Evolving a digital multiplier with the pushgp genetic programming system,” in GECCO ’13 Companion: Proceeding of the fifteenth annual conference companion on Genetic and evolutionary computation conference companion

A recent article on benchmark problems for genetic program-ming suggested that researchers focus attention on the dig-ital multiplier problem, also known as the “multiple output multiplier”problem, in part because it is scalable and in part because the requirement of multiple outputs presents chal-lenges for some forms of genetic programming [20]. Here we demonstrate the application of stack-based genetic program-ming to the digital multiplier problem using the PushGP genetic programming system, which evolves programs ex-pressed in the stack-based Push programming language. We demonstrate the use of output instructions and argue that they provide a natural mechanism for producing multiple outputs in a stack-based genetic programming context. We also show how two recent developments in PushGP dramat-ically improve the performance of the system on the digital multiplier problem. These developments are the “ULTRA” genetic operator, which produces offspring via“Uniform Lin-ear Transformation with Repair and Alternation ” [12], and “lexicase selection, ” which selects parents according to per-formance on cases considered sequentially in random order [11]. Our results using these techniques show not only their utility, but also the utility of the digital multiplier problem as a benchmark problem for genetic programming research. The results also demonstrate the flexibility of stack-based genetic programming for solving problems with multiple out-puts and for serving as a platform for experimentation with new genetic programming techniques