论文标题
强大不确定的两级合作套装覆盖问题的不足透明度
An under-approximation for the robust uncertain two-level cooperative set covering problem
论文作者
论文摘要
本文研究了强大的不确定的两级合作集覆盖问题（RUTLCSCP）。给定两种类型的设施，称为Y具有Y的效果和Z的实用性。问题是要确定要选择两种类型的设施，以便涵盖需求节点，成本最低。它结合了强大，概率和合作覆盖的概念，该概念通过介绍“ $γ$ - 抛光两级合件$α$ - cover”的约束。此外，RutlCSCP的约束宽松经历也是线性近似RutlCSCP（RUTLCSCP-LA-RA-RC）的线性近似值，是通过限制因素的线性近似开发的，并且可以说为一个紧凑型混合Integer线性编程问题。我们表明，在某些情况下，RUTLCSCP-LA-RC（$ \ VAREPSILON $ -SUND-APPROXIMATE解决方案）的解决方案也可以成为RUTLCSCP的解决方案。计算实验表明，在333个实例中的解决方案（总共10125个实例）具有12种类型的类型，这些类型违反了RUTLCSCP的限制，可能是一种有效的不足的解决方案，而其他实例中可行的解决方案则证明是最佳的。
This paper investigates the robust uncertain two-level cooperative set covering problem (RUTLCSCP). Given two types of facilities, which are called y-facility and z-facility. The problem is to decide which facilities of both types to be selected, in order to cover the demand nodes cooperatively with minimal cost. It combines the concepts of robust, probabilistic, and cooperative covering by introducting "$Γ$-robust two-level-cooperative $α$-cover" constraints. Additionally, the constraint relaxed verison of the RUTLCSCP, which is also a linear approximation robust counterpart version of RUTLCSCP (RUTLCSCP-LA-RC), is developed by linear approximation of the constraints, and can be stated as a compact mixed-integer linear programming problem. We show that the solution for RUTLCSCP-LA-RC, $\varepsilon$-under-approximate solution, can also be the solution for RUTLCSCP on some conditions. Computational experiments show that the solutions in 333 instances (10125 instances in total) with 12 types which tinily violate the constraints of RUTLCSCP, can be an efficient under-approximate solutions, while the feasible solutions in other instances are proven to be optimal.
