Generation of variational standard plant room solutions

Generation of variational standard plant room solutions

Benachir Medjdoub a,*, Paul Richens a, Nick Barnard b,1

aThe Martin Centre, University of Cambridge, 6 Chaucer Road, CB2 2EB, Cambridge, UKbOscar Faber, Marlborough House, Upper Marlborough Road, St. Albans, Herts AL1 3UT, UK

Accepted 10 January 2002

Abstract

We have used the object-based CAD programming to take advantage of standardisation to handle the selection, sizing,

layout and (potentially) pipe routing for Low-Pressure Hot Water (LPHW) plant rooms in buildings. Our approach combines

automation and interactivity. From a simple specification of the plant room geometry (an orthogonal polygon with known

obstructions, openings and external walls), and the heating load in kW, our software proceeds through a number of steps. First,

the number and size of standard modular boilers, pumps, etc., are determined from the heat load. Then, a compatible optimising

3D variational solution is generated, using Constraint Logic Programming. To do this, we firstly enumerate a satisfactory

topological solution, and then refine it to form a compatible geometrical solution. The final step generates pipe routes, using

optimisation techniques to minimise the length of pipes and the number of bends. The solution obtained can be modified or

improved by the designer, for which we have interactivity. Modifying the topology of the solution or the geometry of the plant

room is done directly through the graphic interface, e.g. modifying a boiler position is done by dragging; the system

automatically updates the 3D model including the pipe routing while maintaining all the design rules. The solutions generated

by our prototype have been tested against conventional solutions in a benchmarking exercise. Advantages have been underlined

and suggestions for further development have been made.

D 2002 Published by Elsevier Science B.V.

Keywords: Plant room; Pipe routing; Layout configuration; Topological solutions; Interactive modification; Space minimisation

1. Introduction

Standardisation is widely recognised as a key ele-

ment in reducing design time, cutting construction

costs and ensuring efficient design solutions. If the

design of any complex artefact is suitably restricted by

adhering to a library of predefined components and

assembly details, it becomes possible to automate a

great deal of the design process. In the case of heating

and ventilation plants, there are in any case good value-

engineering reasons to use standard components and

details.

Currently, designers solve these problems ‘‘by

hand’’. Starting from the heating load in kW, a

schematic solution is defined. The engineers proceed

to equipment selection, then its location, followed by

pipe routing governed by objective requirements

(minimum surface area, minimum pipe length, mini-

mum bend number. . .). In summary, plant room

physical design amounts to layout configuration fol-

lowed by pipe routing.

0926-5805/02/$ - see front matter D 2002 Published by Elsevier Science B.V.

PII: S0926 -5805 (02 )00006 -7

* Corresponding author. Tel.: +44-1223-331714; fax: +44-

1223-331701.

E-mail addresses: [email protected] (B. Medjdoub),

[email protected] (N. Barnard).1 Tel.: +44-181-784-5784; fax: +44-181-784-5700.

www.elsevier.com/locate/autcon

Automation in Construction 12 (2002) 155–166

Computer support for layout configuration has been

studied for more than 20 years. Studies include techni-

ques such as mathematical programming [1], expert

systems [2,3], genetic evolution [4–6] and constraint

satisfaction [7–9]. Contrary to the aforementioned

approaches to space planning based on full automation,

our approach combines automation and interactivity.

In pipe routing, many problems have been ad-

dressed with genetic algorithms (GA) approach. In

Ref. [11], GA has been used to automate pipe routing;

this approach is limited to 2D and a same line segment

in the solution could represent several pipes. Another

approach based on the Steiner tree has been used to

solve problem routing in the presence of obstacles [12];

this approach is also limited to 2D.

