Development of algorithms to solve different key challenges facing design optimization


Optimization methods play an indispensable role in today’s competitive environment and there are plenty of practical examples where such methods have been used to identify better performing designs (Boeing 787 Dreamliner and NASA ST5 antenna). Increasing complexity of the problems have also led to the development of sophisti- cated mathematical models that can only be solved using computationally expensive numerical simulations such as finite element methods (FEM), computational fluids dynamics (CFD), computational electromagnetics (CEM), etc. Repeated use of such numerical simulations is necessary in the context of optimization, i.e., to identify optimum products and processes with outstanding performance features. In reality, such problems often involve a large number of constraints and often demand multiple performance considerations. Over the decades, population based metaheuristics have proven to be efficient, robust and versatile methods for numerical optimization as they are more amenable to deal with such black-box problems. The major downside of any of these population based metaheuristics is their extremely long run time. Therefore, it is no surprise that the development of fast and efficient metaheuristics is an actively pursued research area. In this thesis, an effort is made to address three key challenges facing the adoption of population based metaheuristics for practical design optimization. The first challenge relates to the development of an efficient and reliable optimization algorithm capable of dealing with constrained optimization problems. In particular, two novel constraint handling mechanisms are introduced i.e., one with the concept of partial evaluation using constraint sequencing and the other involving adaptive constraint handling. The study is motivated by the fundamental question should one evaluate all constraints of a solution even if it has violated one constraint? and what is the difference in the underlying search process if multiple constraint sequences are used?. The second contribution reported in this thesis relates to the development of an algorithm to tackle optimization problems involving more than four objectives, i.e., many objective optimizations. In this context, an algorithm based on decomposition is introduced which extends the capability of the well-known MOEA/D to deal with many objective optimization problems. The algorithm incorporates a systematic sampling scheme and the balance between convergence and diversity during the course of search is maintained via a simple preemptive distance comparison scheme. The third contribution made in this thesis is in the area of robust design optimization where the effects of various formulations are studied in the framework of six-sigma quality. Four different problem formulations of robust design and methods to solve them have been proposed. The performance of these algorithms/schemes is rigorously assessed using well es- tablished benchmark functions and a suite of engineering design optimization problems. The results assessed using various measures clearly indicate that the proposed develop- ments offer competitive advantages over existing schemes. Finally, a summary of the findings of the work is presented. In addition, future issues and directions which could be pursued with the aim of making the algorithms more efficient for handling various types of optimization problems are identified.