Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical optimization problem. Given the outline of each floor, a list of room sizes, and, for each room, the unit to which it belongs, the aim is to compute floor plans such that each room is placed on some floor and the total distance of the rooms within each unit is minimized. The problem can be formulated as an integer linear program (ILP). Commercial ILP solvers exist, but due to the difficulty of the problem, only small to medium instances can be solved to (near-) optimality. For solving larger instances, we propose to split the problem into two subproblems; floor assignment and planning single floors. We formulate both subproblems as ILPs and solve realistic problem instances. Our experimental study shows that the problem helps to reduce the computation time considerably. Where we were able to compute the global optimum, the solution cost of the combined approach increased very little.

中文翻译：

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具有邻近要求的平面规划算法

平面规划是建筑中一项重要而艰巨的任务。在规划写字楼时，属于同一组织单位的房间应该彼此靠近放置。这导致了以下 NP-hard 数学优化问题。给定每个楼层的轮廓、房间大小列表以及每个房间所属的单元，目的是计算楼层平面图，以便每个房间都放置在某个楼层上，以及房间之间的总距离每个单元都被最小化。该问题可以表述为整数线性规划 (ILP)。存在商业 ILP 求解器，但由于问题的难度，只能将中小型实例求解到（接近）最优。为了解决更大的实例，我们建议将问题拆分为两个子问题；楼层分配和规划单层。我们将两个子问题都制定为 ILP 并解决实际问题实例。我们的实验研究表明，该问题有助于大大减少计算时间。在我们能够计算全局最优值的情况下，组合方法的解决方案成本增加很少。