Invited Review

A review of major paradigms and models for the design of civil

engineering systems

L. Valadares Tavares

*

Department of Civil Engineering, Technical University of Lisbon, CESUR, Instituto Superior Tecnico, DEC-IST, Av. Rovisco Pais,

1000 Lisbon, Portugal

Received 1 November 1998; accepted 1 November 1998

Abstract

In this paper, the author presents the ®ve classical paradigms of the process of design in civil engineering and

identi®es a new emerging paradigm: the interactive multi-attribute learning paradigm. This paradigm is studied in terms

of actors, structures and OR instruments which can help to ful®l its application to modern design of civil engineering

systems. Ó 1999 Elsevier Science B.V. All rights reserved.

Keywords: Design; Civil engineering system; Multi-attribute decision making; Paradigm

1. The evolution of the design of civil engineering

systems: Paradigms and challenges

Civil Engineering is devoted to the design and

construction of systems aiming to improve the con-

ditions of social, economic and environmental life.

It is one of the oldest types of engineering as it

was born to ful®l very basic needs of life such as

sheltering, transportation and river control. Some

of the most spectacular glories of the golden years

of technology at the beginning of this century were

achieved by civil engineers such as the railways

adventure, the heights of the new skyscrapers or

the irrigation of deserts by arti®cial lakes con-

tained by new types of dams (Reynolds, 1991).

Nowadays, it remains one of the most signi®-

cant branches of the profession of engineering as it

is shown by indicators such as the percentage of

aliates in engineering societies who are civil en-

gineers or the turnover of civil engineering ®rms

(Florman, 1994).

Creativity (Torrance, 1995) is the key ingredient

for any process of design and Civil Engineering is

no exception. However, the design of civil engi-

neering systems depends also heavily on the

adopted approach which had a very signi®cant

evolution not just described by the progress of the

available technology but also by the way how the

problem of design is formulated. The formulation

of this problem depends on the data and on the

scienti®c results which can be used, (see Vries et al.,

1993) and it describes the speci®c civil engineering

culture of each stage of this process of evolution.

European Journal of Operational Research 119 (1999) 1±13

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*

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The study of such process can be done by the

analysis of the paradigm adopted in each stage to

formulate and solve the process of design (see

Simon, 1969).

The evolution of this paradigm is closely con-

nected to the type of model related to formulate the

problem of design and most of the recent devel-

opments in modelling are based and OR method-

ology and tools.

Until the forties, a lot of expertise to design civil

engineering was accumulated and presented

through empirical relations connecting:

(a) natural exogenous conditions (G) with the

corresponding design loads (L), and

(b) the design loads (L) with the design variables

(X) to be adopted for the civil engineering sys-

tem.

Common examples are:

· G ˆ catchment area of a river basin; L ˆ design

storm; X ˆ reservoir capacity.

· G ˆ expected population using a parking lot;

L ˆ required capacity; X ˆ parking area and size

of access lanes.

In this stage, the activity of design is basically

carried out using models with an empirical nature:

Paradigm A ± The empirical model:

L ˆ f …G†;

X ˆ g…L†:

The important development of analytical

methods since the forties has enabled the substi-

tution of the empirical relationship g(L) by a static

deterministic description of the civil engineering

system relating the design loads (L) with the re-

sponse variables (R). This static model is usually

based on energy equilibrium conditions (e.g., for

structural design), on inventory models (e.g., for

the design of reservoirs) or on mass conservation

laws (e.g., for the design of water supply net-

works). Thus, the previous paradigmatic model

was substituted by the following paradigm:

Paradigm B ± The static descriptive deterministic

method

L ˆ f …G†;
R ˆ q

0

…L; X

0

†;

X

00

ˆ q

00

…R†;

where q

0

is the static behaviour function and X

0

is

a set of design variables. The design is complete by

setting up another set of design variables, X

00

, in

terms of R, X

00

ˆ q

00

(R), in order that the system

will cope adequately with the response variables

(see Templeman, 1982).

