development and application of a hybrid genetic algorithm for resource optimization and management

Development and application of a hybrid genetic algorithmfor resource optimization and management

O. O. UGWU* & J. H. M. TAH

*Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China, and Division of

Civil Engineering and Construction Management, South Bank University, London, UK

Abstract Resource selection/optimization problems are

often characterized by two related problems: numerical

function and combinatorial optimization. Although

techniques ranging from classical mathematical

programming to knowledge-based expert systems

(KBESs) have been applied to solve the function

optimization problem, there still exists the need for

improved solution techniques in solving the combinatorial

optimization. This paper reports an exploratory work that

investigates the integration of genetic algorithms (GAs)

with organizational databases to solve the combinatorial

problem in resource optimization and management. The

solution strategy involved using two levels of knowledge

(declarative and procedural) to address the problems of

numerical function, and combinatorial optimization of

resources. The research shows that GAs can be

effectively integrated into the evolving decision support

systems (DSSs) for resource optimization and

management, and that integrating a hybrid GA that

incorporates resource economic and productivity

factors, would facilitate the development of a more

robust DSS. This helps to overcome the major limitations

of current optimization techniques such as linear

programming and monolithic techniques such as the

KBES. The results also highlighted that GA exhibits the

chaotic characteristics that are often observed in other

complex non-linear dynamic systems. The empirical

results are discussed, and some recommendations

given on how to achieve improved results in adapting

GAs for decision support in the architecture, engineering

and construction (AEC) sector.

Keywords combinatorial optimization, decision support

systems, distributed project management, genetic

algorithms, resource optimization

INTRODUCTION

Many decisions in construction projects usually involve

assigning resources from one task to another. Such

decisions are often required at various levels of a project

life cycle: conceptual level when the project manager

is concerned with the total cost and project feasibility,

tender appraisal; submission level when contractors

are concerned with preparing reasonable and economic

cost estimates that has to be matched with project

resource requirements; and at the operational level

when site and contract managers have to deal with the

realities of daily operational decision-making. For a

given project the resources assigned determines the

method(s) of construction. Therefore, the decision

problems often demand evaluating the best way to

distribute available resources over different tasks that

are necessary for a successful and efficient completion

of the project. Such resource assignment and optimi-

zation problems demand efficient combinatorial com-

putations if all possible options are to be considered,

and decision-making facilitated. This is true irrespect-

ive of the project management level. Consequently,

research into efficient methods of resource optimization

has always been an area of interesting study on its own.

Previous research works on resource optimization

investigated the use of deterministic models in con-

struction decision-making, while other works investi-

gated the use of stochastic models in solving the

problem (Paulson et al., 1987; AbouRizk & Shi, 1994;

Smith et al., 1995).

However, despite the long search for simulation

models that will receive acceptance by practising

engineers, deterministic models still remain the pre-

ferred method for studying planning and scheduling in

the construction industry. Some authors (Schexnayder,

1997) have argued that deterministic models come very

close to the daily practise of engineers and are therefore

favoured. Such models enable practising engineers to

harness their experiences when studying and verifying

the effects of physical features of resources. Conse-

quently, there still remains the need to investigate

simulation models that takes the physical characteristics

of resources into consideration. Genetic algorithms

Engineering, Construction and Architectural Management 2002 9 4, 304317

304 2002 Blackwell Science Ltd

(GAs) offer potential solutions in developing such

stochastic-simulation models. This is because such

physical characteristics can be encoded as a set of

parameters that determine the final cost of the resource

components, using the features of a GA.

The objective of this study is to investigate the

potential application of GA systems in the general

resource selection problem domain. The purpose is to

establish how such efficient computational techniques

can be applied to facilitate decision-making in the area

of resource optimization and management within the

framework of a distributed decision support environ-

ment. The focus is on project management at various

levels of strategic decision-making, and ensuring that

any choice of optimal strategy is underpinned by a

careful analysis of the benefits and costs associated with

implementing all the possible alternatives. In addition,

the sensitivity of the output to changes in certain

parameters that GAs need during execution will be

examined.

The aims of this paper are as follows:

to give a comprehensive treatise on GA and theirpotential applications in the context of resource

optimization and management;

to demonstrate the application of combinatorialdesign techniques (i.e. the interaction between

mathematical modelling and computing technology

such as databases) in solving complex multidi-

mensional problems;

to discuss an empirical investigation on the relia-bility of the proposed GA system as a decision

processing component in resource management;

and

to highlight the challenges and problems in thedevelopment and deployment of GA and other

evolutionary techniques for decision support. It

is intended to provoke some serious research

questions in construction information technology

research.

