Evaluation of Economy in a Zero-sum Perfect Information Game. The Computer
Journal 51(4), 408--418 (2008)
30. Sadikov, A., Bratko, I.: Search versus Knowledge Revisited Again. LNCS vol. 4630 pp.
172--180. Springer, Heidelberg (2007)
Appendix
This research, representing a part of two larger projects, is sponsored by the Ministry
of Science, Technology and Innovation (MOSTI) in Malaysia under their
eScienceFund research grant (01-02-03-SF0188), and the Ministry of Higher
Education (MOHE) in Malaysia under their Fundamental Research Grant Scheme
(FRGS/1/10/TK/UNITEN/02/2).
... Such systems may also take the approach of combining information or knowledge from within the same domain using mathematical logic, statistical modeling or some form of machine learning, which is also used in mainstream AI (Cope, 2005; Eigenfeldt and Pasquier, 2013). A tempting idea is for a computationally creative system to also learn from its own 'experience', much like humans are thought to do (Iqbal, 2011; Grace et al., 2013). However, the methods these systems use tend to be domain or task-specific as well. ...
... The newer composing module is independent of the program's aesthetics evaluation components mentioned earlier. The program's earlier composing module included a 'random' and 'experience table' approach not particularly relevant to this research (Iqbal, 2011). Details about how the existing composing algorithm was modified to accommodate the DSNS approach is provided in Appendix A. Only the third one was applied for all experiments to keep the composing rate reasonably high and consistent for experimental purposes. ...
... Essentially, this approach does not use any 'technology' in composing chess problems and places the pieces on the board purely at random. Details are available in (Iqbal, 2011). CHESTHETICA was allowed to automatically compose using this DSNS approach (and the random one) for a total of 24 hours, i.e. 12 hours on one machine and another 12 hours on another. ...
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We introduce a new artificial intelligence (AI) approach called, the 'Digital Synaptic Neural Substrate' (DSNS). It uses selected attributes from objects in various domains (e.g. chess problems, classical music, renowned artworks) and recombines them in such a way as to generate new attributes that can then, in principle, be used to create novel objects of creative value to humans relating to any one of the source domains. This allows some of the burden of creative content generation to be passed from humans to machines. The approach was tested in the domain of chess problem composition. We used it to automatically compose numerous sets of chess problems based on attributes extracted and recombined from chess problems and tournament games by humans, renowned paintings, computer-evolved abstract art, photographs of people, and classical music tracks. The quality of these generated chess problems was then assessed automatically using an existing and experimentally-validated computational chess aesthetics model. They were also assessed by human experts in the domain. The results suggest that attributes collected and recombined from chess and other domains using the DSNS approach can indeed be used to automatically generate chess problems of reasonably high aesthetic quality. In particular, a low quality chess source (i.e. tournament game sequences between weak players) used in combination with actual photographs of people was able to produce three-move chess problems of comparable quality or better to those generated using a high quality chess source (i.e. published compositions by human experts), and more efficiently as well. Why information from a foreign domain can be integrated and functional in this way remains an open question for now. The DSNS approach is, in principle, scalable and applicable to any domain in which objects have attributes that can be represented using real numbers.
... Such systems may also take the approach of combining information or knowledge from within the same domain using mathematical logic, statistical modeling or some form of machine learning, which is also used in mainstream AI (Cope, 2005; Eigenfeldt and Pasquier, 2013). A tempting idea is for a computationally creative system to also learn from its own 'experience', much like humans are thought to do (Iqbal, 2011; Grace et al., 2013). However, the methods these systems use tend to be domain or task-specific as well. ...
... The newer composing module is independent of the program's aesthetics evaluation components mentioned earlier. The program's earlier composing module included a 'random' and 'experience table' approach not particularly relevant to this research (Iqbal, 2011). Details about how the existing composing algorithm was modified to accommodate the DSNS approach is provided in Appendix A. Only the third one was applied for all experiments to keep the composing rate reasonably high and consistent for experimental purposes. ...
... Essentially, this approach does not use any 'technology' in composing chess problems and places the pieces on the board purely at random. Details are available in (Iqbal, 2011). CHESTHETICA was allowed to automatically compose using this DSNS approach (and the random one) for a total of 24 hours, i.e. 12 hours on one machine and another 12 hours on another. ...
