A Survey of Computational Approaches to Space Layout Planning

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Computational Approaches to Space Layout Planning Hoda Homayouni

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A Survey of Computational Approaches to Space Layout

Planning (1965-2000)

Hoda Homayouni

Department of Architecture and Urban Planning

University of Washington

1. Introduction

Space layout planning is one of the most important and complex parts of any

architectural design process. In order to design a building that responds to most of itsrelated requirements, an architect (or architectural team) should spend much time and

effort on studying the specific situations of the building and all the relationships that

should exist within the building rooms and between the interior and exterior spaces.

Beside the artistic aspect of architectural design that occurs in almost all parts ofthe design process, there is a substantial logical process behind the space layout planning

phase. Architects cannot avoid having numbers of trial and error approach to pass that

step. The combinatorial complexity of most floor plan design problems also makes it

practically impossible to obtain a systematic knowledge of possible solutions using penciland paper.

Therefore, computers would seem to be a very helpful device to provide

architects with a set of possible optimized solutions to the interlocking problems that

exist in this part of design. Many architects and computer scientists have tried to create a

program that could come up with the optimum solution for different constraints andobjectives that exist in architectural design process.

In 1965 Thomas Anderson, a student in civil engineering at the University of

Washington, for the first time, wrote a program called SLAP1. This program locates

activities in relation to one another in order to minimize the total cost of circulation

between two activities. After that many other students and scientists tried to address thisproblem by producing different algorithm with different logics behind them.

Before categorizing the different logical structures and consequently differentprograms that are presented and studied so far, it is worth mentioning that all of these

different approaches begin by propounding numerical definitions for all the constraints

existing in the design situation. There are basically two types of constraints that expressthe design objective requirements:


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Dimensional constraints (geometrical constraints): constraints that are consideredover one place, i.e. constraints on surface, length or width, or space orientation.

Topological constraints: constraints that are considered over a couple of spaces, i.e.adjacency between the rooms, adjacency to perimeter of the building, non-

adjacencies or proximities. The numerical criteria that topologically definearrangements usually come from site analysis questions and user need questions.

1.1 Automated Space Planning Characteristics and SolutionApproaches

Architectural space layout problems tend to be ill-defined (Yoon, 1992) and

over-constrained. Problems that are not well defined are ill-defined (Simon, 1973), in that

the initial constraints on the problem are not fully formulated. Resolving ill-definedproblems is a process of searching for and refining a set of design constraints. Problems

that are over-constrained have no single best solution and thus have too many possible

solutions (Balachandran and Gero, 1987). Automated space planning systems need amethod of providing a good solution from a large set of possible solutions, and a method

of allowing the designer to modify the set of design constraints to continually refine the

problem definition (Arvin and House, 2000). However Tsang et al have shown that there

does not appear to be a universally best algorithm and that certain algorithms may bepreferred under certain circumstances (Tsang et al, 1995). Therefore, in this part a general

categorization from the studied solution approaches is presented while more specification

and details will be presented in section 2.

1.1.1 Categorizing the Solution Approaches

As mentioned earlier, various approaches have been presented toward the

computerized space layout planning objective. But for the sake of simplicity we generallycategorize these different approaches to some main parts according to Galles divisions(Galle, 1981). Obviously each part could contain some subcategories whit different ideas

and details. There are also some approaches that take benefit of the two types or moretogether, in a different phases of computation.

1. On-line machine control and appraisal of the designers layout proposals.2. Stepwise automatic layout generation interactively guided by manual selection of

desirable partial solutions.

3.

Nonexhaustive automatic generation satisfying given constraints.

4. Exhaustive automatic generation satisfying given constraints.5. Automatic generation of optimal or quasi optimal layouts under given constraints.

Approach no. 1 has been advocated primarily by Maver (Maver, 1970) who

argues that human creativity is superior to that of machines in solving real world

problems. This approach is prominently represented by Thng and Davies (Thng and


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Davies, 1975) whose ideas have been taken up by Gentles and Gardner (Gentles and

Gardner, 1978). Although Cross (Cross, 1977) produces some counterevidence, appraisalprograms enable the designer to increase the number of solutions considered. A tenfold

increase has been experienced (Mayer, 1979). But the solutions are still generated

intuitively and the element of randomness in traditional planning remains in the decision-

making.