BACKGROUND

Genetic algorithms belong to the family of artificial

intelligence techniques that are increasingly being

employed to solve optimization problems. Such algo-

rithms mimic the operations of natural selection when

searching for optimal solutions. The power of their

use in applications is derived from their ability to

combine numerical parameter optimization with com-

binatorial searches within an application domain.

Genetic algorithms are therefore uniquely suitable

for solving multidimensional optimization problems

such as resource selection in construction. In prac-

tice, the application of a GA involves designing

artificial chromosome structures that represent a

simple genetic model of the computation, and then

implementing the genetic operators by simple bit-

manipulation operations. Problem-domain analysis

and encoding constitute substantial activities in

designing a GA as a solution to an optimization

problem. The basic building blocks that influence the

efficiency and performance of a GA is the schemata

from which the genetic model representation is

constructed. The underlying details of the schemata

theory are discussed in the seminal book by John

Holland (Holland, 1975).

Genetic algorithms have been successfully applied in

different optimization problems including the famous

Travelling Salesman Problem (TSP) in Operations

Research. Some of the applications in design and

construction management problems include: oil pipe-

line network optimization (Goldberg, 1989), structural

optimization for truss roofs (Koumosis & Georgiou,

1994, Nagendra et al., 1996), determination of the

laying sequence for a continuos girder reinforced

concrete floor system (Natsuaki et al., 1995) and

resource scheduling (Chan et al., 1996).

Bennet et al. (2000) report on the development of

a GA-based decision support system (DSS) for

location of new major housing allocations. Rafiq

et al. (2001) discuss the use of structured GA

(SGA) to generate and evaluate different feasible

design solutions concurrently, within a DSS frame-

work. Borkowski & Grabska (2001) discuss the

application of graphs in layout optimization and

highlight the potential applications of GA in the

layout optimization of trusses. Griffiths & Miles

(2001) present a research project that is investigating

the application of improved GA to optimize shape

discovery in design, using two-dimensional string

representations for the genetic search. Soibelman &

Pena-Mora (2001) describe a distributed multireason-

ing mechanism that incorporates GA and case-based

reasoning within a multiagent system environment to

provide designers with design solutions using a set of

user-defined parameters and constraints. The prob-

lem domain is the conceptual phase of the structural

design of tall buildings.

The above catalogue of research projects shows an

increasing interest on the development and applica-

tion of GA-based systems. Majority of the research

works on GA still focuses on encoding and repre-

senting the required solution as fixed length charac-

ter strings (chromosome structure) and this same

Hybrid GA for resource optimization 305

2002 Blackwell Science Ltd, Engineering, Construction and Architectural Management 9 4, 304317

approach was adopted in our study. However, while

most of the GA applications still focus on one-

dimensional string processing, the work reported in

this paper extended the basic GA by investigating its

application in a two-dimensional matrix problem. In

general, most GAs employ three primary genetic

operators: Reproduction, Crossover, and Mutation.

Details of these genetic operators are exhaustively

discussed in the referenced GA textbooks (Holland,

1975; Goldberg, 1989; Davis, 1991; Rawlings, 1991),

and such finite details do not fall within the scope of

present discussion.