This type of model can be illustrated by the

example of designing a structure in terms of the

speci®ed load (L) where X

0

is the set of parameters

de®ning the structure (geometry, weight, etc.), R is

the set of the generated stresses at key sections of

the structure and X

00

includes the design parame-

ters (type of materials, etc.) achieving sucient

resistance to cope with such stresses.

This approach implies a good deal of inspira-

tion and of experience to set up good X

00

solutions

and the full understanding of the response func-

tions.

The rapid development of science and technol-

ogy after the second world war has provided Civil

Engineering with more e€ective models to describe

the uncertainty and the stochastic nature of the

system's loads and with more accurate models to

describe the physical behaviour of the designed

systems.

The former results have allowed the develop-

ment of advanced risk analyses (Ang and Tang,

1975) and the latter ones have suggested a wide

spectrum of new technological solutions.

This means that (L) is then substituted by a

stochastic process (see, e.g., Tavares, 1977) of the

occurring loads L ˆ fL

t

g and that the static de-

terministic descriptive model can be substituted by

the following static stochastic descriptive model:

Paradigm C ± The static stochastic descriptive

model:

L ˆ fL

t

=Gg;

R ˆ q

0

…L; X

0

†;

X

00

ˆ q

00

…R†;

S…R; X

00

† P a;

where S…R; X

00

† P a is a safety condition being

S…R; X

00

† the probability of non-failure and a the

minimal safety threshold (Ang, 1972; Mass et al.,

1962; Ferry-Borges and Castanheta, 1971).

The formulation of the system's behaviour in

terms of the probabilistic de®nition of its safety is

2

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

the major advantage of this model over B. More

recently, a further model has been proposed con-

sidering the dynamic behaviour of the system, the

dynamic stochastic descriptive model:

Paradigm D ± The dynamic stochastic descrip-

tive model:

L ˆ fL

t

=Gg;

R ˆ q

0

…L; X

0

; t† for 0 6 t 6 T ;

X

00

ˆ q

00

…R†;

s

k

fR; X

00

g 6 a

k

for k ˆ 1; . . . ; k;

where k ˆ 1; . . . ; K corresponds to each mode of

safety to be considered.

This model has been successfully applied to a

wide range of systems under loads generated by

turbulence processes, strong winds, ocean waves,

earthquakes, track unevenness, etc. Usually, the

safety restrictions include a ®rst set of conditions

on the moments and a second set on the maximal

and minimal eigenvalues (Nigam, 1986).

The models C and D require the collection and

treatment of much larger volumes of numerical

data conveniently distributed on time and on

space. This has become feasible due to the expo-

nential advances of the data and computer systems.

The study of R is usually carried out by the sim-

ulation methodology using extensive numerical

experimentation. This formulation can be trans-

formed into the classical problem of the Optimi-

sation Theory where the objective will be expressed

by a scalar objective function, F, and by a set of

restrictions (Rao, 1978; Rau, 1970; Tillman et al.,

1980) producing a new paradigm:

Paradigm E ± The single criterion optimisation:

max

min u ˆ F …L; X †

h

1

…L; X † P 0;

h

2

…L; X † P 0;

h

3

…L; X † P 0;

h

4

…L; X † P 0;

h

5

…L; X † P 0;

with u a scalar function such as the cost to be

minimized or the stability to be maximized, L the

uncontrolled variables and X the decision vari-

ables, h

1

a ®rst set of restrictions describing the

physical behaviour of the system, h

2

a second set of

restrictions de®ning the feasible domains of the

decision variables, h

3

a third set of restrictions

describing legal and normative conditions, h

4

a

fourth set of restrictions describing constraints on

other attributes also important to assess the im-

pact and quality of the achieved design, and h

5

a

®fth set of restrictions concerning the safety

probabilistic conditions.

The theory of optimisation has been intensively

used to ®nd out the design solution achieving the

maximal or minimal value for u.

The modelling of L, the use of simulation

methods to study R and the optimisation of F are

three major contributions of Operational Research

to the theory and the practice of the design of civil

engineering systems (models B, C, D and E).