Approach no.2 was suggested in graph-theoretical terms by Korf (Korf, 1977)and developed by Ruch (Ruch, 1978) for generation of planlike bubble diagrams. Such

methods are likely to produce more solutions than methods of the first type but design

becomes no more systematic than the designers behavior.

Approach no.3 is represented by Weinzapfel and Handel (Weinzapfel and

Handel, 1975), Pfefferkorn (Pfefferkorn, 1975), and Willey (Willey, 1978). Eastmanillustrated the use of his General Space Planner (Eastman, 1971) by procedures also

belonging to this class of purely heuristic methods.

Approach no.4 was introduced by Grason (Grason, 1968) who generated plansas dimensionally feasible embeddings of the duals

1of graphs representing at least the

required adjacencies (edges) between rooms (vertices). According to Steadman(Steadman 1976), Grasons program fails for problems of more than five rooms.

After that, Mitchell, Steadman, and Liggett (Mitchell et al, 1976) implemented

an exhaustive method for solving problems stated in terms of dimensional and adjacency

requirements. It includes, however, a final optimization step. To solve an n-room

problem, their program searches a permanent library of topologically distinct

dissections, i.e., tight rectangular packings of n nonoverlapping rectangles with

unspecified dimensions. For each dissection matching the adjacency requirements,

combinations of wall dimensions are searched so as to minimize, e.g., construction costs.Earl (Earl, 1977) has shown that the algorithm which generated the library is not

exhaustive for n>=16 and the optimization method has been criticized by Gero (Gero,

1977). Later, Bloch (Bloch, 1978), Krishnamurti and Row (Krishnamurti and Row,

1978), efficiently generated all dissections with n


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Flemming (Flemming, 1978) describes another implemented two-step method

which also satisfies adjacency and dimensional constraints. It combines exhaustive searchfor certain topologically distinct equivalence classes of solutions with a linear

programming algorithm searching each class for an optimal representative. The linear

constraints include derived class-specific dimensional constraints ensuring required

adjacencies, and linear approximations of the users area constraints. Flemming presentsa realistic design example with nine rooms: Eight requirements had the form A must beadjacent to B or C, but such alternatives cannot be managed by the program. Therefore

four of the subproblems defined by the possible choices among alternative adjacencies

were selected as test problems. To limit the solution set further, six plausible adjacencyconstraints were added to the first of these problems, and eight constraints were added to

the other three problems.

Approach no.5 is closely related to the field of operational research. For

Example, Armour and Buffa (Armour and Buffa, 1963), Whitehead and Eldars(Whitehead and Eldars, 1964), Gavett and Plyter (Gavett and Plyter, 1966), Seehof et al.

(Seehof et al, 1966) described various methods for generating a schematic layout

minimizing internal traffic while Krejcirik (Krejcirik, 1969) also considered areaminimization. Brotchie and Linzey (Brotchie and Linzey, 1971) developed a

comprehensive cost-benefit model including flows of persons, heat, loads, etc. Some ofthese early techniques were later elaborated and supplemented by Cinar (Cinar, 1975),

Willoughby et al. (Willoughby et al, 1970), Portlock and whitehead (Portlock andwhitehead, 1971), Gawad and Whitehead (Gawad and Whitehead, 1976), Sharpe (Sharpe,

1973), and Hiller et al. (Hiller et al, 1976), among many others. Dudnik (Dudnik, 1973)

and Krarup and Pruzan (Krarup and Pruzan, 1973) discuss optimal architectural spaceallocation and reach divergent conclusions. Unless the highly controversial notions of

numerical utility of imponderables and numerical weighting of incommensurable

desiderata are applied, it is impossible to express all relevant qualities of a floor plan as

an objective function. The measurement technique of Kalay and Shaviv (Kalay andShaviv, 1979) is an interesting attempt to capture the qualitative aspects of dwelling plans

numerically. Radford and Gero (Radford and Gero, 1980) recommend enumeration of

solutions which are Pareto-optimal with respect to several criteria. This method allowsfor incommensurable desiderata but like automated optimization in general, it is faced

with the dilemma of architectural optimization: Either quantify what should not be

quantified or ignore what should not be ignored: the intangible values of architecture.

2 Annotated Bibliographies

In this section brief summaries of different programs that have been presented inthe field of space layout planning automation are presented.


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2.1 Some Computer-aided Approaches to Housing(Schnarsky, 1971)

In this paper two different ideas and consequently two whole differentcomputerized systems have presented.