The functionality of a GA is maximized if it is used

in an unconstrained optimization problem. However,

GAs are usually applied to constrained optimization

problems (COPs), by assigning penalty functions that

transform them into unconstrained problems (Gold-

berg, 1989). The major disadvantage of this approach

is that because the penalty functions are often

arbitrarily assigned, some constraints may be violated

by good solutions that are close to the border of

feasible region. Other approaches include using gen-

etic repair to cushion the effects of possible con-

straint violations by the resulting GA solutions

(Paredis, 1993). These approaches enforce some

synthatic correctness and consequently, they may not

be acceptable in optimization problems that demand

both numerical function and combinatorial optimiza-

tion a distinct characteristic of resource selection

problems. Some authors and researchers have advo-

cated that other tools such as greedy algorithms and

constraint programs be incorporated to sift through

an optimization problem before GA is finally called to

solve the function and combinatorial aspects of the

problem (Davis, 1991; Rawlings, 1991; Watson,

1995). This argument also supports the systematic

approach to planning, and the authors agree with the

thinking. The work that is reported in this paper

represents a significant advancement in GA applica-

tions by integrating with project databases. In this

study, the Structured Query Language (SQL) pro-

cessing algorithm is used to sift through candidate

resources in the database that satisfy duration con-

straints before the combinatorial optimization. This

approach improves distributed resource optimization

and project management. The ensuing sections des-

cribe the problem domain, as well as the solution

strategy we adopted. The coding system that was

found suitable for the problem and the experimental

design for studying the system behaviour are also

discussed. Finally, the empirical results obtained after

analysing the output data are presented and recom-

mendations given for further research.

THE NATURE OF RESOURCE

ASSIGNMENT PROBLEMS

Resource allocation as a network problem

In order to investigate the suitability of GA for resource

assignment and optimization, it is necessary to examine

the problem in a generic context. In this regard

resource assignment is viewed as analogous to network

problem. The following sections discuss the character-

istics of resource-assignment problems when viewed in

this context.

Fig. 1 is a graphical illustration of a resource selection/

combinatorial problem, showing the tasks and resources

network. The problem description is outlined below:

Each ellipse in the network (X1Xm) is a node thatrepresents a construction task, and each circle (Y1

Yn) represents different resources to be assigned.

Thus, the problem depicted here is how to assign

resources (Y1Yn) among tasks (X1Xm) when it

is possible to use the resources (or a combination of

resources) in completing any of the tasks, subject to

constraints on allowable combinations.

The following characteristics of the problem can bededuced from the network shown in Fig. 1 (Ugwu

& Tah, 1998):

It is a function-evaluation/combinatorial prob-

lem. The optimization problem is to find the

best traversal path in the network that minimizes

the total cost of the project tasks.

In order to generate a solution space, the GA

traverses through the network to create a new

chromosome. This chromosome (bit string)

results from a permutation of a list of the cost

indices that is encoded in the problem space and

then generated by scrambling through the order

of the nodes. This is a coevolutionary process.

The problem is epistatic solutions over the

feasible region are closely coupled and small

Figure 1 A network of the resource-assignment problem.

Ugwu, O. O. & Tah, J. H. M.306


alterations in the nodal weightings trigger cumu-

lative effects (perturbations) in the solution space.

Consequently, this affects the fitness of each

traversal path, and also has some impact on the

efficiency of a GA system, often leading to ter-

mination at local optima (Paredis, 1993, 1995).

Each ellipse has multiple cost values, resulting fromits interactions with the circles. These interactions

can be translated into a payoff matrix of order

(m n) by using the generalized resource-alloca-tion formulae described in the following section.

Mathematical model formulation

The resource-based mathematical model expresses the

total cost of a construction process as a function of the

respective tasks performed using available resources,

and the corresponding resource productivity and eco-

nomic attributes (e.g. resource unit costs). The model

considers resource optimization and management as a

generic problem, and is built upon two fundamental

sets of class objects:

a project that consists of at least one task and thetask(s) at hand required to be completed as part of

the project this task completion is a transforma-

tion process; and

the resources that are required to execute the aboveproject task(s).

The mathematical model is given by Equations (1)

and (2) below (Winston, 1994):

MinimizeX

rtxtt 1; T 1subject to:

Xgtxt W 2

where W is the units of a resource available, T the

number of activities to which the resource can be

allocated, gt(xt) the units of resource that are used by

activity t, and rt(xt) the associated cost of using the

resource gt(xt).

A structured modelling approach was employed to

translate this network into the corresponding payoff

matrix (Geoffrion, 1987, 1988, 1992). This is shown in

Fig. 2.

The resulting payoff matrix yields the grid given in

Equation (3):

aij rtxti 1; m : j 1; n 3where aij corresponds to the cost or duration values for

a given locus i, j in the matrix table (Fig. 2). The

application of the matrix is illustrated in the genetic

state-space search (GSSS) shown in Tables 26 in the

Case Study section.

