Local Search Efficiency when Optimizing Unimodal Pseudoboolean Functions

This work is a continuation of our previous papers devoted to exploration of the regular search procedures efficiency in binary search spaces. Here we formulate the problem in a rather general form as a problem of optimization of an unimodal pseudoboolean function given implicitly and obtain analitical estimates of the expected time of a minimum point search for procedures of direct local search. These estimates are polinomial for the case of weakly nonmonotone functions and exponential for the general case of arbitrary unimodal functions. We hope that the proposed result will be usefull first of all for practical applications.