During the last decades, criticism about less

successful civil engineering projects have grown up

all over the world and the need to avoid the per-

verse e€ects of technology has become a dominant

feature of our modern culture (see, e.g., Ellul,

1964; Mumford, 1967; Reich, 1970). Therefore,

new challenges are demanding for more harmonic,

comprehensive and interactive models of the pro-

cess of design in civil engineering:

· the need to give additional attention to the pres-

ervation of environmental conditions;

· the need to design systems better integrated

into the social, economic and political environ-

ments;

· the need to pro®t from new technologies to en-

hance the performance of the designed systems;

· the need to guarantee higher levels of quality

and of its perception by the users;

· the need to achieve higher levels of economy,

particularly in terms of scarce natural resources

such as land, space, water or energy;

· the need to combine the physical design with the

®nancial and commercial design in order that

the feasibility, the eciency and the pro®tability

of the obtained solutions will be maximised;

· the need to consider in the process of design a

wider range of actors and stakeholders through

more or less structured systems (public audits,

groups of advisors, etc.).

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

3

Answering to these needs implies a signi®cant ef-

fort to develop a new paradigm which should be

based on three major principles:

· the design is a complex decision process involv-

ing the interaction of multiple actors due to the

multi-sectoral e€ects of the selection of any de-

sign;

· most of these actors can have di€erent values,

objectives and preferences due to their di€erent

nature;

· the search for a better design implies a learning

process based on multiple comparisons of di€er-

ent alternatives due to the complexity and mul-

tiplicity of relevant perspectives

Thus, the new emerging paradigm can be called

the interactive multi-attribute learning paradigm:

Paradigm F ± The interactive multi-attribute

learning paradigm. The major stages of the process

of design according to this paradigm are:

This approach is much more ``context-orient-

ed'' than the previous paradigmatic models and it

has a cyclic nature as the assessment of the gen-

erated alternatives suggests their improvement.

The applicability of this model requires ecient

and e€ective systems to generate feasible alterna-

tives, to simulate their response, to communicate

their features to the major actors and to assess

their reactions and their preferences.

The adoption of this approach implies also

signi®cant changes in the way civil engineering

design should be taught (Morris and Laboube,

1995).

The recent OR developments provide these in-

struments for most areas of Civil Engineering.

Unfortunately, they are often used to implement

older paradigms rather than to create a new ap-

proach to design civil engineering systems. An il-

lustration of this paradox is the use of visual

computing outputs which just perform the role

played by traditional print-outs rather than es-

tablishing interactive and learning processes with

the actors concerned with the design. The appli-

cation of this new paradigm implies a more de-

tailed analysis of its three major elements:

· identi®cation of actors,

· modelling of structures,

· analysis of instruments.

This is the object of Section 2 where the role of OR

is discussed too.

2. The interactive multi-attribute learning paradigm

for civil engineering design

2.1. The actors

The process of designing a system in civil en-

gineering always should be oriented to ful®l ex-

isting (or forecasted) needs (Feldman and Lindell,

1989). However, the process of understanding,

analysing and modelling such needs is complex not

just because they have multiple attributes but also

because there are di€erent actors involved in the

process of identifying their features:

Bene®ciaries: Those whose needs are supposed

to be ful®lled by the system. Traditionally, these

bene®ciaries are called ``consumers'' as it happens

with the system like a public water supply network

or a commercial centre. However, the concept of

bene®ciary is more accurate because in some cases

there is no e€ective consumption of any good or

service as it may happen if the system is a natural

park.

Users: Those who will participate in the oper-

ation of the system. In most cases, the users are the

same as the bene®ciaries as it is the case of a road,

of a private house or of a commercial area but

many examples of side e€ects illustrate the alter-

native case such as:

(a) the owner of a land which has a much higher

value due to the nearby construction of a high-

way is a bene®ciary but not a user;

4

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

(b) the user of a medical centre which is much

better o€ after a new hospital is opened because

it has decongested that centre is a bene®ciary

but not an user of such a hospital.

The bene®ciaries who do not use the system may

be called indirect bene®ciaries in opposite to the

other ones, direct bene®ciaries.

