A hybrid genetic algorithm with local search: I. Discrete variables: optimisation of complementary mobile phases

Abstract A hybrid genetic algorithm was developed for a combinatorial optimisation problem. The assayed hybridation modifies the reproduction pattern of the genetic algorithm through the application of a local search method, which enhances each individual in each generation. The method is applied to the optimisation of the mobile phase composition in liquid chromatography, using two or more mobile phases of complementary behaviour. Each of these phases concerns the optimal separation of certain compounds in the analysed mixture, while the others can remain overlapped. This optimisation approach may be useful in situations where full resolution with a single mobile phase is unfeasible. The optimisation is based on a local search method which alternates two combinatorial search spaces: one of them defined by combinations of solutes and the other by combinations of mobile phases. This gives rise to a protocol, able to interchange and improve data among both search spaces. An experimental design of algorithm settings was performed to find the optimal computation conditions. Lamarckian and Darwinian strategies, binary and real-value encoding and two ways of establishing the problem (a search space of solutes or mobile phases) were checked. Two problems involving the separation of 10 and 15 solutes with two and three mobile phase experimental factors were optimised up to reach base-line separation. The method was compared with a systematic examination of all candidate solutions and a classical genetic algorithm. The hybrid method, called LOGA (locally optimised genetic algorithm), exceeded the performance of both reference methods.