Our approach to plant room design combines auto-

mation and interactivity. From a simple specification of

the plant room geometry (an orthogonal polygon with

known obstructions, openings and external walls), and

the heating load in kW, our software proceeds through a

number of steps (see Fig. 1). First, the number and size

of standard modular boilers, pumps, etc., are deter-

mined from the heat load. Then, a compatible optimis-

ing 3D variational solution is generated, using

Constraint Logic Programming and particularly the

arc-consistency [13] on integers. To do this, we firstly

enumerate a satisfactory topological solution, and then

refine it to form a compatible geometrical solution. The

final step generates pipe routes, using branch and

bound optimisation to minimise the length of pipes

and the number of bends. Heuristics are used to restrict

the search to promising areas of the solution space. In

this NP-complete problem, dynamic variable ordering

(dvo) heuristics can have a profound effect on the

performance of backtracking search algorithms [14–

16]. Tsang et al. [17] showed that it does not appear to

be a universally best algorithm, and that certain algo-

rithms may be preferred under certain circumstances.

The solution obtained can be modified or improved

by the designer, when we provide further contribution

by concentrating on interactivity. Modifying the top-

ology of the solution or the geometry of the plant room

is done directly through the graphic interface, e.g.

modifying a boiler position is done by dragging; the

system automatically updates the 3D model including

the pipe routing while maintaining all the constraints.

We describe the standard solution design process

in Section 2. The object model of the plant room and

the plant room design rules are presented in Sections

3 and 4. The enumeration algorithm is described in

Section 5. In Section 6, the user interface and

interactivity are presented. Before concluding, the

implementation and benchmarking are presented in

Section 7.

2. Standard solution design process

Applications most suited to standardisation are

characterised by:

� a high degree of repetition between jobs,� a limited number of practical variations, and� minimal interaction with other disciplines and

services.

Fig. 1. Solution levels in our approach.

B. Medjdoub et al. / Automation in Construction 12 (2002) 155–166156

Plant rooms are good examples of suitable

applications. The standard solutions were developed

in consultation with practising engineers. They are

essentially a collection of rules that address the

selection, sizing and location of services equipment.

The rules are in a number of different forms

including:

� Schematics,� Written rules,� Geometric layouts.

The selection of systems for the plant room is based

on its function, e.g. heating, cooling, air handling,

electrical, etc. The selection of equipment for each

system will then be a standard solution defining the

number of plant items and the interconnection config-

uration required to perform the function [18]. These

solutions are typically manifested in the form of sche-

matics (see Fig. 2). Sizing will generally require data in

the form of loads, together with rules. The data may be

calculated externally, generated on the basis of a rule-

of-thumb or supplied from another plant item. For

example, boilers will require a heat load for sizing that

may initially be estimated using a rule-of-thumb based

on the building area, to be replaced by a calculated

value as the design evolves. When the number of plant

items to perform the function is defined, two steps

remain to reach the final solution: item location and

pipe routing.

The location of equipment can be approached from

two extremes. One extreme is to devise a solution

where the general arrangement of the (main) equip-

ment is predetermined on the basis of a fairly rigid set

of rules. This is appropriate for new buildings where

there may be a degree of flexibility concerning the

size and configuration of the plant room. The other

extreme would be to allow the plant to be placed

randomly within the space available. This would

allow it to fit into plant rooms of various sizes. A

number of possible configurations could be produced

and the best selected according to a number of judge-

ment criteria, e.g. spatial requirement, cost, etc. Fig. 3

shows some preferred layouts of modular boilers,

based on general location rules (written rules).

� The boiler room is usually in a separate space

(must be separated from chillers).� Each piece of equipment requires a minimum

maintenance space around it.� All equipment is on a plinth 100 mm high.� Access routes are provided through plant areas:

2000 mm is ideal, 1500 mm is the minimum

requirement.� Double doors leading to the plant room are re-

quired.� A single door for emergency escape must be

located opposite to the main door.� Boiler location is side by side.� Boilers back against a wall.

Fig. 2. Heating system schematic.

B. Medjdoub et al. / Automation in Construction 12 (2002) 155–166 157

As soon as the plant room layout is defined, we

proceed to pipe routing. The priority is for horizontal

orientation minimising the number of bends and the

pipe length.

3. Object model of the plant room

The plant room object model holds three main

classes of objects representing the plant room geom-

etry, equipment and pipework. Each defined class is

characterised by attributes and class constraints.

