Optimization of acoustic array design using the simulated annealing algorithm.

The simulated annealing algorithm [S. Kirkpatrick etal., Science (May 1983)] has been applied recently to a number of underwater acoustics problems. In this paper methods developed in recent years for the optimization of sonar receiver array configurations, including both horizontal and vertical arrays, are reviewed. Optimization of horizontal planar-array configuration to minimize noise gain in a 2-D-isotropic noise field results in highly ordered configurations resembling crystalline or quasicrystalline structures. Vertical-array configuration optimization for conventional beamforming is based on maximization of signal-to-noise ratio at the array output. The optimized vertical-array configurations exhibit far less regularity of spacing, due to the complexity of the acoustic field in the vertical. Nevertheless, the results are readily understood as a trade-off between placement of sensors at depths with high signal-to-noise ratio and separation of sensors to reduce the array noise gain. Optimization for matched-field processing is also considered.