Pressure groups: The public or private interest is

often supported by pressure groups also active in

the process of decision making about a new engi-

neering system. Nowadays, there is a wide spec-

trum of these groups covering private rights (e.g.,

landowners) or addressing public issues like the

environment.

Promoters: Those who are in charge of the

system's development. They play a crucial role in

de®ning the objectives to be achieved by the design

and, in general, they are the ``client'' of the de-

signer. They also carry out the commercialisation

of the system or they sub-contract such roles to

other institution.

Owners: Those who will possess the system.

Traditionally, they were also the promoters but the

general trend is the opposite one.

Project manager: The person or the institution in

charge of the management of the whole process

from the beginning of the conception of the design to

the implementation and certi®cation of the system.

Builders: Those who will implement the sys-

tem's design.

Financial operators: Those who will provide the

®nancial resources.

Licensing authorities: Those who issue the re-

quired licenses and permit to build the system

Controllers and certi®ers: Those who will con-

trol, audit and certify the implementation of the

approved design.

The general network connecting those actors is

presented in Fig. 1. This means that the process of

identifying the needs to be ful®lled by the designer

and the requirements to be considered is a multi-

actor and dynamic process with multiple levels of

Fig. 1. The network connecting the major actors of the process of design in Civil Engineering.

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

5

analysis and of interaction. A poor expression of

such needs leaves the designer abandoned to his

own preferences and then the ®nal degree of sat-

isfaction tends to be higher for himself than for the

client of the designed systems. Therefore, the

process of design should be supported by appro-

priate representations of the reality (descriptive

models) as well as by systems supporting the

communication, the evaluation, the negotiation,

the upgrading of alternatives until converging to

the ®nal decision.

2.2. The structure

The process of design in civil engineering can

now be substantially improved by the development

of a multi-attribute structure to compare alterna-

tive solutions, to suggest new ones and to support

the process of selection of the most convenient

design (highest total quality).

Such a structure is also an important instru-

ment for communication between the multiple

actors already introduced and it will minimise the

risk of ignoring important unplanned e€ects which

may undermine the utility of the new system.

The proposed framework follows a tree-struc-

ture as is presented in Fig. 2. Tree-structures have

been intensively used in many areas of OR and

hence its contribution can be quite substantial.

The top node of this value tree corresponds to the

total quality of each design alternative which is

branched into three major attributes concerning:

· the process,

· the system,

· the context.

The perspectives most directly relevant to the ac-

tors in charge of the legal, the ®nancial and the

construction decisions are included within the ®rst

branch.

The legal aspects depend strongly on the

country where the system is to be built. Financial

assessment can be much improved by scenario or

simulation models and the study of constructabi-

lity or control is becoming a key area in Civil

Engineering (see, Uhlik and Lores, 1998).

Fig. 2. The proposed value tree.

6

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

The second branch concerns the system itself

and its evaluation stems from three major attri-

butes (aesthetics, functionality, economy) which

can be branched down into groups of three other

more speci®c aspects.

The branch concerning ``ful®lment of needs''

within ``functionality'' can be particularly impor-

tant as it can cover major functional bene®ts to

be taken into account and not considered by ®-

nancial analysis. Recent recommendations about

the use of cost±bene®t analysis are helping to

adopt stable procedures with the purpose of es-

timating the relevant bene®ts (Grin and Ro-

nald, 1998).

The third branch covers the attributes describ-

ing the integration of the system into the envi-

ronmental, social, political and cultural spaces.

The comparative analysis of di€erent designs

implies the application of each of these attributes

to each alternative solution and the construction

of decision matrices following this structure.

The construction of such matrices can improve

the process of de®ning the overall quality (Stevens

et al., 1994), can support the appropriate bench-

marking and can also generate additional and

more convenient solutions.

The construction of this matrix implies the

operationalization of the assessment of each al-

ternative in terms of each attribute which re-

quires the de®nition of an appropriate indicator

with a quantitative or qualitative nature (e.g.,

bad, reasonable, good or very good quality). In

several cases, such assessment can be produced

by the average opinion of a group of experts who

express their opinion along an arbitrary scale

(e.g., 0 ® 10). Probabilistic scales can be also

very useful to assess some features (e.g., the risk

of failure). General suggestions for the assess-

ment in terms of each attribute are presented in

Table 1.

