This paper presents a novel method for constraint-based synthesis of uniformly excited non-uniformly spaced linear antenna arrays. The design problem of imposing deep nulls under the constraints of a reduced Peak Side Lobe Level (PSLL) and a fixed First Null Beamwidth (FNBW) is modeled as an optimization problem. This paper addresses the optimization problem by employing penalty function method with Ant Lion Optimization (ALO) algorithm for the desired array pattern with prescribed nulls, PSLL and FNBW. The proposed constraint based optimization is realized by penalizing the undesirable solutions in proportion to error w.r.t design goals. The proposed method is illustrated with the help of design examples for placement of single as well as multiple nulls subject to the PSLL and FNBW constraints. It outperforms other state-of-the-art nature inspired algorithms in terms of accurate null positioning with a significant reduction in PSLL while maintaining a fixed FNBW. It renders a high degree of flexibility to the array synthesis process for controlling the shape of the array pattern as desired by the application at hand.