有序加权平均组合Optimization的建模框架
A modeling framework for Ordered Weighted Average Combinatorial Optimization
摘要：
多目标组合优化处理考虑多个观点或方案的问题。当Pareto解的数量变得相当大或者当需要单个有意义的解时，聚合多个准则以获得全局化目标函数的问题是特别感兴趣的。当优先信息可用且目标具有可比性时，“有序加权平均”或“有序中值”运算符非常有用，因为它们不是将重要性权重分配给特定目标，而是分配给其排序值。本文从建模的角度研究了有序加权平均最优化问题。替代整数规划配方等问题，并研究和比较各自的领域。此外，还研究了它们的相关多面体，给出了一些面族和新的有效不等式族。针对最短路径和最小代价完美匹配这两个著名的组合最优化问题，对所提出的公式进行了具体化，并给出了计算实验的结果和分析。这些结果表明，新的配方加强适当的约束，可以有效地解决中型到大型的实例。
英文摘要：
Multiobjective combinatorial optimization deals with problems considering more than one viewpoint or scenario. The problem of aggregating multiple criteria to obtain a globalizing objective function is of special interest when the number of Pareto solutions becomes considerably large or when a single, meaningful solution is required. Ordered Weighted Average or Ordered Median operators are very useful when preferential information is available and objectives are comparable since they assign importance weights not to specific objectives but to their sorted values. In this paper, Ordered Weighted Average optimization problems are studied from a modeling point of view. Alternative integer programming formulations for such problems are presented and their respective domains studied and compared. In addition, their associated polyhedra are studied and some families of facets and new families of valid inequalities presented. The proposed formulations are particularized for two well-known combinatorial optimization problems, namely, shortest path and minimum cost perfect matching, and the results of computational experiments presented and analyzed. These results indicate that the new formulations reinforced with appropriate constraints can be effective for efficiently solving medium to large size instances.
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