The problem of finding a local minimum:of a functionF(x),xßRnis studied. The paper deals with some member of Rastrigin's random search, family and with the method of random search with reversals. A new practical Adaptive Step Size Random Search, with Reversals (ASSRSB) is.proposed arid analyzed* Computational experience is also reported. ASSRSR is compareD with the adaptive step size random search algorithms of Schumer-steiglitz And White-day, and with the Newton-Raphson and Fletcher-Powell, methods.