An acoustic imaging system for forming acoustic beams approximating an optimum acoustic beam for the directional transmission or reception of acoustic energy. Maximum and minimum dependent beamform factors are determined from initial beamform factors and an initial parent population of chromosomes is generated, each chromosome including a gene corresponding to a dependent beamform factor and representing an initial candidate beam and subsequent parent populations are generated by cloning of the surviving populations. A child population is generated by exchanging statistically selected pairs of genes of the parent population and generating a mutated population. A surviving population is selected from the mutated population of the mutated population with a fitness criteria. When a chromosome of the surviving population meets the solution criteria, the genes of the surviving population having the best match to the fitness criteria are selected to forming a beam.