Stochastic and Deterministic Search Algorithms for Global Optimization: Molecular Annealing and Adaptive Langevin Methods

Optimization is important in physical and engineering sciences for the problems such as Lagrangian formalism in mechanics, finding the optimal electron density in quantum chemistry, designing minimum-cost networks in computer science. Searching for global minima by overcoming local minima is a fundamental issue in optimization. This dissertation develops adaptive annealing methods which are physicsbased. Two optimization strategies drive a system from a high-entropic state to a low-energetic state. The molecular annealing narrows the searching scope down by controlling the acceptance ratio from higher to lower values. The adaptive Langevin equation uses the heavy ball’s inertia of mass and adaptive damping effect unlike in the ordinary Langevin equation in which the second-order term in time is absent. To obtain the predefined double stranded (ds) DNA in a large amount from six fragments of single stranded (ss) DNAs, we performed molecular annealing using silicon-based simulation and with wet-lab experiments. This combination process solves the theorem-proving problem based on resolution refutation. Also, the heavy ball with friction (HBF) model with an adaptive damping coefficient is proposed for the ball to search for a global minimum in Rosenbrock and Griewank potentials. This adaptive damping coefficient was obtained from