3.1. Plant room geometry

The plant room geometry can be an orthogonal

polygon with known obstructions, openings and exter-

nal walls. We can also provide columns (see Fig. 4).

The object structure of the plant room geometry

includes three classes: space, door and column. Each

class is characterised by a reference point (x, y, z), a

length l, a width w and a height h. In Fig. 4, the plant

room is an L-shape with two doors and one column.

The L-shape corresponds to: space1–space2. The

reference points, l, w and h are integer-constrained

variables. We use an arc-consistency2 on integers

constraint programming technique, which explains

the need for a distance increment; but this is not too

restrictive as the scale used is the millimetre. We do

not need orientation variables for the plant room

objects because the layout generation process is done

for known plant room geometry. Thus, the geomet-

rical parameters of the plant room objects are con-

strained variables with one value. In the case of a

nonrectangular prism (e.g. circular column), its

bounding box will be considered in the computation-

al process.

3.2. Equipment

The equipment is described in four subclasses:

boiler, pump, pressurisation unit and control panel.

Each class is characterised by a reference point (x1, y1,

z1), a length l, a width w, a height h, and an orientation

ori. The reference point, l, w and h are integer-con-

strained variables. The orientation attribute is a con-

strained discrete variable defined over the domain

{0j, 90j, 180j, 270j}, the length, the width and the

height are fixed variables. As is indicated in Fig. 5,

each piece of equipment requires a minimum space

for the maintenance. A class constraint is defined to

ensure the four possible configurations corresponding

to the four possible orientations. This constraint gen-

erates a choice point leading to four constrained

subproblems; these are shown in Fig. 6.

3.3. Pipework

The pipe class is defined by a set of points and a

radius r (see Fig. 7). Each pair of successive points

defines a segment of the pipe (i.e. (P1,P2), (P2,P3)

and (P3,P4) are the three segments of the pipe shown

Fig. 3. Favourite geometric layout.

2 ‘‘If there is a binary constraint Cij between the variables xi and

xj, then the arc (xi; xj) is arc consistent if for every value aaDi (Di is

the domain of xi), there is a value baDj such that the assignments

xi= a and xj= b satisfy the constraint Cij. Any value aaDi for which

this is not true, i.e. no such value b exists, can safely be removed

from Di, since it cannot be part of any consistent solution: removing

all such values makes the arc (xi; xj) arc consistent. Note that we

have only checked the values of xi; there may still be values in the

domain if xj which could be removed if we reverse the operation and

make the arc (xj, xi) consistent’’ [13].


Fig. 4. Plant room geometrical representation.

Fig. 5. Geometrical representation of the plant room equipment.


in Fig. 7). An orientation ori is associated with each

part. All the attributes are integer-constrained variables

except the orientation, which is a constrained discrete

variable defined over the domain {xj, yj, zj}. A class

constraint is defined to ensure that two successive parts

have different orientation. We consider the number of

bends equal to the number of pipe segments minus 1.

Two following class constraints have been defined

so as to ensure the geometry consistency of the pipe.. The segment connection constraint:

Segment connection constraint (I: list-of-succes-

sive-segments)

n= length (l)

P1 = segment starting point

P2 = segment end point

For i varying from 1 to n� 1

segmenti�P2�x = segmenti�P1�xsegmenti�P2�y = segmenti�P1�ysegmenti�P2�z = segmenti�P1�z

End constraint

. The orientation constraint:

Orientation constraint (I: list-of-successive-seg-

ments)

n = length (l)

For i varying from 1 to n� 1

segmenti�orientation p segmenti + 1�orientationEnd constraint

4. Plant room design rules

The plant room design rules are expressed by

constraints. These constraints are applied implicitly

by the system and can be divided into two categories:

topological and dimensional. Topological constraints

define continuity and neighbourhood in a building,

while dimensional constraints define distances and

angles [19].

4.1. Dimensional constraints

Dimensional constraints assign a minimal or a

maximal value to the object-constrained variables.

This constraint is expressed by equality or inequality,

i.e. boiler�l= 532.

