论文标题
二次不可分割的资源分配问题，具有广义界限约束
Quadratic nonseparable resource allocation problems with generalized bound constraints
论文作者
论文摘要
我们研究了在分散的能源管理（DEM）领域出现的二次不可分割的资源分配问题，在该领域中，电力网络中的不平衡必须最小化。在此问题中，给定资源分配给一组分为子集的活动，并将成本分配给了同一子集内活动的总体分配资源。我们通过$ O（n \ log n）$最差的时间复杂性得出了两种有效的算法，以解决此问题。对于所有子集具有相同大小的特殊情况，这些算法之一甚至在子集大小的情况下以线性时间运行。这两种算法均受到可分离凸资源分配问题的精心研究的断点搜索方法的启发。对真实数据和合成数据的数值评估都证实了这两种算法的理论效率，并证明了它们在DEM系统中的集成适用性。
We study a quadratic nonseparable resource allocation problem that arises in the area of decentralized energy management (DEM), where unbalance in electricity networks has to be minimized. In this problem, the given resource is allocated over a set of activities that is divided into subsets, and a cost is assigned to the overall allocated amount of resources to activities within the same subset. We derive two efficient algorithms with $O(n\log n)$ worst-case time complexity to solve this problem. For the special case where all subsets have the same size, one of these algorithms even runs in linear time given the subset size. Both algorithms are inspired by well-studied breakpoint search methods for separable convex resource allocation problems. Numerical evaluations on both real and synthetic data confirm the theoretical efficiency of both algorithms and demonstrate their suitability for integration in DEM systems.
