Algorithms for Floor Planning with Proximity Requirements

TL;DR

This paper addresses the complex NP-hard problem of floor planning with proximity constraints by splitting it into two ILP-based subproblems, significantly improving computational efficiency while maintaining near-optimal solutions.

Contribution

It introduces a novel two-step ILP-based approach for large-scale floor planning with proximity requirements, enhancing solution scalability and efficiency.

Findings

Splitting the problem reduces computation time substantially.

The combined approach yields solutions close to the global optimum.

Experimental results demonstrate effectiveness on realistic instances.

Abstract

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.