The first system begins with filling out a detailed questionnaire and ends with a

robotic factory producing the unique, responsive house. The major portion of this paper

deals with an explanation of possible techniques used to accomplish this system. The

various techniques can be combined to form house design generating systems:

TECHNIQUE 1- SYSTEMATIC COMBINATION: Using the userquestionnaire information, the system will select the size and shape of each part from a

predetermined array of parts. How each part relates to the next can be defined by such

physical limitations as jointery, structure, life systems, and most important circulation.

Working within the rules of assemblage all of the combinations can be generated. Figure1 and Figure 2 illustrates the steps of this process as it might apply to three parts of a

house.

Figure 1. Parts A, B, C are selected from an array of predetermined parts

Figure 2. Implicit in these parts are rules for assemblage


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TECHNIQUE 2- TOPOLOGICAL PLACEMENT: This technique says that

different parts of the house should be placed based upon topological objectives. To solvethe internal arrangement problem a technique known as hierarchical decomposition can

be used. This takes the random list of elements and interactions extracted from the

questionnaires and finds the optimal clusters.

TECHNIQUE 3- EVALUATION OF ALTERNATIVES: As the many

combinations are generated, each can be evaluated. The highest scoring solutionsrepresent those that best meet the needs of the user.

TECHNIQUE 4- WHEN YOU CANNOT MAKE A DECISION, GUESS!

Random number techniques allow the computer to make irrational decisions.

TECHNIQUE 5- LAY DOWN THE IMPORTANT PARTS FIRST: This

technique provides a strategy which grows a plan beginning with the most critical part

and adding less important ones based upon the next highest relationship to what has

already been located.

TECHNIQUE 6- CANNED EXPERTISE: It is possible to instruct the

generating program to emulate basic planning laws that apply to any users requirement.This can be done by pre-solving the arrangements of all the manufactured modules at the

subsystem level.

TECHNIQUE 7- GENERIC SOLUTIONS: This would generate all of the

possible combinations of manufactured parts once.

TECHNIQUE 8- LET THE USER TRY HIS HAND: Now set the user down to

an interactive graphic display tube and let him try to combine his parts. After each move

by the user, the program evaluates the current arrangement and offers criticism, cost, andencouragement.

After explanation about ways to get computers to design responsive houses,

another concept that almost negates the need to develop the option 1 system has beenpresented in this paper. The idea is houses from a kit of parts. Here the user buys his

house in parts and puts it together himself. As Kenneth Allinson (Allinson, 1970) has

points out, a house of modules could exist that modules are added and removed as

performance demands vary. One may even pay for it by credit card or return it likebottles. This option also presents the problem of conflict and infringements on the rights

of others.

2.2 An Approach to Computerized Space Planning UsingGraph Theory (Grason, 1971)

This paper treats computerized space planning by discussing methods for the

solution of a formal class of floor plan design problems. These methods have beenimplemented in an experimental computer program called GRAMPA (stands for GRAph


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Manipulating PAckage). The methods of solution depend on a special linear graph

representation for floor plans called the dual graph representation.

As shown in Figure 3 a space is defined to be either a room or one of the four

outside spaces. A problem statement will consist of a set of adjacency and physicaldimension requirements that have to be satisfied, and a problem solution is a floor plan

that satisfies all of the design requirements.

Figure 3. A typical floor plan

In this approach, in applying graph theory to floor plan layout, rooms are

pictured as labeled nodes possessing certain attributes, such as intended use, area, and

shape. Adjacencies between rooms are indicated by drawing lines (edges) connecting the

nodes representing those rooms. These notions can be implemented by dealing with thedual graph of a floor plan which is itself treated as a linear graph. An example of such a

floor plan graph is shown in Figure 4, with black nodes. In the floor plan graph, edges

and nodes will be called wall segments and corners respectively.

This special type of dual graph of the floor plan is the design representation tobe used for the class of problems described in this paper. The general idea of its

application is to first set down the four nodes and four edges of the dual graph thatrepresent the four outside walls of a building. Then nodes and edges are added one by

one to the dual graph in response to design requirements and other considerations until acompleted dual graph is obtained.

The incomplete dual graphs that are produced in the intermediate stages of thisdesign process present special problems. Since edges can be colored, directed, and

weighted, it is not always clear whether or not there exists at least one physically

realizable floor plan satisfying the relationships expressed in the incomplete dual graph.To treat this problem, appropriate properties of the dual graph representation have been

developed and are presented in this paper, but there is not sufficient space here to

describe these methods.