Preprint
Full-text available
We introduce a new artificial intelligence (AI) approach or technique termed, the 'Digital Synaptic Neural Substrate' (DSNS). This technique uses selected attributes from objects in various domains (e.g. chess problems, classical music, renowned artworks) and recombines them in such a way as to generate new attributes that can then, in principle, be used to create novel objects of creative value to humans relating to any one of the source domains. This allows some of the burden of creative content generation to be passed from humans to machines. The approach was tested primarily in the domain of chess problem composition. We used the DSNS technique to automatically compose numerous sets of chess problems based on attributes extracted and recombined from chess problems and tournament games by humans, renowned paintings, computer-evolved abstract art, photographs of people, and classical music tracks. The quality of these generated chess problems was then assessed automatically using an existing and experimentally-validated computational chess aesthetics model. They were also assessed by human experts in the domain. The results suggest that attributes collected and recombined from chess and other domains using the DSNS approach can indeed be used to automatically generate chess problems of reasonably high aesthetic quality. In particular, a low quality chess source (i.e. tournament game sequences between weak players) used in combination with actual photographs of people was able to produce three-move chess problems of comparable quality or better to those generated using a high quality chess source (i.e. published compositions by human experts), and more efficiently as well. Why information from a foreign domain can be integrated and functional in this way remains an open question for now. The DSNS approach is, in principle, scalable and applicable to any domain in which objects have attributes that can be represented using real numbers. http://arxiv.org/abs/1507.07058
... This provides a reasonable basis of comparison for the role of conventions when it comes to beauty in the game. CHESTHETICA, a computer program which incorporates the model, was used to compose, as required, three-move mate problems [10] and also evaluate the aesthetics of such sequences. Computer-generated compositions tend to feature just one forced line and fewer, more easily identifiable conventions. ...
... The latter approach relies on a database of human compositions to determine piece-placement probability. Further details are available in [10]. These computer-generated compositions were constrained into adhering (randomly) to two, three or four conventions from a list of five namely, no 'cooked' problems, no dual in the solution, no 'check' in the key move, no captures in the key move and no key move that restricts the enemy king's movement. ...
... Another direction worth pursuing would be the development of a formalized, objective method of classifying and ranking conventions with regard to their roles in compositions. The knowledge and possibly technology gained from all this would likely improve the quality of automatic chess problem composition [10] and add significantly to the wealth of artworks available to us [13]. ...
Conference Paper
Full-text available
In improving the quality of their chess problems or compositions for tournaments and possibly publication in magazines, composers usually rely on ‘good practice’ rules which are known as ‘conventions’. These might include, contain no unnecessary moves to illustrate a theme and avoid castling moves because it cannot be proved legal. Often, conventions are thought to increase the perceived beauty or aesthetics of a problem. We used a computer program that incorporated a previously validated computational aesthetics model to analyze three sets of compositions and one set of comparable three-move sequences taken from actual games. Each of these varied in terms of their typical adherence to conventions. We found evidence that adherence to conventions, in principle, contributes to aesthetics in chess problems – as perceived by the majority of players and composers with sufficient domain knowledge – but only to a limited degree. Furthermore, it is likely that not all conventions contribute equally to beauty and some might even have an inverse effect. These findings suggest two main things. First, composers need not concern themselves too much with conventions if their intention is simply to make their compositions appear more beautiful to most solvers and observers. Second, should they decide to adhere to conventions, they should be highly selective of the ones that appeal to their target audience, i.e. those with esoteric knowledge of the domain or ‘outsiders’ who likely understand beauty in chess as something quite different.
... All the necessary information regarding its logic, workings and validation can be obtained by the interested reader in [4]. A computer program called CHESTHETICA, which incorporates the model, was used to automatically compose three-move mate problems [5] and evaluate their aesthetics. This was necessary in the first experiment (see section 3.1) – in which we tested the idea that adherence to more conventions leads to increased beauty – because human compositions tend to contain more variations (alternative lines of play) and variety of conventions than was feasible to calculate manually for each composition. ...
... In short, pieces are placed at random on the board or based on the probability where they are most likely to be in a chess problem. They are then tested using a chess engine to see if a forced mate exists; see [5] for a more detailed explanation. The 'experience' approach tends to be slightly more effective at composing than the random one and the two are tested here also as an extension of previous work (ibid). ...
