This paper introduces an integer linear program for a variant of the linear ordering problem. This considers, besides the pairwise preferences in the objective function as the linear ordering problem, positional preferences (weighted rank) in the objective. The objective function is mathematically supported, as the full integer linear program is motivated by the instant run-off voting method to aggregate individual preferences. The paper describes two meta-heuristics, iterated local search and Memetic algorithms to deal with large instances which are hard to solve to optimality. These results are compared with the objective value of the linear relaxation. The instances used are the ones available from the LOP library, and new real instances with preferences given by juries.

本文介绍了一种用于线性排序问题变体的整数线性规划。除了作为线性排序问题的目标函数中的成对偏好之外，这还考虑了目标中的位置偏好（加权排名）。目标函数在数学上得到支持，因为完整的整数线性程序是由即时决选投票方法驱动的，以汇总个人偏好。该论文描述了两种元启发式算法、迭代局部搜索和模因算法来处理难以求解最优的大型实例。将这些结果与线性松弛的目标值进行比较。使用的实例是 LOP 库中提供的实例，以及评审团给出的偏好的新真实实例。