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Figure 4. Floor plan graph with dual graph

In addition to simply storing the structural description of the dual graph, the

computer data representation must be configured in such a way that it is easy to

determine whether the graph is planar or not. It must also be easy to generate the variouspossible geometric realizations of the dual graph. A geometric realization of a planar

graph is simply one of the possibly many ways in which it can be drawn in a plane. Fourdifferent realizations of a particular planar graph are shown in Figure 5.

Figure 5. Four planar realizations of a graph


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Since in a partially completed dual graph each planar realization corresponds to

a topologically different set of floor plans it is important to be able to generaterealizations with great facility.

To deal with the problems mentioned above, a special graphical grammar calledthe planar graph grammar (PGG) was developed. The general intent of this grammar is to

divide a graph into a set of hierarchically organized subgraphs. Each of these subgraphs

can be treated as a separate entity, and if it is connected to the rest of the graph, it is by atmost two nodes. These subgraphs are free to rotate about these nodes to create the various

realizations of the graph. Other such degrees of freedom in creating realizations are

also possible.

The grammar allows one to deal with planarity in an inductive manner. That is,

given a graph that is planar and described in terms of the planar graph grammar, if a newedge is to be added to that graph a test can be developed to tell whether the resultant

graph will also be planer. This test assumes that each of the special subgraphs is already

planar. It then checks to see if the proposed edge can be connected to the two endpoints

without crossing an edge of one of these subgraphs. This method is extremely fast, and itscomputation time increases only linearly with the size of the graph considered. The

computation time for other methods generally increases more than linearly with the size

of the graph.

At the next level, the program has two jobs to accomplish: (1) It must satisfy thephysical dimension requirements. It does this by selecting nodes on the boundary of the

region in question and assigning dimensions to them from the design requirement list. (2)

It must fill the region with edges representing those adjacencies not specifically

requested by the design requirements. Here the program does an exhaustive search of allpossible design solutions.

2.3 Modeling Architectural Design Objectives in PhysicallyBased Space Planning (Arvin et. al, 2000)

In the physically based space planning program, the designer creates a space

plan by specifying and modifying graphic design objectives rather than by directlymanipulating primitive geometry. The plan adapts to the changing state of objectives by

applying the physics of motion to its elements.

In fact, in this approach, the architect defines programmatic objectives in the

usual manner, and these objectives are then modeled as physical objects and forces used

in a dynamic physical simulation.

The spaces and walls are modeled as point masses, with adjacencies between

spaces that are modeled as springs connecting the masses. Objectives specified in thearchitectural program are translated into forces applied to the masses.

In the first phase the topological objectives apply forces to the center of a space.For collision detection, in this step boundary shapes are treated as circles so spaces are


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able to slide around each other. The dynamic simulation starts to run until the system is in

equilibrium, which is defined as the point in time when the magnitudes of all velocitiesare below a small threshold.

At the second phase topological objectives are turned off and geometricobjectives apply forces to the polygonal edges of space boundaries. Also space

boundaries are switched from a circular to a polygonal representation in this phase.

Collision detection and response then act to keep spaces from overlapping, resulting in anarrangement that is very close to a recognizable building floor plan.

Once a geometric simulation has reached equilibrium, the designer can begin to

analyze and interact with the design by directly manipulating the graphic model rather

than by respecifying design objectives in the language of the underlying system. The

mass-spring representation allows the graphic model to adapt to those changesimmediately. The intention here is not simulating the actual behavior of building

elements, but simulating the way architects may view and interact with design elements

during their conception. Sample pictures for the process are shown in Figure 6.

Figure 6. Sample results


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2.4 Dynamic Space Ordering at a Topological Level in SpacePlanning (Medjdoub et. al, 2000)

This approach and its implementation within ARCHiPLAN prototype is basedon a constraint programming approach which importantly avoids the inherent

combinatorial complexity for middle size space layout problems. In fact, this is acomplementary approach to Schwarz et al (Schwarz et al. 1996) that is based on a graph-theoretical model. In this approach the topological level is a part of the computation

process, but the evaluation of the solutions is done at the geometrical level. It is restricted

to the small size problems (does not exceed nine rooms) and the shape contour of thebuilding is a result of the design process. This allows architects to be the actors of the

design at the topological level when choosing between feasible sketches and composing

interactively an objective function for finding the best corresponding geometrical

solutions.