4.2. Topological constraints

Topological constraints comprise:

� Inclusion constraint, i.e. all the objects are inside

the plant room.

Fig. 6. The four possible orientations of the boiler.

Fig. 7. Geometrical representation of a pipe with a set of four points

(P1, P2, P3, P4) corresponding to two bends.


� Non-overlapping constraint between the plant

room components and pipework.� Adjacency constraint, i.e. between the control

panel and the walls.

4.2.1. Inclusion in the plant room

This simple constraint consists of four conjunctive

inequalities over x1, x1, z1, y2, y2, z2 in order to be

inside of the current plant room. In the case of L-

shape or T-shape (see Fig. 3), equipment and pipe-

work are inside space1 and do not overlap space2.

4.2.2. Non-overlapping

A non-overlapping constraint expresses the fact

that two elements cannot overlap each other; it is

automatically applied between all pairs of elements.

Fig. 8 shows the position permitted for e2�x2, e2�y2and e2�z2 (e2�z2 represents the constrained variable z2of element e2) by the non-overlapping constraint

between two elements e1 and e2. The non-overlap-

ping constraint introduces a new non-overlapping

variable with six values {E,W,N,S,A,U}. This varia-

ble divides the space surroundings into six parts (see

Fig. 8) but not symmetrically. Indeed, we observe

that the N and S values give more solutions than the

E and W values. This asymmetry is made to avoid

any redundant solution. It is the instantiation of these

non-overlapping variables and the adjacency varia-

bles, which if proven consistent, gives a topological

solution.

The non-overlapping constraints between plant

room equipment introduce variables with four values

{E,W,N,S} as they are all on the same floor. Between

the pipework and the equipment, the variables gen-

erated have five values {E,W,N,S,A}, as the pipework

can be located above the equipment.

4.2.3. Adjacency

The adjacency constraint is applied between the

control panel and the plant room walls.

The application of this constraint creates a new

discrete constrained variable named adjacency varia-

ble defined over the domain {E,W,N,S}, standing for

east, west, north and south walls. In fact, each

adjacency constraint and its consequent adjacency

variable introduce a choice point in the tree search

(see Fig. 9). The adjacent constraint is a ‘‘dæmon’’

constraint for which an instantiation of the adjacency

variable triggers a propagation and consequently, a

domain reduction, thanks to the arc-consistency tech-

nique. During enumeration, corner solutions are only

enumerated once.

In our application, the following disjunctive form is

supported: e1(adjacent#1)e2 or e1(adjacent#2)e3 with

Fig. 8. General non-overlapping constraint.


e2 p e3. It is applied in the case of L-shape or T-shape

plant room. In Fig. 2, the control panel is constrained to

be adjacent to space1 walls or to space2 walls.

5. Enumeration algorithm

To generate the solution, we follow two steps.

First, we generate the plant room layout, which

determines the equipment location. Then, we proceed

to pipe routing minimising the length of pipes and the

number of bends.

5.1. Plant room layout generation

In this step, our objective is to enumerate the first

satisfactory topological solutions, and then refine it to

form a 3D compatible geometrical solution.

The topological solution is based on Medjdoub and

Yannou [10] definition: Each space layout Constraint

Satisfaction Problem (CSP) where the n(n� 1)/2 (n

being the number of items) non-overlapping variables

and adjacency variables are instantiated and which

remain geometrically consistent (i.e. for which at least

one geometrical solution exists) is a topological sol-

ution.

Contrary to Medjdoub’s approach, we enumerate

just the first satisfactory topological solution. Dy-

namic variable ordering (dvo) heuristics are used to

restrict the search to promising areas of the space tree.

These heuristics are not only used for a better per-

formance of the backtracking search algorithms, but

also to lead to a better topology solution if it exists.