... Despite the slightly higher mean composing efficiencies using the 'experience' approach, they were not different to a statistically significant degree from the mean composing efficiencies of the random approach. As anticipated in [5], using conventions as a filter significantly reduces the productivity of the automatic composer.Table 2 shows the results in terms of aesthetics. The increase of 0.067 in aesthetic value in using 3 conventions instead of 2 was minor but statistically significant; two sample t-test assuming unequal variances: t(1425) = -2.72, ...
Conference Paper
Full-text available
Composition conventions are guidelines used by human composers in composing chess problems. They are particularly significant in composition tournaments. Examples include, not having any 'check' in the first move of the solution and not 'dressing up' the board with unnecessary pieces. Conventions are often associated or even directly conflated with the overall aesthetics or beauty of a composition. Using an existing experimentally-validated computational aesthetics model for three-move mate problems, we analyzed sets of computer-generated compositions adhering to at least 2, 3 and 4 comparable conventions to test if simply conforming to more conventions had a positive effect on their aesthetics, as is generally believed by human composers. We found slight but statistically significant evidence that it does, but only to a point. We also analyzed human judge scores of 145 three-move mate problems composed by humans to see if they had any positive correlation with the computational aesthetic scores of those problems. We found that they did not. These seemingly conflicting findings suggest two main things. First, the right amount of adherence to composition conventions in a composition has a positive effect on its perceived aesthetics. Second, human judges either do not look at the same conventions related to aesthetics in the model used or emphasize others that have less to do with beauty as perceived by the majority of players, even though they may mistakenly consider their judgements 'beautiful' in the traditional, non-esoteric sense. Human judges may also be relying significantly on personal tastes as we found no correlation between their individual scores either.
... Prior to ANN calculation, input and output data were normalized by applying min-max normalization [23]. The input data are loaded to the ANN inputs in the ANN calculation [24,25]. The training process was repeated 100,000 times, investigating different ANN topologies, with a different number of neurons in hidden and output layers (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), different activation functions, and initial different weight coefficients and biases values. ...
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Thesis
Full-text available
One of the best examples of a zero-sum perfect information game is chess. Aesthetics is an important part of it that is greatly appreciated by players. Computers are currently able to play chess at the grandmaster level thanks to efficient search techniques and sheer processing power. However, they are not able to tell a beautiful combination from a bland one. This has left a research gap that, if addressed, would be of benefit to humans, especially chess players. The problem is therefore the inability of computers to recognize aesthetics in the game. Existing models or computational approaches towards aesthetics in chess tend to conflate beauty with composition convention without taking into account the significance of the former in real games. These approaches also typically use fixed values for aesthetic criteria that are rather inadequate given the variety of possibilities on the board. The goal was therefore to develop a computational model for recognizing aesthetics in the game in a way that correlates positively with human assessment. This research began by identifying aesthetics as an independent component applicable to both domains (i.e. compositions and real games). A common ground of aesthetic principles was identified based on the relevant chess literature. The available knowledge on those principles was then formalized as a collection of evaluation functions for computational purposes based on established chess metrics. Several experiments comparing compositions and real games showed that the proposed model was able to identify differences of statistical significance between domains but not within them. Overall, compositions also scored higher than real games. Based on the scope of analysis (i.e. mate-in-3 combinations), any such differences are therefore most likely aesthetic in nature and suggest that the model can recognize beauty in the game. Further experimentation showed a positive correlation between the computational evaluations and those of human chess players. This suggests that the proposed model not only enables computers to recognize aesthetics in the game but also in a way that generally concurs with human assessment.
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This book is a critique of Artificial Intelligence (AI) from the perspective of cognitive science - it seeks to examine what we have learned about human cognition from AI successes and failures. The book's goal is to separate those "AI dreams" that either have been or could be realized from those that are constructed through discourse and are unrealizable. AI research has advanced many areas that are intellectually compelling and holds great promise for advances in science, engineering, and practical systems. After the 1980s, however, the field has often struggled to deliver widely on these promises. This book breaks new ground by analyzing how some of the driving dreams of people practicing AI research become valued contributions, while others devolve into unrealized and unrealizable projects.
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