While certain data values such as the task quantity

are defined by the user (based on project details) the

output of a given resource is determined by certain

productivity factors, such as size, capacity, correction

factors (resource attributes), and the type and nature

of the material encountered at site (material attrib-

utes). For a given resource within each resource group,

there is therefore a corresponding cost and duration

attached to its usage. The task and resource attributes

are both indexed directly to their respective classes/

objects and stored in the project database. The model

has been applied in the earthwork operations domain

and details of the application domain are discussed in

(Ugwu, 1999). Table 1 summarizes the variables

expressed in the mathematical model:

Constraints in evaluating the objective function

Time constraints (task and project duration)

A set of duration constraints must be satisfied for a

given assigned resource. The general expression for the

duration constraint is given as:

Xi

Xj

Qmti; j; NRoti; j; N

Dt 4

where Rot is the output of a given resource R in

performing task t, Qmt is the quantity of task under

consideration, and Dt is the task duration. The general

objective function also allows for a mixture of resourc-

es. In generating the mathematical model, the unit

costs of resources are assumed deterministic here and

are user-specified. The unit costs of labour, and plant

are also assumed constant in this study but it may vary

Figure 2 Payoff matrix structure of the resource-assignment

problem.



with work conditions at various sections along a project

profile. Previous works have been undertaken to gen-

erate models and programs that compute and simulate

these unit costs (Easa, 1987, 1988, 1989) and it is not

considered to be within the scope of this research.

Equation (1) is the objective function that underpins

this research. Equation (4) was imposed by using a

parameterized query to sift through all possible candi-

date resources in the project database, before the

preprocessed data set is passed on to the GA for

functional and combinatorial optimization. This

approach is underpinned by the fact that the existing

SQL processing algorithms are extremely powerful,

robust, and very suitable for the kind of constraint

manipulation that is desired in this type of combina-

torial problem. The next section discusses the incor-

poration of this objective function in the formulated

genetic model.

MODEL FORMULATION

The genetic model representation of the resource

assignment problems incorporates two important de-

cision-making parameters cost and duration. Using

such a model would ensure that a users choice of

construction resource(s) or resource combination is

underpinned by a careful analysis of the costs and

benefits associated with implementing all the possible

alternatives. In addition, the sensitivity of the output to

changes in certain of the parameters that GAs need

during execution was examined as part of the experi-

ment designed for the system testing/validation. The

ensuing section describes the algorithmic procedures of

the hybrid GA.

A hybrid genetic algorithm for resource

assignment

This section describes the hybrid GA that is integrated

with a project database to perform combinatorial

optimization. The database maintains the following

task-schedule information task/activity ID, names and

description, activity durations, assigned resources,

resource IDs and the corresponding productivity and

economic factors, etc. The project database was

implemented in Microsoft Access and used for persist-

ent storage of task-schedule data. The hybrid GA uses

parameterized structured query that is passed to the

database engine, to extract details of tasks and resource

productivity/economic attributes from the database.

The extracted data are then used to process the

associated costs and duration for each resource

assigned to various tasks. Figures 3 and 4 show the

database and structural relationship between the

Table 1 Description of variables in the mathematical model.

Indices, sets and relation

p* P* Projects (P* various types of construction projects)r R Resources (R contains three types of resources: plant, labour, material)p P Plant is an ordered set classified by functional and operational usesl L Labour is an ordered set classified by typem M Material is an ordered set, classified by typest T = {e.g. e, h, f, c} Task is an ordered set by sequence of construction (e.g. excavation, haulage,

filling, compaction in earthworks construction)

Constants

Ur for r R Unit cost of resource (assumed deterministic and is user specified)Variables

Po Plant productivity (but assumed constant over section i, j)

Lo Labour productivity (but assumed constant over section i, j)

Qmt for r R Quantity of tasks handled by a resource group over the section i,j as extracted fromproject contract drawings and specifications but is user defined

DP, DT Project and task duration, respectively determined by specifications in the

conditions of contract

Cr (for r R = {plant, labour, material}) Cost of a given resource element r, the cumulative sum of which gives total cost ofconstruction/earthwork operations over the section(s) of interest to the user

Constraints

DT DP Duration limit constraintC 0 Cost limit constraint over section i, jru ra (for r R) Resource utilization constraint: resource utilization ru must be less than or equal to

resource availability ra. The user certifies satisfaction of initial availability

constraints

Objective function As given in Equation (1)



various database table objects project, tasks, resources

and resource assignment.

