基于结构可置信性鲁棒优化算法的离散优化问题研究

传统优化设计认为问题的参数(如材料属性和外加载荷等)是确定的,并且设计变量通常是连续的.而在实际应用中产品制造和测量等存在不可避免的误差,并且工程需要的设计结果(如钢筋截面尺寸等)往往是离散的.即使对于考虑了不确定性参数影响的连续最优解,经过圆整处理后也很可能产生较大偏差甚至变得不可行.针对该难点,本文结合非概率不确定性鲁棒优化算法,建立与离散的基于圆整策略的优化算法列式等价的鲁棒优化列式及用于解决离散优化问题的可置信性鲁棒优化方法.并进一步研究了离散变量不确定性优化问题的可置信性鲁棒优化求解方法,利用非线性半定规划进行高效求解,可严格保证所得结果的可行性.本文揭示了传统离散优化思想和不确定性优化思想的内在联系,完善了优化设计理论体系,为后续相关研究提供了全新思路和示范.

A study on discrete optimization problem based on confidence structural robust optimization algorithm

It is always assumed the parameters in traditional optimization design problems (such as material properties, applied loads) are deterministic and continuous variables. Due to the unavoidable uncertainties in manufacturing or measurement, however, in practical applications, the desired results in engineering are often discrete. Even if the continuous optimal solution considers the influence of uncertain parameters, after rounding, it is likely to produce large deviations or even become no longer feasible. Combining the robust optimization algorithm considering non-probabilistic uncertain parameters, a confidence-robust optimization method equivalent to the discrete optimization sequence based on the rounding strategy is proposed for solving discrete optimization problems. The confidence-robust optimization solution method of discrete optimization problems with uncertain parameters is further studied using nonlinear semi-definite programming efficiently, which can strictly guarantee the feasibility of the obtained results. It is expected to reveal the underlying connection between traditional discrete optimization ideas and uncertain optimization ideas, improve the theoretical system of optimization design, and provide new ideas and demonstrations for subsequent related research.