Pareto Efficiency in Robust Optimization
将帕累托效率概念引入鲁棒优化，指出经典方法可能产生非帕累托最优解，并提出验证和生成帕累托鲁棒最优解的方法，计算成本低，在投资组合、库存和项目管理中效果显著。
This paper formalizes and adapts the well-known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology for linear optimization problems. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and we illustrate via examples how this could lead to inefficiencies and suboptimal performance in practice. We provide a basic theoretical characterization of Pareto robustly optimal (PRO) solutions and extend the RO framework by proposing practical methods that verify Pareto optimality and generate solutions that are PRO. Critically important, our methodology involves solving optimization problems that are of the same complexity as the underlying robust problems; hence, the potential improvements from our framework come at essentially limited extra computational cost. We perform numerical experiments drawn from three different application areas (portfolio optimization, inventory management, and project management), which demonstrate that PRO solutions have a significant potential upside compared with solutions obtained using classical RO methods. This paper was accepted by Gérard P. Cachon, optimization.