|Budget Amount *help
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 2002 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 2001 : ¥1,100,000 (Direct Cost : ¥1,100,000)
In order to develop an automatic design method of meta-heuristics searching, we have mainly studied minimization of AND-EXOR expressions, which is one of the computationally hard problems. The expressions which we deal with are EXOR-sum-of-products expressions (shortly ESOPs) which are expressions such that arbitrary products terms are combined by EXORs.
We implemented a simple but huge time consuming algorithm, which applies simple transforming rules to ESOPs repeatedly, and collected sequences of applied rules to discover subsequences to reach efficiently the minimum ESOPs. Though our goal is an automatic method to discover efficient subsequences, we found manually some properties of efficient retrieval sequences. Using these properties, we develop a new faster algorithm of minimizing ESOPs :
(1) The proposed algorithm can compute efficiently exact minimum ESOPs for all six-variable functions and for some seven-variable functions. For five-variable functions, there were some efficient algorithms but no efficient algorithms for six-varible functions have been known so far. The key point of our algorithm is a pruning method of searching space, which depends on the lower and upper bounds of parameters of searching.
(2) Some acceleration methods of the above algorithm are developed and experimental results demonstrate the effectiveness of these methods. For the first time, we have obtained the exactly minimum ESOPs for four benchmark functions, con1, misex1, rd53, and sqrt8.
Some results obtained during the process of this research project have been presented at international conferences.