一种两阶段求解LED光谱匹配系数高效全局优化算法  

A Two-Stage Efficient Global Optimization Algorithm for Solving LED Spectral Matching Coefficient

作　　者：王永军 吴贵文 黄河[1] 李同军 WANG Yong-jun;WU Gui-wen;HUANG He;LI Tong-jun(School of Artificial Intelligence,Wenzhou Polytechnic,Wenzhou 325035,China;School of Information and Engineering,Wenzhou Business College,Wenzhou 325035,China;School of Information and Engineering,Zhejiang Ocean University,Zhoushan 316022,China)

机构地区：[1]温州职业技术学院人工智能学院,浙江温州325035 [2]温州商学院信息工程学院,浙江温州325035 [3]浙江海洋大学信息工程学院,浙江舟山316022

出　　处：《光谱学与光谱分析》2024年第6期1591-1599,共9页Spectroscopy and Spectral Analysis

基　　金：温州市重大科技创新攻关项目(ZG2022012);国家自然科学基金面上项目(61773349)资助。

摘　　要：用单色发光二极管(LED)组份合成目标光谱在现实中有重要意义。当单色LED组成成份多、目标光谱合成精度要求高时,求解光谱组成成份的比例问题变成了超定方程组非负解的组合优化难题。智能优化类算法提高了解的全局最优性,但若没有利用目标函数的数学解析性质,其收敛速度慢,解的精度不高。梯度类算法收敛到局部解的速度快且精度高,但至今没有成熟理论技术求解非凸优化全局最优解,且问题中非负解的要求限制了该类算法的收敛速度。同时,目标函数的最小二乘信息在求解时没有得到充分利用。基于目标函数的数学可解析性、表现形式的二次非线性格式、最终解的非负要求,提出了一种两阶段优化算法LLR_LBFGS。第一阶段进行无约束的线性拟合,得到目标函数的最小二乘近似理论解,第二阶段借助带约束的拟牛顿方法LBFGS进一步求取问题的非负全局最优解。以标准目标光谱CIE-A、CIE-D65、CIE-D50、CIE-D55、CIE-D75的最佳拟合为研究对象,对比了新方法与拉索回归算法(LASSO)、岭回归算法(RIDGE)、差分进化算法(DE)、粒子群算法(PSO)及遗传算法(GA)的求解精度和运行速度,以及决策系数R 2。基于实际工业案例的数值结果表明,LLR_LBFGS能够较快地锁定全局解的范围,收敛速度更快;能够借助目标函数的数学可解析性提高解的精度。两个阶段的衔接融合能够获得较好的全局最优解的起始点和高精度的最优解。该方法对解决LED光谱拟合问题潜力大,有普适性。基于该设计思路,可以在算法的两个阶段中,组合设计更多、更灵活的光谱配比解决方案。这对于求取LED光谱匹配最优解的智能优化类方法改善效果有较好的启发意义。The synthesis of the required target spectrum with monochromatic light-emitting diodes(LED)is of great significance in reality.When multiple components of the LEDs are needed,and the accuracy required for the target spectrum synthesis is high,solving the problem of the proportion of the components becomes a combination optimization problem with a non-negative solution of the over-determined set of linear equations.Generally speaking,the approximately global solutions can be found for the heuristic-based methods.However,the convergence speed to the worldwide optimizer is low partly because the objective functions analysis properties,such as gradient information,are not used.Gradient-based algorithms converge to local solutions fast and with high accuracy,but the requirement for non-negative solutions in the problem limits their global convergence.Meanwhile,the least squares information of the objective function was not fully utilized in previous research.In this paper,a two-stage optimization algorithm,named LLR_LBFGS,is proposed based on the mathematical analytic properties,the quadratic nonlinear format of the objective function,and the non-negative requirements for the final solution.In the first stage,unconstrained linear fitting is carried out to obtain the unique solution of the least squares theory of the expressions.In the second stage,the non-negative global optimal solution of the problem is further obtained with the help of the constrained quasi-Newtonian method LBFGS.Taking the fitting of standard target spectra CIE-A,CIE-D65,CIE-D50,CIE-D55 and CIE-D75 as the research object,the new method is compared with the Lasso Regression Algorithm(LASSO),Ridge Regression Algorithm(RIDGE),Differential Evolution Algorithm(DE),Particle Swarm Optimization(PSO)and Genetic Algorithm(GA)in solving the same problem in terms of accuracy,running speed,and the decision coefficient R 2.The numerical results based on actual industrial cases show that the LLR_LBFGS converge faster,and the solution accuracy is higher because t

关 键 词：光谱学 LED光谱匹配 线性拟合 LBFGS 高效 全局优化 

分 类 号：O433.4[机械工程—光学工程]