Antenna arrays are essential components in present 5G wireless communication systems. They are playing a major role in beamforming and interference suppression in desired directions. In present wireless communication scenarios, placing nulls in the interference directions and control of sidelobe power is essential due to an increase in EM pollution. To achieve this, antenna arrays with suitable beamforming algorithms need to be developed to generate the array patterns with low peak sidelobe level (PSLL) and desired nulls in the sidelobe angular region. Many traditional and evolutionary algorithms have been successfully applied to linear array synthesis. But most of the methods are stuck at local optima and lead to local solutions with low accuracy. To overcome this, a new improved Invasive Weed Optimization with Laplace Distribution (MLIWO) method is introduced in this paper for the synthesis of linear antenna arrays. Additionally, this work focuses on aperiodic linear antenna arrays, which provide better control over the radiation pattern without the need for non-uniform amplitude and phase excitations. The primary objective is to enhance the basic IWO algorithm performance by introducing a Laplace-based mutation in the weed position update equation. The proposed algorithm is applied to optimize the element positions of the linear array to suppress the PSLL and place the nulls in the desired directions. The proposed MLIWO method is applied to synthesize the 28 and 32-element linear antenna arrays. The numerically synthesized results are compared with existing state-of-the-art genetic algorithms, particle swarm optimization, ant colony optimization, etc, and array designs reported in the literature. Simulation results indicate that the MLIWO method outperforms other methods in terms of accuracy and convergence speed. Finally, this proposed MLIWO method offers an effective method for designing efficient antenna arrays for defence and communication applications.