Mixed discrete fuzzy nonlinear programming for engineering design optimization

Based on the observation that there is only a limited research work on optimization techniques for nonlinear design problems containing mixed-discrete design variables and fuzzy information, and the literature discussing this situation is scarce, a systematic study has been done by the author in this work. Several computational techniques and algorithms have been developed and/or investigated in the fields of mixed-discrete optimization, fuzzy set-based single objective optimization, multiobjective optimization and multistage decision-making.The mixed-discrete optimization technology forms the fundamental aspect in all the work considered. Two methods, combining the advantages of random search and deterministic search algorithms, are first introduced in this thesis. One is called mixed discrete synthetic approach (MDSA), in which the solution procedure can be divided into three steps and in each step different kind of algorithm is applied in accordance with specific requirements and characteristics. The other developed method is the mixed discrete hybrid genetic algorithm (MDHGA), in which the GA is used only to determine the optimal feasible region surrounding the global optimum point and an discrete iterative algorithm can be employed subsequently to find the final optimal solution.A novel approach, called mixed-discrete fuzzy nonlinear programming (MDFNLP), is proposed to provide a promising capability for solving mixed-discrete fuzzy programming problems. In the process, a wrong definition stated by Shih and Lai is corrected and right conclusions have been reached. With appropriate extensions to the combinations of game theory and dynamic programming, this approach can also be used to deal with mixed-discrete fuzzy multiobjective optimization problems (combined with game theory), or fuzzy multistage decision-making problems (combined with dynamic programming). An integrated optimization program base is developed to carry out numerical studies on a large number of real-life problems covering a variety of research fields. The numerical results demonstrate the high reliability and efficiency of the techniques developed in this research.Given the challenges of the problems, the significant contributions and perspectives of future work in mixed discrete fuzzy design optimization are discussed at the end of this research