Optimal blending under general uncertainties: A chance-constrained programming approach
Optimal blending under general uncertainties: A chance-constrained programming approach
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DOI：
10.1016/j.compchemeng.2023.108170
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Y. Yang
中科院分区：
文献类型：
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作者：
Y. Yang
针对具有线性混合规律和一般参数不确定性的配料规划问题，提出了一种优化算法。其目的是通过仔细确定原料配比，使最终产品大概率地满足所有质量指标，实现生产利润最大化。依赖于确定性优化的传统方法不能考虑参数的不确定性，因此可能不会产生概率可行解。该工作将混合规划问题描述为一个联合机会约束规划(CCP)。利用布尔不等式分解联合约束，用高斯混合模型刻画不确定性分布，可以得到CCP的守恒确定性近似。通过二阶锥体松弛、分枝定界、基于最优性的边界收紧和重构线性化技术，可以找到确定性逼近的全局最优解。提出了一种风险水平调整方法，在允许后验评估的情况下，降低了解的保守性，进一步提高了解的目标值。以钢铁和汽油生产为算例，验证了该优化方法的求解时间、概率可行性和解的质量。
An optimization algorithm is proposed for blend planning with linear mixing law and general parameter uncertainties. The objective is to make the final product satisfy all quality specifications with high probability, and maximize the production profit by carefully determining the feedstock ratio. Conventional approaches that rely on deterministic optimization fail to account for parameter uncertainty, and thus may not generate a probabilistic feasible solution. The proposed work formulates the blend planning problem as a joint chance-constrained program (CCP). Using Boole’s inequality to decompose joint constraints and the Gaussian mixture model to characterize uncertainty distributions, a conservative deterministic approximation of CCP can be formulated. Through second-order cone relaxation, branch-and-bound, optimality-based bound tightening, and reformulate-linearization techniques, the global optimum of deterministic approximation can be found. A risk level adjustment procedure is presented to reduce the conservativeness and further improve the objective value of the solution if posterior evaluation is allowed. Two numerical cases, including steel and gasoline productions, are studied to show the solving time, probabilistic feasibility, and solution quality of the proposed optimization method.