Parallel global optimization with deterministic approaches

Abstract

Global optimization is important both in theory and practical applications. The objectives of the research conducted in this thesis are twofold. The first one is to construct methods which aim to reduce the effort needed to solve global optimization problems. The second objective is to investigate suitable parallel models for those methods to speed up the computation, which is especially important for time-consuming problems. Two partitioning approaches are proposed in this research for unconstrained and constrained problems, respectively. For unconstrained optimization, a new global optimization approach, TRIOPT (TRIangulated OPTimization), is proposed. TRIOPT is based on partitioning the feasible region D geometrically by triangulation so that search can be conducted in smaller subregions of interest. This consequently increases the reliability in locating the global optimum and reduces the number of function evaluations required. The partitions (simplices) are assessed by the aggregated entropies calculated from the transformed values of the vertices, which lead to a dynamic degree of parallel search in the feasible region D. A novelty in the search scheme is that once a partition narrows down to a small size, its vertices are eliminated from the available sample set. This change of global information triggers a re-calculation of transformed values and guides the search to new subregions. TRIOPT employs a Master/Slave architecture for parallel processing according to its algorithmic characteristics. The master processor controls the dynamic degree of parallelization, and the slave processors evaluate the samples. In constrained optimization, interval analysis is applied since it can conveniently check the feasibility of a certain search area rather than a single i