Effectiveness Analysis of Multiple Initial States Simulated Annealing Algorithm, a Case Study on the Molecular Docking Tool AutoDock Vina.

Simulated Annealing (SA) algorithm is not effective with large optimization problems for its slow convergence. Hence, several parallel Simulated Annealing (pSA) methods have been proposed, where the increase of searching threads can boost the speed of convergence. Although satisfactory solutions can be obtained by these methods, there is no rigorous mathematical analyses on their effectiveness. Thus, this article introduces a probabilistic model, on which a theorem about the effectiveness of multiple initial states parallel SA (MISPSA) has been proven. The theorem also demonstrates that the increasing parallelism in pSA algorithm with the reducing of search depth in each thread could obtain almost the same probability of finding the global optimal solution. We validated our theorem on AutoDock Vina, a widely used molecular docking tool with high accuracy and docking speed. AutoDock Vina uses a pSA strategy to find optimal molecular conformations. Under the premise that the total searching workload (i.e., thread number * iteration depth of each thread) remains unchanged, the docking accuracy from an aggressively parallelized SA searching method is almost the same or even better than those from the default exhaustiveness (parallelism degree) configuration of AutoDock Vina. Taking complex '1hnn' as an example,with the increase (125x) in the number of initial states (from 8 to 1000) and the decrease in the search depth for each thread (from 15540 to 124, or 1/125 of the original search depth), the mean energy is -7.80 and -7.94, while the mean RMSD is 3.4 and 3.14, respectively. The result also implies that a considerable speedup (in this case 125x in theory) can be obtained by a highly parallelized SA algorithm implementation.