GPU-Based Global Optimization for Engineering Design1

Design optimization has important applications in many engineering fields, where the goal is to find the best design within the available means. In many practical applications, finding the best design can bring significant profit, quality, and performance advantages. However, popular design optimization methods, such as gradient-based methods and heuristic methods, often become trapped in local optima and fail to find the global optimum that corresponds to the best design, leading to inconsistent or incorrect assumptions and applications. In this article, a novel global optimization method designed for graphics processing unit (GPU)-based massively parallel computing is introduced to efficiently enclose the global optimum for continuous design optimization problems, where the objective and constraint functions have analytic expressions. Using interval arithmetic, coupled with the computational power of GPU, the method iteratively rules out the regions in the design space where the global optimum cannot exist and leaves a finite set of regions where the global optimum must exist. Because of the rigor of interval arithmetic, the method is guaranteed to enclose the global optimum in the regions within a user-specified width tolerance for design optimization problems, even in the presence of rounding errors. The GPU-based global optimization method is validated through two case studies of the Ackley function and launch vehicle design. The results show that the method successfully encloses the global optimum that corresponds to the best design in each case study, while both a typical gradient-based method and a popular heuristic method become trapped in local optima that correspond to inferior designs.