Optimized Evolutionary Strategies in Conformational Sampling

Novel genetic algorithm (GA)-based strategies, specifically aimed at multimodal optimization problems, have been developed by hybridizing the GA with alternative optimization heuristics, and used for the search of a maximal number of minimum energy conformations (geometries) of complex molecules (conformational sampling). Intramolecular energy, the targeted function, describes a very complex nonlinear response hypersurface in the phase space of structural degrees of freedom. These are the torsional angles controlling the relative rotation of fragments connected by covalent bonds. The energy surface of cyclodextrine, a macrocyclic sugar molecule with N = 65 degrees of freedom served as model system for testing and tuning the herein proposed multimodal optimization strategies. The success of GAs is known to depend on the peculiar hypotheses used to simulate Darwinian evolution. Therefore, the conformational sampling GA (CSGA) was designed such as to allow an extensive control on the evolution process by means of tunable parameters, some being classical GA controls (population size, mutation frequency, etc.), while others control the herein designed population diversity management tools or the frequencies of calls to the alternative heuristics. They form a large set of operational parameters, and a (genetic) meta-optimization procedure was used to search for parameter configurations maximizing the efficiency of the CSGA process. The specific impact of disabling a given hybridizing heuristics was estimated relatively to the default sampling behavior (with all the implemented heuristics on). Optimal sampling performance was obtained with a GA featuring a built-in tabu search mechanism, a “Lamarckian” (gradient-based) optimization tool, and, most notably, a “directed mutations” engine (a torsional angle driving procedure generating chromosomes that radically differ from their parents but have good chances to be “fit”, unlike offspring from spontaneous mutations). “Biasing” heuristics, implementing some more elaborated random draw distribution laws instead of the ‘flat’ default rule for torsional angle value picking, were at best unconvincing or outright harmful. Naive Bayesian analysis was employed in order to estimated the impact of the operational parameters on the CSGA success. The study emphasized the importance of proper tuning of the CSGA. The meta-optimization procedure implicitly ensures the management, in the context of an evolving operational parameterization, of the repeated GA runs that are absolutely mandatory for the reproducibility of the sampling of such vast phase spaces. Therefore, it should not be only seen as a tuning tool, but as the strategy for actual problem solving, essentially advocating a parallel exploration of problem space and parameter space.