Thus, the designer can select from the user interface

(by choosing between vertical or horizontal layout as

indicated in Fig. 2) which topology the search algo-

rithm will investigate first. This choice drives the

heuristic behaviours. First, the pieces of equipment

are ordered as follow: boilers, pumps, pressurisation

units and control panels. In the case of horizontal

layout configuration, we start by instantiating the non-

overlapping variable between the second and the first

boiler in the list. The ‘‘east’’ orientation value will be

chosen first to guarantee the alignment between the

two boilers. If the choice is not consistent, we back-

track and we choose the ‘‘south’’ value to ensure that

the two pieces of equipment will be paralleled and

aligned to the ox axis. We do this until all the non-

overlapping constraints are instantiated, then we

obtain the topological solution.

To refine the topological solution to a 3D geo-

metrical solution, we instantiate the geometrical

parameters of the plant room equipment. We use the

classical dvo heuristic for ordering the geometrical

variables, thus, the priority is given to the variable

with the smallest domain. Because of the arc-consis-

tency technique on integers, which deals with discrete

variables, the system performs well particularly on

orthogonal polygon layouts.

5.2. Pipe routing

The pipe routing is the last step of the enumeration.

As soon as we have obtained a consistent 3D geo-

metrical solution, we determine from our user inter-

face the wall through which the Low-Pressure Hot

Water (LPHW) mains pass. The algorithm proceeds in

three steps. First, the bends number variables are

instantiated, the smallest values being chosen first.

Then, the non-overlapping variables between pipes

and pipes/equipment are instantiated. Finally, we

instantiate the pipe reference points minimising the

length of each pipe using the ‘‘branch and bound’’

algorithm [20]. This is the most common approach

used in constraint programming to find the optimal

solution. First, we create a constrained variable rep-

resenting the objective function and find an initial

solution, then we introduce a new constraint that the

value of the objective variable must be better than in

Fig. 9. Adjacency between the control panel and the plant roomwalls.


the initial solution. We repeatedly solve the new

problem and tighten the constraint on the objective

variable until the problem becomes insoluble: the last

solution found then is the optimal solution [13]. Fig.

10 shows three different solutions of two pipes with

different z1 and z2.

6. User interface and interactivity

Our approach is based on interactivity. The user

interface is composed of several panels as it is shown

in Fig. 11. As an example, we are going to generate

and modify a plant room of 1 MW, and demonstrate

how easy it is to use this system.

The first step is to generate the first satisfactory

solution (see Fig. 12b) from the defined plant room

geometry (see Fig. 12a). In this example, the heuristic

of a vertical layout has been selected. The second step

is to generate pipework; to do this, we select the wall

where the LPHW and the flue pipe pass through and

run the search algorithm by clicking on a button. As

indicated in Fig. 12c, the LPHW pipes pass through

the north wall and the flue pipe passes through the

west wall. After obtaining a complete 3D solution, it

is possible to make any modification. To modify the

pipes passing through walls, we just have to select

them and drag them around the walls. The flue pipe is

dragged from its initial position (see Fig. 12c) to a

new one as indicated in Fig. 12d. The same search

algorithm of pipe routing is used with fixed values for

all the pipes except the flue pipe.

Other features are offered by the system: plant room

geometry modification and topology modification.

Through the user interface, it is possible to modify

the shape or size of the plant room and to add, move or

delete columns and doors. From the examples shown

in Fig. 12d, by simply dragging the plant room

geometry, the system generates a new solution corre-

sponding to the new updated plant room geometry.

Thus, it is very easy to minimise the plant room area

while maintaining all the constraints, i.e. the solution

shown in Fig. 12e corresponds to the minimum plant

room area for 1 MW. If the designer would like to

explore other topologies, he/she has to simply select

the component and drag it to the desired position. The

system generates a new solution with the desired new

topology. If no solution exists, the previous one is

maintained. The interaction between automation and

interactivity is driven by the mouse state. When we

select and drag a piece of equipment, we are in the

interactive mode, thus, the system behaves as a clas-

sical CAD tool. When the mouse is up, we move to the

automatic mode, thus, the new situation generated by

the dragging routing will be solved (e.g. if we drag a

boiler on the east of the pump, as soon as the mouse is

up, the system will try to find a solution automatically

corresponding to the new topology).

