摘要
许多配比问题涉及到求解给定多个冲突的目标,这些相互冲突的目标通常会产生一组Pareto最优解.采用线性规划法处理这类问题时通常是将多目标转换为单目标,再进行求解,但这一求解过程依赖权重的选取,且难以获得Pareto最优解.针对线性规划法在多目标配比求解问题中的缺陷,为给出多目标配比问题最优计算方法及配比方案,降低工业生产成本,通过多元回归理论结合优化算法,给出一种计算多目标配比问题的通用方法.首先,根据实际要求进行数据处理,剔除异常值;其次,根据多元回归理论,得出配料配比与产物的预测公式并进行精确度检验;最后,采用优化算法获得Pareto最优解.将该方法应用到C_(4)烯烃制备分析问题中,得到乙醇转换率高达82.7%,C_(4)烯烃的选择性高达50.3%.实例仿真说明该方法实用性强、运算简便,能够更快确定最优配比,对实际的生产具有一定的指导意义.
Many matching problems involve solving for a given number of conflicting objectives,and these conflicting objectives usually result in a set of Pareto optimal solutions.The linear programming method is usually used to deal with such problems by converting the multiple objectives into a single objective,which is then solved.However,this process is dependent on the selection of weights and it is difficult to obtain Pareto optimal solutions.To address the shortcomings of the linear programming method in multi-objective proportioning problems,a general method for calculating multi-objective proportioning problems is given by combining multiple regression theory with optimisation algorithms in order to give the optimal proportioning method and proportioning scheme for multi-objective proportioning problems and to reduce industrial production costs:firstly,the data are processed according to the actual requirements and the outliers are eliminated;secondly,according to multiple regression theory,the ingredient proportioning and product Finally,an optimisation algorithm is used to obtain the optimal Pareto solution.The method was applied to the analytical problem of C_(4) olefin preparation,resulting in a high ethanol conversion rate of 82.7%and a high C_(4) olefin selectivity of 50.3%,which is realistic.The simulation results show that the method is practical,simple and useful for practical production.
作者
钟毅
王毅
ZHONG Yi;WANG Yi(School of Mathematics and Physics,China University of Geosciences,Wuhan,Hubei 430074,China)
出处
《数学建模及其应用》
2022年第4期93-100,共8页
Mathematical Modeling and Its Applications
基金
国家自然科学基金(12171443,11801532)
教育部产学合作协同育人项目(220606627240216)。