This level of data and information storage improves

the robustness of the GA because the services it

provides (functional and combinatorial optimization)

is independent of the data on which it acts in perform-

ing such services. The distinct feature also means that

the imposition of genetic operators such as reproduc-

tion, crossover, and mutation do not result in an

arbitrary loss of information, as the knowledge about

the problem domain on which the combinatorial

optimization takes place is stored in the project data-

base. Figure 5 shows the formulated hybrid GA with all

its delineating features.

The algorithm modifies the simple GA (Holland,

1975; Goldberg, 1989), in order to incorporate the

specific data structure requirements of the problem. It

is based on generating and mapping a fitness network

Figure 3 A view of the database table

objects.

Figure 4 Relationship between the database table objects (project, tasks, and resources).



that constitute the genetic search space. This fitness

network which encapsulates information related to a

given resource or construction method and tasks, was

then mapped into a set of genes with the associated cost

values within a defined chromosome structure (a one-

to-one genetic mapping). Solutions include identifying

optimum combination of resources and tasks that

minimize the total cost of construction over the feasible

region. The initial constraint fitness maps the value of

each gene as the cost of completing the tasks with a

given resource.

An initial population was generated from which the

algorithm learns and imposes the genetic operators and

consequently coevolves other feasible solutions within

Figure 5 Hybrid genetic algorithm for resource selection and optimization.



the search space. Therefore, the fitness network serves a

dual purpose by integrating two general paradigms:

genetic search and state-space search. Some authors have

advocated the adoption of this GSSS approach in

solving COPs (Paredis, 1993, 1995). This is the

approach we adopted in solving the problem. However,

a salient feature of this hybrid GA is that all analytical

computations are based on the actual resource produc-

tivity and economic data extracted from the project

database. Ugwu (1999) and Ugwu & Tah (1999)

discuss details of the decision-support framework and

the underlying system architecture that underpin this

level of integration of the GA in a prototype DSS.

The genetic model

The proposed genetic model/coding encapsulates the

payoff value of a gene at a given locus. The genetic

search space is illustrated in the system validation

section (see Tables 15). The string representation is

given in Equation (5).

Chromosome: Cij ; Dij j1;N

i1;M 5

where Cij is the cost value of a gene, Dij the corres-

ponding duration, and i, j define the locus of a gene in

the chromosome structure.

In this model, a gene defines a type of resource (e.g.

construction plant) and the locus defines the task to

which the resource has been assigned. Thus, values of a

gene at a given locus corresponds to the cost and

duration of executing a given task with a particular

assigned resource. For example, a 7-bit chromosome

defined as 1011001 represents a resource allocation

model that assigns two different resources to seven

different tasks. This type of binary chromosome repre-

sentation can precisely match to a given set of resource

assignments provided the chromosome contains

enough bit strings to define the various possible

resource assignments. In this model, the GA maintains

a population with fixed size of chromosomes (length

and depth).

CASE STUDY

A pipe laying project was selected for this case study

because it involves earthwork operations which was

initially chosen as a test bed for the prototype imple-

mentation of the proposed model. The example project

used for the validation is based on a detailed typical

construction project information as documented in

Carvalbo & Turner (1969). The requirements for

resource optimization and project management were

identified and analysed from the project documents.

The following tasks were identified: Huts delivery, Huts

assembly, Workshop delivery, Workshop assembly,

Tanker greasing pit, Access Road Section 1, Trench

for Tunnel Section VI, Trench for Tunnel Section VII,

Trench for Tunnel Section VIII, Trench for Tunnel

Section IX, Stone Filling over Tunnel Section VI,

Stone Filling over Tunnel Section VII, Stone Filling

over Tunnel Section VIII, Stone Filling over Tunnel

Section IX. Two resources (a digger crane and truck-

mounted vehicle that could be converted for digging)

are available for use in executing the outlined tasks.

The extracted task and resource attributes were used to

populate the appropriate database table objects. The

problem involves optimizing the tasks and resource

assignments from the case study project.

GA system testing and validation

The test on the GA system was carried in the context of

sequential decision-making problem outlined in the

preceding section. In order to apply GA, the project is

broken down into the above component tasks, and

there are two items of interest (control variables): 15

tasks, and two candidate construction resources that

satisfy availability and duration constraints. A

Table 2 A sample preprocessed cost data sets for combinatorial optimization.

Resource ID P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15

ML1 30 30 10 10 10 10 100 40 40 20 10 10 10 10 10

TV1 150 150 50 50 50 50 500 200 200 100 50 50 50 50 50

Table 3 A sample preprocessed duration data sets for combinatorial optimization.

