Constant time steepest descent local search with lookahead for NK-landscapes and MAX-kSAT

Abstract

A modified form of steepest descent local search is proposed that displays an average complexity of O(1) time per move for NK-Landscape and MAX-kSAT 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 descent can be executed in O(1) time using the Hamming distance 2 neighborhood average as the fitness function. In practice, the modifications needed to prove O(1) complexity can be relaxed with little or no impact on runtime performance. Finally, steepest descent local search over the mean of the Hamming distance 2 neighborhood yields superior results compared to using the standard evaluation function for certain types of NK-Landscape problems.