Addressing adjacency constraints in rectangular floor plans using Monte-Carlo Tree Search

Highlights

• The proposed algorithm efficiently addresses adjacency constraints for floor plan.

• Both adjacency and non-adjacency constraints are tackled.

• The algorithm is based on Monte-Carlo Tree Search based reinforcement learning.

• The proposed algorithm is time-efficient, lightweight, and scalable.

Abstract

Manually laying out the floor plan for buildings with highly-dense adjacency constraints at the early design stage is a labour-intensive problem. In recent decades, computer-based conventional search algorithms and evolutionary methods have been successfully developed to automatically generate various types of floor plans. However, there is relatively limited work focusing on problems with highly-dense adjacency constraints common in large scale floor plans such as hospitals and schools. This paper proposes an algorithm to generate the early-stage design of floor plans with highly-dense adjacency and non-adjacency constraints using reinforcement learning based on off-policy Monte-Carlo Tree Search. The results show the advantages of the proposed algorithm for the targeted problem of highly-dense adjacency constrained floor plan generation, which is more time-efficient, more lightweight to implement, and having a larger capacity than other approaches such as Evolution strategy and traditional on-policy search.

Introduction

Laying out a floor plan is one of the key tasks in architecture design. It involves making decisions on the design and layout of all the rooms, usually in a 2D space, to satisfy various geometric and topological constraints. Conventionally, this has been a manual trial and error drawing process, where different pieces are adjusted, rearranged and reconfigured repetitively until a suitable floor layout that satisfies the various requirements eventually emerges [1]. This iterative manual process requires a significant amount of human labour and time, and becomes ever less possible as the size and complexity of the design problem increases. Due to the iterative and repetitive nature of this problem, automated computational techniques have replaced the manual design process and become the main approach for generating floor plans [2].

Many computational algorithms including heuristic search, mixed-integer programming have been successfully developed to generate satisfactory floor plans [3]. Especially, the evolutionary methods which have dominated this field in the last decade can generate a variety of layouts. However, the adjacency constraints tackled by most of these approaches are small-in-scale, and more importantly sparse-in-density, where the number of rooms is within 10 and the number of constraints is usually equally around (or at least no more than twice) the number of rooms. For example, Camozzato et al. [4] proposed a procedural method to generate a floor plan of 8 rooms with only 1 adjacency constraint. In [5], the authors illustrate a rectangular dissection method through an example of only 4 rooms with 3 adjacency constraints. Case study [6] tackles totally 9 adjacency constraints within 9 rooms, so the number of adjacency constraints is still no more than the number of rooms. Therefore, these approaches become inefficient with increased scale and density due to their limited scalability. For example, Rodrigues et al. [7] have applied the evolutionary methods to generate floor plans for a hotel up to 30 rooms, however the total number of adjacency constraints is only 34 and therefore still leads to a sparse adjacency matrix. Also, their case is not to generate a rectangular floor plan, therefore rooms can be placed in a more creative way with flexible boundaries. Finally, their algorithm had a runtime of 52 min on a 4GHz 8-core computer with multi-threading, which is not expensive when considering all kinds of granular constraints that were tackled in the original work. However, in case to address adjacency constraints only in initial floor plan, it may become not worth to apply the same approach. In addition to being limited to the small-scale and sparse-density of the adjacency constraints, this work hasn't considered the non-adjacency constraints. This paper tried to address the limitation of existing algorithms to handle high density topological adjacency and also non-adjacency constraints.

Topological adjacency constraint is one of the most important requirements during floor plan generation process, which defines the adjacency conditions between any pair of rooms. The complexity of topological adjacency constraints can be represented in terms of three factors: scale, density, and type of constraints. The first factor, the scale of constraints refers to the number of rooms n_room to place in a floor. Rooms can be any enclosed space. The larger number of the rooms we have, the larger scale of the adjacency constraints we need to tackle. The second factor, the density of constraints refers to the ratio between the number of constraints and the number of rooms n_constraints/n_rooms. For example, in residential floor plans, the adjacency constraints are often small-in-scale and sparse-in-density where there are only a limited of total rooms, and the number of constraints is roughly equal to or even less than the number of rooms. Whereas in other complex scenarios such as hotel and school planning, the problem usually have high-dimensional and dense adjacency constraints with a larger number of rooms to locate, and the constraint density may be much higher. The third factor, the type of adjacency constraint refers to adjacency constraints and non-adjacency constraints that need to be tackled while generating the floor layout. Adjacency constraint is very common in most types of floor plan design, which requires two rooms to be next to each other. Non-adjacency constraint which requires that two rooms must not be adjacent, though less common, is also necessary for some practical problems. For example, in a hospital floor plan, some rooms are not only required to be adjacent to other rooms for convenient circulating reasons, but also required to be non-adjacent to some other rooms for isolation and infection control.

This paper proposes an efficient and lightweight algorithm which focuses on tackling highly dense adjacency constraint matrix, and taking into consideration both the adjacency and non-adjacency constraints. It uses off-policy Monte-Carlo Tree Search (MCTS) based reinforcement learning algorithm to solve this problem. The rest of this paper is divided into four sections. Section 2 gives a brief review of the related computational approaches on floor plan layout design. Section 3 first introduces the MCTS method and the problem definition, and then presents the proposed off-policy MCTS for solving the floor plan problem with highly-dense adjacency and non-adjacency constraints. Section 4 demonstrates two practical case studies to evaluate the capabilities of the proposed algorithm. Limitation and future work are discussed in Section 5. Finally, conclusions are drawn in Section 6.