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Adequate radiation shielding is vital to the safe operation of modem commercial medical cyclotrons producing large yields of short-lived radioisotopes. The radiological shielding constitutes a significant capital investment for any new cyclotron-based radioisotope production facility; hence, the shielding design requires an accurate cost-benefit analysis often based on a complex multi-variant optimization technique. This paper demonstrates the application of a Genetic Algorithm (GA) for the optimum design of the high yield target cave of a Medical Cyclotron radioisotope production facility based in Sydney, Australia. The GA is a novel optimization technique that mimics the Darwinian Evolution paradigm and is ideally suited to search for global optima in a large multi-dimensional solution space. [ABSTRACT FROM AUTHOR]