This paper presents the design problem of
furniture arrangement in a residential interior living space, and
addresses it by means of evolutionary computation. Interior
arrangement is an important and interesting problem that occurs
commonly when designing living spaces. It entails determining
the locations of interior elements such as tables, seating elements,
projection screens etc., in order to satisfy objectives. Despite it’s
commonality, it is a challenging problem that entails mainly soft
objectives, related to perception and ergonomics, as well as
challenging constraints. This paper is an attempt to address this
problem by means of Evolutionary Computation. We discuss the
problem formulation focusing on perceptual aspects of the
various elements of space. In particular, we formulate a three
objective problem with the following objectives: Maximization of
visual perception of openings to the outside, maximization of
inter-person visual perception, from the seating places, and
maximization of the “openness” of space. We provide results
from a comparison of two MOEAs, namely NSGA-II and HypE.
http://www.aleeshainstitute.com/interior-designing-course.php
The design discipline of Interior Architecture focuses on
the elaborated analysis of design problems related to living
spaces and applies ‘the elements and principles of design’ for
their solutions [1]. One of the most common and yet
overlooked problems in interior architecture is the arrangement
of furniture in a living space. As simple as it sounds, the
solution of such a problem requires the comprehension of a
spatial organization that structures interior space within
architectural boundries. Although we recognize the mastery
that may occur from an experienced designer spending a
significant amount of their creative effort in designing an
interior space, we find that it would be beneficial in any case to
consider a computational system that could serve as support in
the creative process.
The challenge for such a problem as interior design and
arrangement is to well define all factors that leads to a
successful spatial organization. Quality of a design should
incorporate a wide variety of design factors, including, but not
limited to, functional, ergonomic, perceptual and aspects of
scale. For defining the goals of the computational system, we
are inspired by criteria for spatial definiton which were derived
from the definitions presented in [2]. In the following section
we explain what we mean with the terms interior space, interior
circulation, interior scale, hierarchy and Connections in interior
spaces.
A. Definitions
We first go through definition of some terms in order to
contextualize the research.
Interior Space: An interior consists of form and space when
boundries are made possible through architectural structure.
For our case we take a living space inside an apartment for our
interior space.
Interior circulation: The circulation in interior spaces
determine the connections between areas. The arrangement of
interior elements, entrances to other interior spaces and to
outside determines interior circulation.
Interior scale: The scale is related with the immediate
environment. For the interiors the scale should be related to the
human ergonomics.
Connections in interior spaces: There are three types of
connections in an inteiror space: visual, functional and
structural. Visual connections in an interior space is provided
with openings within planes. Doors and windows ensure visual
connection in an interior space. The functional connections are
determined by the relationships between different activites in a
living space such as dining, watching TV, relaxing. Structural
connections are defined as the junctions between structural
elements such as between floor to wall and wall to ceiling.
B. Previous Works
Computational Decision Support systems for interior layout
and furniture arrangement have attracted attention in some
sutdies.
In [3], the author proposes a pattern-based mutation
scheme, which allows a series of predetermined elements to be
interchanged in an indoor environment. However, the positions
of the elements are held fixed, and as such the search space is
dramatically constrained. In [4], [5], authors have considered the problem of interior
arrangement of office functions and furniture, both in
rectangular as well as polygonal spaces. However, their
objective functions consisted only of criteria regarding the
functionality of the solutions. As such, soft aspects such as
perception and openness could not be addresses by this
approach.
In [6], authors have considered the placement of furniture
in an interior space focusing on ergonomic criteria. They
propose addressing the optimization problem by the use of
Simulated Annealing algorithm. However, the authors do not
discuss the issue of conflicting objectives in the problem at
hand.
Lastly, in [7], authors use interior design guidelines to
generate a density function with respect to positioning of
furniture. They sample the distribution to generate solutions.
This approach, while quite unique, does not directly guarantee
satisfiability of goals, as well as relying on user input to guide
the system.
In view of the works presented above, this paper considers
an approach to addressing the interior arrangement problem by
means of Soft Computing. In particular, we make use of Visual
Perception definitions, and Evolutionary Computation.
We formulate the interior furniture arrangement problem as
a constrained real parameter optimization problem with 16
Decision Variables and three Objective Functions. As will be
explained in detail, our decision variables correspond directly
to element positions within the space, and objective functions
focus on soft aspects of space such as visual perception and the
perception of openness.
For simplicity, in the current version of the proposed model
we do not consider quality of access in the space, apart from
the basic clearance requirements, e.g. around tables, in front of
seating elements etc. However, it is our plan to include specific
access-related design goals in the near future.
We formulate a scenario that concerns furniture placement
in a living room of an apartment residence. The rectangular
space has dimensions of roughly 5.5m x 5.0m, with one corner
of the rectangle occupied by a balcony. One of the sides of the
living room has a large opening to the outside. A diagram of
the space in question is available in Fig. 1.
A. Decision Variables
We define a total of 16 decision variables (DVs). For each
of the four pieces of furniture to be arranged, correspond three
DVs: Two control the position of the element in space, px, py ,
and one controls it’s rotation, rxy . Position variables form real
numbers, while rotation is a discrete variable.
In principle, the scheme described above should be enough
to fully describe an instance of our interior space arrangement.
However, we have found it is beneficial as for the results, to
include four additional variables, which would control the
ordering of the furniture with respect to their anchor points. In
other words, we first specify four anchor points using the 12
variables discussed above, and subsequently we assign one
element to each, according to an ordering, which is itself
subject to optimization.
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