Resource ID P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15

ML1 3 3 1 1 1 1 10 4 4 2 1 1 1 1 1

TV1 1 1 0.5 0.5 0.5 0.5 2 1 1 0.5 0.5 0.5 0.5 0.5 0.5



two-dimensional binary code string representation was

used to model the decision-making parameters that are

of interest (i.e. the cost and duration values associated

with a given assigned resource). Each population

consists of the binary strings 1 or 0, and both the bit-

string breadth and depth are fixed. The GA evaluates

the fitness of a given population set (chromosome)

using preprocessed cost and duration data sets extrac-

ted from the database (Tables 2 and 3).

The combinatorial optimization process begins with

a set of initial populations, which are randomly gener-

ated for subsequent use by the GA (Tables 46).

The user inputs include the values of certain GA

optimization parameters, such as the number of gen-

erations, the mutation rate, and the crossover site.

There are no strict restrictions on the users choice of

GA optimization parameters. However, from the trial

tests, the values used for number of generations and

mutation rates ranged from 2002000 to 0.00.3%,

respectively. The GA uses these to learn and dynam-

ically generate other populations (a coevolutionary

process), and then generates, as a final output, the

cumulative cost of completing the tasks with various

possible combinations of resources (i.e. method(s) of

construction). The data structure of each output

(chromosome) was designed to generate five sets of

coded results, and each stream of the solution repre-

sents a possible combination of resources, and the

associated cost. This is desired because in a DSS the

user makes the final choice on the basis of other

practical considerations, such as some logistics related

to the project management.

A typical structure of such output data is illustrated

below:

Optimization parameters:

No. of generations 800Bit mutation rate 0.1Crossover rate 1Strings correspond to construction methods (alternative

combination of resources)

String no. 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0String no. 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1

Table 4 Genetic coding/representation of the search space using bit vectors.

Resource

combination P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15

String 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

String 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

String 2 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1

String 3 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0

String 4 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0

Table 5 Randomly generated initial population of costs (Cij).

Resource


String 0 30 30 10 10 10 10 100 40 40 20 10 10 10 10 10

String 1 150 150 50 50 50 50 500 200 200 100 50 50 50 50 50

String 2 150 30 10 50 50 50 100 40 200 20 10 50 10 50 50

String 3 30 30 50 10 10 10 500 200 40 20 50 10 50 50 10

String 4 150 30 50 50 50 10 500 40 40 100 10 10 50 50 10

Table 6 Randomly generated initial population of duration (Dij).

Resource


String 0 3 3 1 1 1 1 10 4 4 2 1 1 1 1 1

String 1 1 1 0.5 0.5 0.5 0.5 2 1 1 0.5 0.5 0.5 0.5 0.5 0.5

String 2 1 3 1 1 0.5 0.5 1 4 1 0.5 1 0.5 0.5 0.5 0.5

String 3 3 3 0.5 1 1 1 2 1 4 0.5 0.5 1 0.5 1 0.5

String 4 1 3 0.5 0.5 0.5 1 2 4 4 1 1 1 0.5 0.5 0.5



String no. 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0String no. 3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0String no. 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0Value of objective function for each string

String no. 0: 630String no. 1: 750String no. 2: 350String no. 3: 390String no. 4: 510

Thus for a given test run, the system is able to outline

the cost implications of various strategies combina-

tions of tasks and resources (Fig. 6).

In its present form, the decision-maker decodes and

interprets the output from the system. Further research

is required to enable the GA system decode the output

by itself, and classify the resulting bit strings in terms of

the coded variables, i.e. the task names and description

of the construction method(s). The experimental

design to study the behaviour of the GA is discussed

in the following sections, together with some of the

observations that were made during the various sto-

chastic-simulation sessions.

Experimental design

The experiment to study the behaviour of the GA

system was designed to measure a set of output data for

a given test run. Various statistical indicators were then

used to measure the reliability of the system as a search/

optimization tool for decision support, by comparing

the output with the actual best solution of the problem.

It was also necessary to measure the sensitivity of the

system to changes in the optimization parameters

number of generations and mutation rate. The follow-

ing data were recorded:

maximum (best) value minimum (worst) value

average value, and execution time in seconds.

