Development of a "monty hall" analog for heuristic all-at-once optimization

Past studies in Multidisciplinary Design Optimization (MDO) have shown that All-at Once (AAO) optimization can be an extremely intuitive and useful alternative means to approach the solution of a multidisciplinary analysis and optimization simultaneously. However, its utility has shown to decrease for larger problems with higher degrees of non-linearity and non-convexity. The present research presents a new heuristic optimization algorithm intended for solving coupled (multidisciplinary) design problems posed in the form of an AAO optimization. The hope is that the algorithm presented and developed herein can be used to improve upon past findings where conventional gradient-based optimization methods have been found to fail. The algorithm is modeled after the structure and decision process behind the famous "Monty Hall" problem, which gained its name from the host of the 1970's TV show, "Let's Make a Deal". The algorithm developed in this research has also been modeled after numerous other popular heuristic optimization algorithms which promote the concepts of exploration as well as exploitation of the design space, namely simulated annealing, tabu search, and genetic algorithms. The algorithm will first be presented on a small, simple, well-known test problem to most easily demonstrate its characteristics and assess its functionality. Thereafter, the algorithm will be implemented on two additional multidisciplinary system simulations of greater size and complexity, both of which will be generated using the previously developed CASCADE MDO simulation tool. For all test systems, the performance of the new method will be compared to other optimization approaches, such as gradient-based methods (using MS Excel's internal solver), simulated annealing, and a pure random search.