df-pn + df-pn Evalution Functions for df-pn + in Shogi based on Prediction of Proof and Disproof Numbers after Expansion

Transcription

1 df-pn + df-pn + df-pn df-pn + df-pn + df-pn 30 df-pn + df-pn Evalution Functions for df-pn + in Shogi based on Prediction of Proof and Disproof Numbers after Expansion TOMOYUKI KANEKO, TETSURO TANAKA, KAZUNORI YAMAGUCHI and SATORU KAWAI Evaluation functions for checkmate search in Shogi-game are proposed, that are suitable for df-pn + search. They estimate initial values of proof number and disproof number in a newly expanded state in the search. We trained evaluation functions so that they predict proof numbers and disproof numbers of a given state after expansion by normal df-pn search of specified number of nodes. The parameters in our evaluation functions were statistically determined by means of least mean squares, by using states appeared in real game records. Our experiments showed that df-pn + search combined with the proposed evaluation functions were actually more efficient than df-pn search without any evaluation function, for proving or disproving states appeared in real game records. With the best evaluation function, the number of node expanded was reduced to half on average.. Graduate School of Arts and Sciences, The University of Tokyo {kaneko,kawai}@graco.c.u-tokyo.ac.jp Information Technology Center, The University of Tokyo {ktanaka,yamaguch}@mail.ecc.u-tokyo.ac.jp ) ( )

2 df-pn 5) 3 df-pn df-pn df-pn pn ) 300 5) 4) GHI df-pn 5) GC 4) df-pn df-pn + 6) df-pn and-or df-pn + df-pn 6 6) 3) df-pn + df-pn + df-pn + 2) ACG03 df-pn + 9),) PN* 7),0) df-pn 5) 6) df-pn df-pn ( ) : 5) pn df-pn pn pn 2

3 (df-pn) 0 0 min( ) ( ) ( ) min( ) 4) 3.2 df-pn ) ( ) (,) (h proof h disproof) ) h ( ) cost cost proof, cost disproof cost (cost proof, cost disproof) h df-pn + h cost 6) (h) df-pn (ps ) ps ps ps 0, 20, 40 3 ( ) ( 2 ) : ( a ) df-pn (ps) ( b ) ( 3 ) (e) 24 0, (n) 24 0, , GPS 3) (n2) 24 (n) 4.3 3

4 2 (df-pn + ) 0 0 h proof h disproof min( + cost proof) ( + cost disproof) ( + cost proof) min( + cost disproof) ps ,000 8) df-pn ps df-pn 5) 4) GHI 5) 2 50 (ps) ( ) = (, ps) (ps, ) 3 4 ps ps 2 ps ) 3 frequency frequency histogram of proof numbers proof number ps 0 ps 20 ps histogram of disproof numbers disproof number ps 0 ps 20 ps 40 (ps) ) 4 6 ps r mse 4 templates/templates.html 4

5 6 (h) ps r mse r mse e n n e, n, n h (null ) h (, ) (, ) cost 0 (null ) GPS 3) (piece ) 2 GPS df-pn uniq total cost 8 h cost null null e 0 null n 0 null n2 0 null e 20 null n 20 null n2 20 null e 40 null n 40 null n2 40 null null piece e 0 piece n 0 piece n2 0 piece e 20 piece n 20 piece n2 20 piece e 40 piece n 40 piece n2 40 piece ( ) h cost uniq total uniq total null null e 0 null n 0 null n2 0 null e 20 null n 20 null n2 20 null e 40 null n 40 null n2 40 null null piece e 0 piece n 0 piece n2 0 piece e 20 piece n 20 piece n2 20 piece e 40 piece n 40 piece n2 40 piece n2 h 5

6 7 GPS unique nodes (n2+null) unique nodes (n2+piece) unique nodes (null+null) (n2,ps=20) ( ) unique nodes (null+piece) (n2,ps=20) ( ) ( ) unique nodes (n2+null) unique nodes (n2+piece) unique nodes (null+null) (n2,ps=20) ( ) unique nodes (null+piece) (n2,ps=20) ( ) ( ) cost cost h n2 (ps=20) (clocks/position) e n n null Opteron 2.2GHz (Turbolinux AMD64 8.0) 0 6

7 e+0 e+0 cycles (e+piece) cycles (e+piece) e+0 e+0 7 (e) ( ) 0 (e) ( ) e+0 e+0 cycles (n+piece) cycles (n+piece) e+0 e+0 8 (n) ( ) (n) ( ) e+0 e+0 cycles (n2+piece) cycles (n2+piece) e+0 e+0 9 (n2) ( ) 2 (n2) ( ).3 5 h ps=20 e, n, n2 3 cost cost e, n 7

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