Industrial process systems need to be optimized, simultaneously satisfying financial, quality, and safety criteria. To meet all of those potentially conflicting optimization objectives, multiobjective optimization formulations can be used to derive optimal trade-off solutions. In this work, we present a framework that provides the exact Pareto front of multiobjective mixed-integer linear optimization problems through multiparametric programming. The original multiobjective optimization program is reformulated through the well-established ϵ-constraint scalarization method, in which the vector of scalarization parameters is treated as a right-hand side uncertainty for the multiparametric program. The algorithmic procedure then derives the optimal solution of the resulting multiparametric mixed-integer linear programming problem as an affine function of the ϵ parameters, which explicitly generates the Pareto front of the multiobjective problem. The solution of a numerical example is analytically presented to exhibit the steps of the approach, while its practicality is shown through a simultaneous process and product design problem case study. Finally, the computational performance is benchmarked with case studies of varying dimensionality with respect to the number of objective functions and decision variables.

中文翻译：

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混合整数线性规划问题的多目标优化：一种多参数优化方法

需要优化工业流程系统，同时满足财务、质量和安全标准。为了满足所有这些潜在冲突的优化目标，可以使用多目标优化公式来得出最佳权衡解决方案。在这项工作中，我们提出了一个框架，该框架通过多参数规划提供多目标混合整数线性优化问题的精确帕累托前沿。原始的多目标优化程序通过成熟的 ε-约束标量化方法重新制定，其中标量化参数的向量被视为多参数程序的右侧不确定性。然后，算法过程将得到的多参数混合整数线性规划问题的最优解推导出为 ε 参数的仿射函数，从而显式生成多目标问题的帕累托前沿。数值例子的解决方案被解析地展示以展示该方法的步骤，而其实用性通过同时的过程和产品设计问题案例研究来展示。最后，计算性能的基准是针对目标函数和决策变量的数量的不同维度的案例研究。同时通过过程和产品设计问题案例研究显示其实用性。最后，计算性能的基准是针对目标函数和决策变量的数量的不同维度的案例研究。同时通过过程和产品设计问题案例研究显示其实用性。最后，计算性能的基准是针对目标函数和决策变量的数量的不同维度的案例研究。