Optimization by random search with jumps

We give a random optimization (RO) algorithm to optimize a real-valued function of n real variables. During the optimization process, interpolation points are examined to follow valleys, and jumps to new starting points are executed to avoid numerous iterations in local minima. Convergence with probability one to the global minimum of a function is proved. The proposed RO method is a simple, derivative-free and computationally moderate algorithm, with excellent performance compared to other RO methods. Seven functions, which are commonly used to test the performance of optimization methods, are used to evaluate the performance of the RO algorithm given here.