Structure prediction of titania phases: Implementation of Darwinian versus Lamarckian concepts in an Evolutionary Algorithm

Darwinian and Lamarckian schemes within evolutionary algorithms have been implemented and optimised. We compare the performance of these two approaches applied to the problem of structure prediction of the titania polymorphs. A number of well-known phases have thus been reproduced as well as several plausible novel microporous and dense structures. Two different potential parameter sets, within the Born model description of a solid, were employed. Following the Lamarckian concept in a genetic or more generally in an evolutionary algorithm, all new candidate structures are immediately relaxed (analogous to the ageing process in nature); consequently, competition within any current population to procreate only occurs between mature candidate structures, which correspond to local minima on the energy landscape. In the Darwinian scheme, no local optimisation is performed, which should result in significant saving in CPU time per candidate structure considered. We show, however, that the Lamarckian scheme (which ultimately searches for the global minimum on a simplified landscape) is more successful and efficient at generating the target structures. Analysis of why the Lamarckian scheme produced a perfect success rate uncovered a weakness in the Darwinian approach when diversity of the population is allowed to reduce, and further methodological developments are suggested.