A possibility-based solution framework for interval uncertainty-based design optimization

Abstract

A possibility-based solution framework called the equivalent deterministic method (EDM) is proposed to solve optimization problems with interval uncertainty, which provides an efficient tool for interval uncertainty-based design optimization. First, an interval uncertainty-based design optimization model is established based on the possibility theory and current or reference design from experienced designers. Second, the equivalent deterministic method is proposed to transform the interval optimization problem into a series of interval analyses and deterministic optimizations that are alternately solved, which decouples the double-loop nested optimization into an iterative solving process. The novelties and advantages of the proposed method lie in two aspects. First, the shift scalar is deducted in the objective function and constraints in the possibility degree space, rather than the uncertain design variables and parameters, through which the violated constraints rapidly move toward the flexible region and the design points are optimized progressively. Second, interval analysis methods that calculate the interval responses and possibility, rather than the maximum and minimum points, can be integrated into the proposed method, which enhances the application scope for the existing interval optimization methods. Finally, a mathematical example and two engineering applications are utilized to demonstrate the performance of accuracy and efficiency.