Here, two constraint groups are defined in an extensible library: (1) specification

constraints; (2) research space reduction constraints.

Specification constraints regroup dimensional and topological constraints. Theyare applied by the user and stored in a functional diagram. These constraints are

introduced into ARCHiPLAN interactively by graph handling and incremental

construction. Then adjacency and non-overlapping check applied between all pairs of

spaces. Of course, pairs of rooms which are already constrained to be adjacent verify thenon-overlapping constraint. Figure 7 shows permissible positions for e2x2 and e2 y2 (e2y2

represents the constrained variable y2 of space e2) by the non-overlapping constraint

between spaces e1 and e2. This constraint is dependent on the minimal space dimensionnotion.

Figure 7. Permissible position for (e2.x2, e2y2) after non-overlapping constraint with e1. The

partitioning of the surroundings of a space in {E,W,N,S} is given.

Research space reduction constraints allow the combinatorial reduction. They

regroup the incoherent space elimination constraint, the symmetry constraint, thetopological reduction constraint and the propagation orientation constraint.


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Also, a particular dynamic variable ordering (dvo) heuristic, named dso

(dynamic space ordering) is developed based on the most constrained space position.Comparatively to the dvo heuristics, the dso heuristic is based on the space ordering and

particularly on the space reference points. To implement this heuristic, a new attribute in

space class called degree of constraint dg-cont has introduced. The more the space is

constrained, the higher the dg-cont value is and the more the non-overlapping andadjacency variables corresponding to this space have a chance to be instantiated first. The

initial value of dg-cont is calculated from the adjacency constraints with the building unit.

If two spaces have an equal dg-cont value, the space with the highest average surface areais chosen and if it is not sufficient to distinguish this space, the first in the list is chosen.

After the detection of the most constrained space with the building unit, its

corresponding adjacency variables with the building unit are instantiated. After each

space choice, one updates dynamically the dg-cont values of the remaining spaces. The

process runs until all topological variables are instantiated but a backtracking isperformed as soon as an inconsistency is detected. At this point the graphic representation

of a topological solution is generated which reveals slight overlapping of rectangles in the

same way as a sketch.

Figure 8. Some topological solutions of the house with two floors.


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The optimization stage consists of minimizing an objective function, called cost

function. The Branch and Bound optimization method leads to the determination of theglobal optimum of a geometrical solution. This is not the case with expert systems

approaches (Damski et. al., 1997) or evolutionary approaches (Jo et. al., 1998) which lead

to satisfactory solutions.

The objective functions minimize the wall length or the corridor surface area.

Thus one of the major objectives that remains is to carry out multi-criteria optimization.The optimal geometrical solution of each topological solution is displayed in a collector

of geometrical solutions. The most important function of this collector is to realize a

classification of the topological solutions from the minimal objective function value ofthe geometrical solutions related to each topology. It can be noted that several

geometrical solutions can correspond to the same optimum. In that case, they are all

enumerated.

Figure 9. Some optimal geometrical solutions of the house with two floors.


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3 Conclusion

Several results could be inferred from reviewing computational approaches to

space layout planning at the first glance:

1. There is a demand for more comprehensive software to simplify the designprocess.2. Different techniques and methods are presented in this field where each has

focused on different areas of space layout planning and optimization.

3. Most of these approaches have stopped in the research stage and are not evolvedinto the marketing stage.

To get to the point, one of the reasons that these programs are not applicable inthe marketing stage is their excessive runtime. On one hand, the runtime of these

programs increases exponentially by increasing the objectives so that the program can not

handle calculating complexities. On the other hand, the best application of such programscould be the complex projects. In fact, architects usually have enough experience and

knowledge to solve the design objectives in small projects that they do not need to use

additional helping software. Furthermore, architects are capable to consider aesthetic

aspects of design while this job is not easy for programmers.

Future work would involve finding the best program among the presentedmethods which its runtime could become close to a linear function of the number of

objectives. Also, according to the limitations that exist in using different forms for

different spaces, the chosen program should be able to present solutions at the end of

topological stage. This will let the architect to use his tact and aesthetic aspects in thedesign.

In fact, an imaginable near future for these approaches, is the situation that the

software could help the architect in the design process especially in analyzing and

optimizing tasks. It is important to highlight that the software should be an assistant to thearchitect and not the opposite.

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A Survey of Computational Approaches to Space Layout Planning

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