7. Implementation and benchmarking

This application is developed in Java Modeling

Language (JMDL) as embedded in MicroStation/J,

Fig. 10. Three different pipework solutions.


and ECLiPSe3, the Constraint Logic Programming

system. We use Java Native Interface (JNI4) as the

programming interface between ECLiPSe and JMDL.

We use MicroStation/J5 to hold the object model and

for 3D rendering.

The final stage of the work was to benchmark

the implemented standard solutions against current

practices, which are typically in the form of sche-

matics (see Fig. 2). Benchmarking focussed on the

space requirements of the solutions and the layout

configuration [21,22]. Thanks to the space allow-

ance optimisation used to minimise the plant room

surface area and the heuristics, the benchmarking

showed that the implemented solutions were in

close current design practice as indicated in Fig.

3. The solutions were also comparable to current

designs in terms of equipment selection and sizing.

From this benchmarking exercise, advantages have

been underlined and some comments have been

made in order to improve the system.

The main comments are:

� The pipe routing and more precisely the

interactivity of pipe modification need to be

improved. The designer should be able to mod-

ify interactively the position of bends inside the

plant room.� The system is limited to orthogonal polygon (L-

shape and T-shape) problems.� The system does not deal with complex geo-

metry.� The system cannot solve large models over 2 MW.

The main advantages are:

� The interactive layout modification.� The interactive plant room area minimisation has

been particularly appreciated.� The 3D solution.

The outputs from the implemented tools and the

benchmarking exercise have demonstrated that it is

Fig. 11. User interface panels.

3 ECLiPSe is a trademark of IPC-PARC at Imperial College

London.4 JNI is a trademark of Sun Microsystems.5 Microstation/J is a trademark of Bentley Systems.


possible to produce reasonable designs using standard

solutions. Our approach deals with middle size prob-

lem (50 objects and 15 connections) because of the

NP-completeness of the problem.

8. Conclusion

The use of standard solutions in conjunction with

IT has the potential to significantly reduce design

costs by reducing design time, for which it is esti-

mated to be typically in the region of 10–20% [18],

improve quality and produce additional benefits else-

where in the supply chain. The idea to have a com-

promise between full automation and interactivity

gives the designer full control of the design while as-

sisting him to solve complex problems automatically.

This compromise is the main difference with the

aforementioned approaches in space planning and

pipe routing. Several aspects were discussed: the con-

straints and the plant room item structure, the algo-

rithm of solution enumeration.

Fig. 12. (a,b,c,d,e,f) 1 MW plant room solution and its modification.


The implemented user interface shows an interac-

tive system for plant room design; easy to use with

high-level modification of plant room layout topol-

ogy, pipework position and plant room space geom-

etry. Output from the solutions such as 3D visual-

isation is beneficial to other parties in the supply

chain.

Acknowledgements

This project is funded by EPSRC6 and DETR7

under the LINK8 Meeting Client Needs through

Standardisation programme in UK. There are more

than 10 partners including Oscar Faber, BSRIA,

Hamworthy3, Pullen Pumps, Bentley Systems, Tay-

wood Engineering, The SCI, Sainsburys, Sheppard

Robson, Carrier, Woods, Waterloo, Delta, Biddles,

CADAC, and IES Facet.

The programming was carried out at the Martin

Centre CADLAB (University of Cambridge, Depart-

ment of Architecture), which is supported by

Informatix of Tokyo.

References

[1] W.J. Mitchell, J.P. Steadman, R.S. Liggett, Synthesis and op-

timization of a small rectangular floor plans, Environment and

Planning B (3) (1976) 37–70.

[2] J.M. Andre, Vers un systeme d’aide intelligent pour l’ame-

nagement spatial: CADOO, Colloque International d’IA de

Marseille (1986) 31–48.

[3] U. Flemming, A generative expert system for the design of

building layouts, Artificial Intelligence in Engineering: De-

sign, Elsevier, New York, 1988.

[4] J.H. Jo, J.S. Gero, Space layout planning using an evolution-

ary approach, Artificial Intelligence in Engineering 12 (3)

(1998) 149–162.

