Projection-based robust optimization with symbolic computation
Projection-based robust optimization with symbolic computation
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DOI：
10.1016/j.compchemeng.2021.107380
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Chenglin Zheng;Fei Zhao;Xi Chen
中科院分区：
文献类型：
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作者：
Chenglin Zheng;Fei Zhao;Xi Chen
稳健对应重构是处理稳健优化问题中数据不确定性的一种常用技术。用对偶理论推导稳健的对应公式是非常重要的，特别是对于复杂的不确定性集。为了减少对稳健对应点的依赖，本文提出了一种新的求解反问题的方法。该方法基于可行空间投影，无需构造鲁棒对应解，即可找到鲁棒解。将RO模型转化为半代数系统，采用改进的柱面代数分解方法将高维可行空间投影到目标函数和不确定性参数的低维空间。通过求解极大化问题，并利用极大极大决策准则，可以选择最终的鲁棒解。对非线性规划问题和稳健设计优化问题的算例分析表明，该方法能有效地获得稳健解。
Robust counterpart reformulation is a common technique used to deal with data uncertainty in robust optimization (RO) problems. The derivation of the robust counterpart formulation using the duality theory is nontrivial, especially for complex uncertainty sets. To reduce the dependence on robust counterparts, a novel method is proposed in this article for RO problems. Based on the feasible space projection, the proposed method can locate robust solutions without formulating the robust counterparts. RO model can be reformulated as a semi-algebraic system and a modified cylindrical algebraic decomposition method is applied to project the high-dimensional feasible space on the low-dimensional space of the objective function and uncertainty parameters. By solving the maximization problem and using the max-max decision criterion, the final robust solution can be selected. The case studies, involving problems of nonlinear programming (NLP) and robust design optimization problems, show that the proposed method can obtain the robust solution effectively.