基于效用理论的交互式线性最优化鲁棒性方法
A Utility Theory Based Interactive Approach to Robustness in Linear Optimization
摘要：
我们处理不确定性线性规划问题，利用加权分析中心的概念和多准则决策领域的概念。在介绍了我们的方法，我们开发了强大的优化交互式切割平面算法，基于凹和准凹效用函数。除了实际优势外，由于我们方法的灵活性，我们能够证明在Bertsimas和Sim [14]的理论框架下，该框架建立了鲁棒最优化问题的某些凸公式的存在性，由我们的算法生成的鲁棒最优解至少与由许多其他鲁棒优化算法生成的任何解一样，理论框架。我们提出了一些可靠的解决方案的可行性概率界，并通过计算实验来评估我们的方法。
英文摘要：
We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. After introducing our approach, we develop interactive cutting-plane algorithms for robust optimization, based on concave and quasi-concave utility functions. In addition to practical advantages, due to the flexibility of our approach, we are able to prove that under a theoretical framework due to Bertsimas and Sim [14], which establishes the existence of certain convex formulation of robust optimization problems, the robust optimal solutions generated by our algorithms are at least as desirable to the decision maker as any solution generated by many other robust optimization algorithms in the theoretical framework. We present some probabilistic bounds for feasibility of robust solutions and evaluate our approach by means of computational experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