2.3. The instruments

Multiple types of instruments can be applied to

the presented structure based on Multicriteria

Decision Theory and on Negotiation Theory.

Several analyses are particularly important.

2.3.1. Checking the consistency of the decision

matrix data

The assessment of each alternative is not an

easy task and therefore procedures should be im-

plemented to reveal any inconsistency and to cor-

rect it. Models based on Relational Systems of

Preference such as the Pre-Order, Quasi-Order

(Roy, 1985) or Hyper-Order (Tavares, 1988) can

be successfully used.

2.3.2. Elimination of unsatisfactory alternatives

Usually, minimal levels of satisfaction are set

up for each attribute and hence a preliminary

screening can eliminate any alternative not com-

plying with one or more of these levels.

2.3.3. Synthetic assessment of alternatives

A long list of models have been proposed to aid

the process of multi-attribute comparison of dis-

crete alternatives but many of them are hardly

applicable to the studied problem. The most tra-

ditional approach is based on the synthetic as-

sessment of each alternative through a weighted

average of the assessment in terms of each attrib-

ute (compensatory approach). This is the most

common model implying:

(a) a metric scale for the scalar assessing each al-

ternative, i, in terms of each attribute, j, u

ij

.

(b) the transformation of each metric scale into

a value function.

Several models can be used to build such a func-

tion, v, using a constant and linear relation: v

ij

ˆ

…u

ij

ÿ m

ij

†=…M

j

ÿ m

j

† if a higher u

ij

is preferable to

a lower one or v

ij

ˆ …M

j

ÿ u

ij

†=…M

j

ÿ m

j

† other-

wise, M

j

and m

j

being the maximal and the mini-

mal bounds of u

ij

.

These limits can be drawn up from the set of

alternatives or can be reasonable extremes for the

acceptable domain of u

ij

. This last option avoids

the unstability which may occur with the former if

changes in the set of alternatives are introduced

during the process of analysis.

More sophisticated models can help the actors

to construct the value function, point by point, as

it is in the case of Macmodel (Tavares, 1998) (see

Fig. 3).

(c) the construction of a weighted average,

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

7

v

i

ˆ

X

N

jˆ1

k

j

v

ij

;

where k

j

are appropriate coecients (0 6 k

j

6 1

with

P

j

k

j

ˆ 1) expressing the relative importance

of each attribute j as one has

dv

ik

dv

il





v

i

ˆc

te

ˆ ÿ

k

l

k

k

;

which represents the trade-o€ for any pair of at-

tributes (k, l).

Obviously, this approach can be applied at

several levels of the tree and the total quality of

each alternative will be assessed by v

i

. The ranking

of alternatives should follow the decreasing or-

dering of this scalar.

This approach has implied the adoption of a

metric scale for the assessment of each attribute

which can be less obvious for more qualitative

aspects.

Also, two major drawbacks can be pointed out:

· the choice of k

j



is dicult and controversial

Table 1

Assessment of attributes
Attribute

Suggested indicators

Scale

Legal compliance

Probability of the design being approved

0±1 ( ± )

Duration of the process of approval

0, 1 (months)

Financial feasibility

Risk of a ®nancial loss (R)

ÿ1, +1

Expect net presented value (NPV)

ÿ1, +1 (monetary units)

Internal rate of return (IRR)

0, +1 ( ± )

Constructability and control

Degree of constructability

(0±10) ( ± )

Cost of control

(0, +8) (monetary units)

Aesthetics

Style, harmony, consistency

Experts judgement

(0±10) ( ± )

Functionality

Ful®llment of needs

Degree of satisfaction of the users

(0±10) or other bene®c scales ( ± )

Response to normal conditions

Life span

(0, +1) (years)

Response to extreme conditions

Rate of degradation

0±100 (%)

Probability of failure under extreme

conditions (winds, seismic e€ects, etc.)

