In antenna design, it is important to optimize the amplitude weights of a linear antenna array to achieve low peak sidelobe level (PSLL). This paper deals with a linear inequality constraint on array factor to get maximum response in look direction and reduced sidelobe levels in a specified stop band region. Linear regular array as well as thinned linear array is optimized using a constrained genetic algorithm (CGA). The convergence of the optimization algorithm is also reported and its utility is shown in getting a desired antenna beam pattern with fewer radiating elements. Thinning is achieved by iteratively applying CGA which results in reducing the number of elements by 28% and overall transmitted energy by 27%, keeping a specified beam width first null (BWFN) with considerable reduction in PSLL.