A novel algorithm on beam pattern synthesis for linear aperiodic arrays with arbitrary geometrical configuration is presented in this paper. Linear aperiodic arrays are attractive for their advantages on higher spatial resolution and lower sidelobe. However, the advantages are attained at the cost of solving a complex non-linear optimization problem. In this paper, we explain the Improved Genetic Algorithm (IGA) that simultaneously adjusts the weight coefficients and inter-sensor spacings of a linear aperiodic array in more details and extend the investigations to include the effects of mutual coupling and the sensitivity of the Peak Sidelobe Level (PSL) to steering angles. Numerical results show that the PSL of the synthesized beam pattern has been successfully lowered with the IGA when compared with other techniques published in the literature. In addition, the computational cost of our algorithm can be as low as 10% of that of a recently reported genetic algorithm based synthesis method. The excellent performance of IGA makes it a promising optimization algorithm where expensive cost functions are involved.