Global Optimization: Software and Applications

Mathematical models are a gateway into both theoretical and experimental understand- ing. However, sometimes these models need certain parameters to be established in order to obtain the optimal behaviour or value. This is done by using an optimization method that obtains certain parameters for optimal behaviour, as described by an objective function that may be a minimum (or maximum) result. Global optimization is a branch of optimization that takes a model and determines the global minimum for a given domain. Global opti- mization can become extremely challenging when the domain yields multiple local minima. Moreover, the complexity of the mathematical model and the consequent lengths of calcu- lations tend to increase the amount of time required for the solver to find the solution. To address these challenges, two software packages were developed to aid a solver in optimizing a black box objective function. The first software package is called Computefarm, a distributed local-resource computing software package that parallelizes the iteration step of a solver by distributing objective function evaluations to idle computers. The second software package is an Optimization Database that is used to monitor the global optimization process by storing information on the objective function evaluation and any extra information on the objective function. The Optimization Database is also used to prevent data from being lost during a failure in the optimization process. In this thesis, both Computefarm and the Optimization Database are used in the context of two particular applications. The first application is quantum error correction gate design. Quantum computers cannot rely on software to correct errors because of the quantum me- chanical properties that allow non-deterministic behaviour in the quantum bit. This means the quantum bits can change states between (0, 1) at any point in time. There are various ways to stabilize the quantum bits; however, errors in the system of quantum bits and the sys- tem to measure the states can occur. Therefore, error correction gates are designed to correct for these different types of errors to ensure a high fidelity in the overall circuit. A simulation of a quantum error correction gate is used to determine the properties of components needed to correct for errors in the circuit of the qubit system. The gate designs for the three-qubit and four-qubit systems are obtained by solving a feasibility problem for the intrinsic fidelity ii(error-correction percentage) to be above the prescribed 99.99% threshold. The Optimization Database is used with the MATLAB ’s Global Search algorithm to obtain the results for the three-qubit and four-qubit systems. The approach used in this thesis yields a faster high- fidelity (≤ 99.99%) three-qubit gate time than obtained previously, and obtained a solution for a fast high-fidelity four-qubit gate time. The second application is Rational Design of Materials, in which global optimization is used to find stable crystal structures of chemical compositions. To predict crystal structures, the enthalpy that determines the stability of the structure is minimized. The Optimization Database is used to store information on the obtained structure that is later used for identification of the crystal structure and Compute- farm is used to speed up the global optimization process. Ten crystal structures for carbon and five crystal structures for silicon-dioxide are obtained by using Global Convergence Par- ticle Swarm Optimization. The stable structures, graphite (carbon) and cristobalite (silicon dioxide), are obtained by using Global Convergence Particle Swarm Optimization. Achieving these results allows for further research on the stable and meta-stable crystal structures to understand various properties like hardness and thermal conductivity

Proceedings, MSVSCC 2018

Proceedings of the 12th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 19, 2018 at VMASC in Suffolk, Virginia. 155 pp