Properties of a genetic algorithm equipped with a dynamic penalty function

A genetic algorithm aiming for finding the global minimum and multiple deep local minima of a function exhibiting a complex landscape is studied. A feedback dynamic penalty function is used as a means to direct the algorithm to look for new local minima. The penalty is applied in close vicinity of all minima found before the current search stage. The last one, where the population tends to be trapped in, is treated smoothly. The penalty becomes progressively active there causing that the population progressively transfers outside the trapping area. The method ascertains that, unlike in more classical approaches, after finding the global minimum and a number of local ones on the way, the algorithm continues the exploration and identifies new local minima. Performance tests are described for a task of indexing of a powder diffraction pattern. The presented way of constructing the penalty function is to some extent problem specific, but the applied scheme may be adapted to other global search and optimisation problems, in particular to those requiring identification of multiple deep local minima.