(0±1) ( ± )

Economy

Initial cost

Investment

(0, +1) (monetary units)

working cost

Annual operational cost

(0, +1) (monetary units/year)

Maintenance and repair cost

Expected cost due to maintenance

during the life span

(0, +1) (monetary units)

Social and political integration

Public satisfaction

(0±10) ( ± )

Acceptance by central or local

administration

(0±10) ( ± )

Environmental equilibrium

Environmental impact

Speci®c indicator (BOD, etc. with speci®c scales)

Cultural heritage

Risk of ecological disturbances

(0±1) ( ± )

Disturbance or enhancing of cultural

values

(0±10) ( ± )

Risk of loss of cultural identity

(0±1) ( ± )

8

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

Fig.

3.

Ex

ample

s

of

Macmo

del

display

s.

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

9

(see, e.g., Association Qualitel, 1980; Wiegand

and Keller, 1980);

· the synthesis producing v

i

is just a weighted av-

erage which may not represent conveniently the

decision maker. For instance, one may have

P

j

k

j

v

ij

>

P

j

k

j

v

kj

but if v

kj

 v

ij

for some j



,

then the decision maker may not accept that i

is better than k.

The former problem can be approached by sensi-

tivity analysis and a model was proposed with this

objective (Trident, Tavares, 1984). This model

produces the mapping of k

j



for three dimen-

sions as it is required by the presented framework

(see example in Fig. 4).

The latter problem can be solved by adopting

an alternative approach to the synthetic assess-

ment of each alternative: pairwise comparisons.

This approach is developed in Section 2.3.4.

2.3.4. Pairwise comparison of alternatives

The study of pairwise comparisons between

alternatives can be carried out using the interesting

concept of ``outranking'' proposed by Roy (1985):
i outranks j…iS

j

† if two conditions are fulfilled:

Concordance condition:

X

k

j

with v

ij

ÿ

h

P v

kj

i X

k

j









P A;

Fig. 4. Example of the Trident analysis for ®ve alternatives X

1

; . . . ; X

5

(the indi€erence lines are denoted by X

i

ˆ X

i

0

).

10

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

Discordance condition:

max

j

v

kj

ÿ



ÿ v

ij



6 B:

where A, B are thresholds to be de®ned. Obviously,

A has to be greater than or equal to 0.5. The dis-

cordance condition expresses the so-called ``Veto

condition'' which may be very signi®cant in many

instances. The outranking relation does not have

the same properties as the preference relation as it

is not transitive or even anti-symmetrical.

A graph of outranking relations can be pro-

duced considering that each alternative is repre-

sented by each mode and those alternatives not

being outranked by others (or if belonging to cir-

cuits whose nodes never receive an outranking

relation) will be the candidates to the ®nal selec-

tion (see example in Fig. 5).

An obvious extension of the presented relation

of outranking is specifying B in terms of j, B

j

.

Another extension of this relation can be devel-

oped by substituting the concordance condition by

a weighted condition:

X

k

j

v

ij

P

X

k

j

v

kj

and keeping the discordance condition.

Several models ± Electre (Roy, 1985) ± were

developed following this approach.

2.3.5. Negotiation and upgrading of alternatives

A small set of alternatives can be pre-selected,

k 2 K, in terms of the previous analysis and then a

process of negotiation between the multiple actors

and of learning about how to improve the alter-

natives should take place.

A process of negotiation is a necessary condi-

tion to achieve acceptance by key actors and such

a process contributes also to a better modelling of

their value functions and of the coecients of

relative importance of the de®ned attributes. Sev-

eral models can be used to support this process of

negotiation (Mumpower and Rorbaugh, 1996).

This process implies learning to have a better

understanding about the strong and the weak as-

pects of each alternative and so multiple sugges-

tions tend to be produced to improve the K

alternatives.

Then, new alternatives can be generated from

each k, G

k

ˆ k

1

; k

2

; . . .

f

g with the purpose of up-

grading k. A more re®ned model can be used to

assess the achieved level of upgrading for each

generated alternative.

