Adaptive algorithms for sequential linear and quadratic programming with interior-point methods and fuzzy heuristics

Interior-point algorithms are a new class of optimization routines which exhibit several theoretical and practical advantages over other methods for linear and quadratic programming. One goal of this work was to investigate the question of whether interior-point methods would prove as efficient when used to solve nonlinear engineering design problems. This was tested by using a primal-dual interior-point solver in sequential linear programming and sequential quadratic programming paradigms. The results show that interior-point methods do perform well for large-scale nonlinear engineering optimization. Interior-point methods take fewer iterations in less time to solve large-scale problems than simplex-based algorithms, and are immune to constraint degeneracy. These two features make interior-point methods well suited to engineering optimization. A second focus of this work was the development of fuzzy heuristics to make the sequential linear and quadratic programming algorithms adaptable. While most optimization algorithms are derived from mathematical theory, certain algorithm parameters are often chosen from some acceptable range of values based on a programmer\u27s judgement. Fuzzy logic was chosen to adaptively modify these values on-the-fly . The resulting adaptive sequential linear programming algorithm not only performed better than the original sequential liner programming algorithm, but also performed as well or better than state-of-the-art sequential quadratic programming algorithms when solving large-scale problems. The simplicity of the sequential linear programming algorithm, coupled with adaptability from the fuzzy rules resulted in a robust, high-performance algorithm