Global Optimization using Monte Carlo Tree Search in discrete State Lattices

Global Optimization is a highly researched area with applications in different scientific fields. The goal to find the overall best solution to a problem has been tried to solve with many different approaches. Two of the more popular algorithms are the Genetic Algorithms and the Monte Carlo methods which both have the idea of using random numbers to find global optima. In this thesis, a new Global Optimization algorithm is proposed that is influenced to an extent by the two latter methods, among others. This new method is at its core a modified variant of the Monte Carlo Tree Search, which is usually applied in the gaming domain. The idea of the algorithm is that it operates on a binary subset lattice. All elements of this subset lattice are encoded as binary strings that can be viewed as discrete states in the solution space. This form of states is based on the idea of the state representation in Genetic Algorithms. The name of the algorithm can be justified by means of this short description: (binary) Subset Lattice Monte Carlo Tree Optimization. Furthermore, two enhancements of the base version of the algorithm are presented. Firstly, the UCD algorithm is integrated which provides a mathematical framework in order to make the most use of transpositions. Secondly, the RAVE algorithm is added. This AMAF-technique has the task to spread rewards in more regions of the lattice. After careful research, it can be assumed that the UCD algorithm is used for the first time in combination with RAVE. The performance of the algorithm is first tested on artificial benchmark functions by comparing it with a Genetic Algorithm. Additionally, the performance is investigated on the more complex Lennard-Jones Atomic Clusters problem. The results of these experiments indicate that the Subset Lattice Monte Carlo Tree Optimization is able to find optima in particularly large solution spaces. In case of such solution spaces, it outperformed the Genetic Algorithm. In contrast to that, the newly proposed algorithm has difficulties to converge to global optima at even simple test functions. In these cases, the algorithm only improved its solution up to a certain point. These results lead to suggestions of how this first version of a new optimization algorithm can be enhanced in the future.