[5] J.S. Gero, V.A. Kasakov, Evolving design genes in space lay-

out planning problems, Artificial Intelligence in Engineering

12 (3) (1998) 163–176.

[6] M.A. Rosenman, The generation of form using an evolution-

ary approach, in: J.S. Gero, F. Sudweeks (Eds.), AI in Design

’96, Kluwer Academic Publishing, Netherlands, 1996, pp.

643–662.

[7] C. Baykan, M. Fox, Constraint Satisfaction Techniques for

Spatial Planning, in: P.J.W. ten Hagen, P.J. Veerkamp (Eds.),

Intelligent CAD Systems III, Practical Experience and Evalu-

ation, Springer Verlag, Berlin, 1991, pp. 187–204.

[8] A. Aggoun, N. Beldiceanu, Extending CHIP in order to solve

complex scheduling and placement problems, Mathematical

and Computational Modeling 17 (7) (1993) 57–73.

[9] Ph. Charman, Une approche basee sur les contraintes pour la

conception preliminaire des plans de sol, CERMICS-INRIA,

France, 1994.

[10] B. Medjdoub, B. Yannou, Separating topology and geometry in

space planning, Computer Aided Design 32 (1) (2000) 39–61.

[11] D.G. Kim, Automated pipe route generation using genetic

algorithms, MSc thesis in Information Technology: Knowl-

edge Based Systems, Department of Artificial Intelligence,

University of Edinburgh, 1995.

[12] J.L. Ganley, J.P. Cohoon, Routing a multi-terminal critical net:

Steiner tree construction in the presence of obstacles, Proceed-

ings of the International Symposium on Circuits and Systems,

1994, pp. 113–116.

[13] B.M. Smith, A Tutorial on Constraint Programming, Report

95.14, School of Computer Studies, University of Leeds, UK,

1995.

[14] F. Bacchus, P. van Run, Dynamic variable ordering in {CSPs},

in: U. Montanari, F. Rossi (Eds.), Principles and Practice of

Constraint Programming, Lecture Notes in Computer Science,

Cassis, Springer Verlag, France, 1995, pp. 258–275.

[15] I.P. Gent, et al., An empirical study of dynamic variable order-

ing heuristics for the constraint satisfaction problem, in: E.C.

Freuder (Ed.), Principles and Practice of Constraint Program-

ming, Lecture Notes in Computer Science, Springer Verlag,

Berlin, 1996, pp. 179–193.

[16] B.M. Smith, S.A. Grant, Trying harder to fail first, in: H. Prade

(Ed.), European Conference on Artificial Intelligence (ECAI),

Wiley, UK, 1998, pp. 249–253.

[17] E.P.K. Tsang, J.E. Borrett, A. Kwan, An attempt to map the

performance of a range of algorithm and heuristic combina-

tions, Hybrid Problems, Hybrid Solutions, Proceedings of

AISB, IOS Press, Amsterdam, 1995, pp. 203–216.

[18] N. Barnard, Building Services Standard Solutions: Rules and

Data, Oscar Faber report R16998, St. Albans, Hertfordshire,

England, 1999.

[19] Ph. Boudon, et al., La geometrie chez l’architecte: Etude ex-

ploratoire, UP-architecture, Nancy, France, 1972.

[20] G. Carpaneto, M. Dell’amico, P. Toth, A branch-and-bound

algorithm for large scale asymmetric travelling salesman prob-

lems, ACM Transactions on Mathematical Software 21 (1995)

410–415.

[21] M. Hejab, C. Parsloe, Space and weight allowances for build-

ing services plant, The Building Services Research and Infor-

mation Association, Technical Note TN 9/92, Bracknell,

Berkshire, England, 1993.

[22] P. Burberry, Space for services: 5. Distribution and sizing,

Architects’ Journal (5 March 1986) 32–36.

6 The Engineering and Physical Sciences Research Council.7 The Department of Environment, Transport and the Regions.8 The LINK scheme is the UK Government’s principal

mechanism for promoting partnership in pre-competitive research

between industry and the research base.


Generation of variational standard plant room solutions

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