In this paper, a novel algorithm on beam pattern synthesis for linear aperiodic arrays with arbitrary geometrical configuration is proposed. The algorithm is based on an improved genetic algorithm (IGA) that simultaneously adjusts the weight coefficients and inter-sensor spacings of a linear aperiodic array. A novel section-based crossover and a self-supervised mutation process are developed to improve the convergence performance. The results from simulation illustrate that with the IGA, the peak sidelobe level (PSL) of the synthesized beam pattern has been successfully lowered. In addition, the computational cost of the proposed algorithm can be as low as being about 10% of that of a recently reported genetic algorithm based synthesis method. The robustness of the proposed IGA has been illustrated clearly from the statistic of multiple independent runs too. The excellent performance of the IGA makes it a promising optimization algorithm where expensive cost functions are involved.