Continuous optimization is never easy: the exact solution is always a luxury demand and the theory of it is not always analytical and elegant. Continuous optimization, in practice, is... Show moreContinuous optimization is never easy: the exact solution is always a luxury demand and the theory of it is not always analytical and elegant. Continuous optimization, in practice, is essentially about the efficiency: how to obtain the solution with same quality using as minimal resources (e.g., CPU time or memory usage) as possible? In this thesis, the number of function evaluations is considered as the most important resource to save. To achieve this goal, various efforts have been implemented and applied successfully. One research stream focuses on the so-called stochastic variation (mutation) operator, which conducts an (local) exploration of the search space. The efficiency of those operator has been investigated closely, which shows a good stochastic variation should be able to generate a good coverage of the local neighbourhood around the current search solution. This thesis contributes on this issue by formulating a novel stochastic variation that yields good space coverage. Show less
In this thesis the Langevin equation with a space-dependent alternative mobility matrix has been considered. Simulations of a complex molecular system with many different length and time scales... Show moreIn this thesis the Langevin equation with a space-dependent alternative mobility matrix has been considered. Simulations of a complex molecular system with many different length and time scales based on the fundamental equations of motion take a very long simulation time before capturing the functional and relevant motions. This problem is called critical slowing down. To avoid this problem multi-scale simulation methods are applied, which permits the use of different size time steps and thus enables acceleration of the relevant (slow) movements. The aim of this thesis is to develop a stochastic quasi Newton method, such that by incorporating multi-scaling the relevant motions are effectively taken with larger time step. Due to the integration of the slow motions with a larger time step, critical slowing down can be avoided. The proposed stochastic quasi Newton method enables automatic multi-scaling in the Langevin dynamics and contributes to efficient calculation of the noise term. The construction of the proposed method also enables the construction of a limited memory version for the mobility. This results in a method where less storage is needed. Together with the reduction of the computation time and the multi-scaling property, a powerful method for molecular simulations has been provided. Show less
