Constant time Steepest Ascent Local Search with Statistical Lookahead for NK-Landscapes

A modified form of steepest ascent local search is proposed that displays an average complexity of O(1) time per move for NKLandscape problems. The algorithm uses a Walsh decomposition to identify improving moves. In addition, it is possible to compute a Hamming distance 2 statistical lookahead: if x is the current solution and y is a neighbor of x, it is possible to compute the average evaluation of the neighbors of y. The average over the Hamming distance 2 neighborhood can be used as a surrogate evaluation function to replace f . The same modified steepest ascent can be executed in O(1) time using the Hamming distance 2 neighborhood average as the fitness function. A modified form of steepest ascent is used to prove O(1) complexity, but in practice these modifications can be relaxed. Finally, steepest ascent local search over the mean of the Hamming distance 2 neighborhood yield superior results compared to using the standard evaluation function for certain types of NK-Landscape problems.