The principal continuation and the killer heuristic

Enhanced iterative-deepening search

“…One of them, the principal variation, is the move sequence actually chosen if the players follow the minimax principle. The other w − 1 paths are called refutation lines [1,13]; they serve to prove the inferiority of their particular root move. Current principal variation and refutation lines are re-expanded first during each new iteration.…”

“…This makes the TSP an ideal vehicle for studying the effectiveness of the proposed IDA* enhancements under various b h . In our experiments, we used city coordinates that have been randomly drawn from the integer intervals [1,25], [1,50], [1,75] and [1,100]. This results in heuristic branching factors (of the simple IDA*) ranging from 1.71, 1.29, 1.20 to 1.13, respectively.…”

“…As is customary, we used the minimum spanning tree [4] of the remaining cities to estimate the completion cost of the partial tour. Table 2 shows the experimental results with city coordinates drawn from the intervals [1,50] and [1,100]. The performance is given relative to IDA* in terms of node expansions and CPU time consumption.…”

“…Instead of plotting the performance relative to the domain of the city coordinates, we took the heuristic branching factor achieved with the simple IDA* as a performance measure. (In other words, the shown b h 's of 1.13, 1.20, 1.29, 1.71 correspond to the city coordinate domains [1,100], [1,75], [1,50] and [1,25]. )…”

“…Among the data that can be reused, move ordering and node scoring information is of special importance. Various memory functions have been invented to store this and other information: refutation or killer tables [1], transposition tables [30,26] and history tables [23]. Taken together, the memory functions not only pay for themselves by yielding better frontier node evaluations, but also produce searches that are faster than a direct depth-d search [13].…”