Improved harmony search algorithm with differential operator for absolute value equation

Absolute value equation is equivalent to a non-differentiable NP-hard problem in its general form. In this paper, an improved harmony search is presented for solving NP-hard absolute value equation with unique solution and multiple solutions. Combining with mutation strategy in differential evolution algorithm, the pitch-adjusted operation in classical harmony search is replaced by difference operator, meanwhile, in order to maintain diversity of population, scaling factor F is generated by chaotic sequence. Numerical results show that the improved harmony search algorithm has strong ability of exploration, and can obtain as many solutions to the absolute value equation as possible.