面向造纸生产系统非线性多维度问题的求解器设计与应用

Design and Application of Solvers for Nonlinear and Multidimensional Problems in Papermaking Production Systems

关键词:  信赖域内点法  多起点优化算法  求解器  非线性优化

Key Words:Trust region interior point method  Multi-start optimization algorithm  Solver  Nonlinear optimization

摘要:造纸工业智能化转型过程涉及大量高维数学模型的动态、实时求解问题。由于造纸生产系统的非线性、多维度和不确定性等特点，导致描述造纸生产的数学模型往往由庞大的方程组构成，同时，因造纸过程生产波动较大、生产切换频繁，需对复杂模型组频繁、高效的进行求解，以满足动态生产优化的需求。研究面向造纸模型求解问题的求解器，是解决该问题的关键。本研究针对造纸生产模型非线性非凸求解的特点，基于信赖域内点法和TikTak多起点优化算法，设计了面向非线性多维度造纸生产系统的全局优化求解器，实现了对复杂生产约束和不确定初始条件的高效求解。结果表明，本求解器在造纸干燥部优化案例中以100%的成功率找到全局最优解，单个案例平均求解时间为0.81秒，表现出高度稳健性。此外，在造纸能量系统优化案例中成功求解并节约了59.67%的计算资源和9.67%的计算时间。

Abstract:The intelligent transformation of the paper industry involves solving dynamic and real-time problems in numerous high-dimensional mathematical models. Due to the nonlinearity, multidimensionality, and uncertainty inherent in paper production systems, the mathematical models describing these processes often consist of extensive sets of equations. Furthermore, frequent production fluctuations and transitions necessitate efficient and frequent resolution of these complex model sets to meet the demands of dynamic production optimization. Developing solvers tailored to the challenges of paper production models is key to addressing this issue. This study focuses on the characteristics of nonlinear, non-convex problems in paper production models and designs a global optimization solver for nonlinear, multidimensional paper production systems based on the trust-region interior-point method and TikTak multi-start optimization algorithm. The proposed solver achieves efficient resolution of complex production constraints and uncertain initial conditions. Results demonstrate that the solver achieved a 100% success rate in finding the global optimum in a paper drying section optimization case, with an average solving time of 0.81 seconds per instance, exhibiting high robustness. Additionally, in a paper energy system optimization case, the solver successfully reduced computational resource usage by 59.67% and computation time by 9.67%.