Actually, recent research (Simonson and

Tuersky, 1992; Meyer and Johnson, 1995) shows

that the assessment of the total quality by the

consumer can be particularly sensitive to the

strong advantage of one alternative, i, if compared

to another, k, in terms of one or a few speci®c

attributes which can have a symbolic value for the

consumer (e.g., the modernity, youngness, luxury,

etc.), S, and which de®ne the so-called motivational

®eld (Levy, 1959; Belck, 1988). Each dimension of

this ®eld correspond to one perceptual attribute

and to one-dimensional force driving the decision

maker to make his selection (Beech, 1990).

In Civil Engineering, many examples of this

problem occur in areas like the home and oce

markets or in the design of commercial and cul-

tural centres (Butler and Richmond, 1990). Evi-

dence has been collected showing that the

introduction of a speci®c feature in the design of a

private home like the existence of a whirlpool or of

an automated kitchen system may change sub-

stantially the comparison done by the clients. The

same applies to oces including less usual features

such as a hall with a decoration including dynamic

elements or showing a multi-screen projection.

The presented approaches (compensatory and

outranking models) are not particularly appro-

priate to cope with this situation and so an alter-

Fig. 5. Example of an outranking graph for six alternatives

fx

1

; . . . ; x

6

g producing a sub-set of candidates to the best al-

ternative ˆ fx

1

; x

3

; x

5

; x

6

g:

L. Valadares Tavares / European Journal of Operational Research 119 (1999) 1±13

11

native model can be proposed: the symbolic model.

This model is based also on a pairwise approach

but adopts a new relation ± the advantage relation

± instead of the outranking relation. This relation

is de®ned by: i A k (i has an advantage relation

over k) if and only if:

max

j2S

…v

ij

ÿ v

kj

† P c

advantage condition; where S is sub-set of
symbolic attributes;

X

k

j

…with v

ij

h

6 v

kj

†

i

=

X

k

j





6 D

mass discordance condition; max…v

kj

ÿ v

ij

† < E;

veto discordance condition;

where C is the advantage threshold, D the mass

discordance threshold and E the veto discordance

threshold. The ®rst condition is applied just to the

sub-set of symbolic attributes.

This relation expresses the relative advantage

accomplished by the alternative i over k despite a

weight mass favouring k because of the excep-

tional advantage of i over k in terms of, at least,

one attribute. The selection of C should be done

considering that C is the minimal di€erence pro-

ducing the advantage e€ect. It should be noted

that the veto threshold, E, expresses the maximal

di€erence in favour of the alternative k allowing a

favourable result to i and therefore it is reasonable

assuming that C should be greater than E. If so,

the following results can be proved (where i

k

means that there is no advantage relation of i over

k and where ; means that there is no implication):

1. iAk ) k

i (anti-symmetrical property),

2. iAm and mAk;iAk (no transitivity proper-

ty),

3. If [iAm and mAm

0

and . . .m

00

Aq] then it may

also happen qAi (circuit property).

3. Conclusions

The evolution of the process of designing civil

engineering systems was discussed and ®ve major

paradigmatic models were identi®ed:

· the empirical model,

· the static descriptive deterministic model,

· the static stochastic descriptive model,

· the dynamic stochastic descriptive model,

· the single criterium optimisation.

Recent developments and challenges suggest

another approach which was described by the in-

teractive multi-attribute learning paradigm.

This model is based on a more systematic ex-

ploration of the space of the alternative feasible

solutions and on their assessment in terms of

multiple attributes by the di€erent actors inter-

acting within the process of decision.

This approach helps to model the process of

design as a decision-making process following the

inspired de®nition of engineering design proposed

by the Accreditation Board for Engineering and

Technology (1991):

``Engineering design is the process of devising a

system, components or a process to meet desired

needs. It is a decision-making process (often iter-

ative), in which the basic sciences, mathematics,

and engineering sciences are applied to convert

resources optimally to meet a stated objective.

Among the fundamental elements of the design

process are the establishment of objectives, and

criteria, synthesis, constructions, testing and eval-

uations''.

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