The average value measures the overall quality of the

system output for a given test run, higher values

representing improved solutions. The execution time

is an indication of the computing resources consumed

by the system. For a given set of parameters, the

program was executed 40 times and results were

recorded in all cases. The output data were analysed

using a statistical and a spreadsheet package. These

tools facilitated a study of certain statistics and various

levels of data exploration, which in turn revealed some

interesting characteristics of GA systems (see Table 7).

Figure 6 Graph showing typical

minimum cost profiles for the various

outputs.

Table 7 Performance data of 40 test runs.

No. of generations

Statistic 100 200 400 800

Pmutation = 0.0

Avg. minimum cost () 437.00 559.00 452.00 449.00

Standard deviation 97.93 81.013 88.27 89.67

Maximum () 590.00 590.00 590.00 590.00

Minimum () 350.00 350.00 350.00 350.00

Pmutation = 0.1

Average minimum cost () 413.00 457.00 408.00 432.00


Maximum () 590.00 790.00 590.00 790.00

Minimum () 350.00 350.00 350.00 350.00

Pmutation = 0.2



Maximum () 630.00 750.00 990.00 750.00

Minimum () 350.00 350.00 350.00 350.00

Pmutation = 0.4



Maximum () 750.00 750.00 830.00 790.00

Minimum () 350.00 350.00 350.00 350.00



RESULTS

The graphs of best, worst, and average best were

analysed (Fig. 7).

Because of some chaotic characteristics exhibited by

the GA system, statistical analysis of the output focused

on determining the level of replication of output for

different input parameters. The range of values,

frequency distribution, and the proportion of results

that satisfy a certain range are the indices that can be

used to determine the reliability of the system as a DSS

component. The solutions for which the maximum

output lie over the range 85100% of the best solution

were also measured (Table 8; Fig. 8).

From the results of the experiments (Tables 48;

Figs 68), the following observations are made:

1. GA systems are very efficient tools for complex

combinatorial searches over a highly multimodal

parameter space.

2. A cross-impact analysis was carried to study the

effect of changes in the values of the optimization

parameters on the output generated by the system

on the different trial runs. It was observed that

keeping one of the optimization parameters con-

stant and varying the value of the other did not

result in a predictable output pattern (Fig. 6).

Also, an ANOVA test did not indicate a significant

correlation between the output data sets for dif-

ferent values of the parameters (GA system varia-

bles). Such chaotic behaviour is usually

characteristic of other complex dynamic systems.

The random nature of the stochastic modelling/si-

mulation and the cumulative impact of the genetic

operators (crossover and mutation) may induce

these perturbations.

3. In general, mutation appears to distort the perform-

ance of the system increasing the computation

time without necessarily improving performance

(Fig. 8). The variation in the execution time with

the number of generations and the probability of

mutation shows a logarithmic relationship. The

time generally increases with the optimization

parameters. This translates to computer processing

resources utilized (cost), and can be very significant

for a GA used in industrial applications.

4. Although the GA system generates the cost profile

for various options as an output, a DSS will enable

the project manager to investigate other options so

as to be well informed of the consequences of

taking a particular action. Hence, the GA system

will be optimized if it is used as a component of a

DSS in a wider context, and integrating of GA with

the project database allows for a wide range of

applications in real-time or real-life situations

(Ugwu et al., 1998).

DISCUSSION AND ANALYSIS

OF THE RESULTS

This paper has reported a research project that inves-

tigated a new approach to resource optimization and

management using hybrid GAs and a solution strategy

that is based on the object-oriented paradigm. The

study also investigated the efficiency and behaviour of a

GA system as a DSS component for distributed

Figure 7 Graph of the GA output for 40

test runs.

Table 8 Proportion of output within the range 85100% of best

solution.

No. of generations

Pmutation 100 200 400 800

0.0 77.5 85.0 80.0 80.0

0.1 85.0 75.0 65.0 72.5

0.2 87.5 75.0 72.5 77.5

0.4 77.5 67.5 70.0 70.0



decision-making in project management. The paper

discussed a genetic model that represents the problem

space for construction method selection and resource

optimization/management.

The hybrid GA uses a resource cost model that

expresses project costs and duration in terms of task

details, the physical characteristics (technical and pro-

ductivity attributes) of construction resources, and the

economic data such as resource unit costs. By adopting

this solution strategy, the authors proposed two levels

of knowledge utilization in GA-based resource optimi-

zation and management:

Declarative knowledge in which project, task andresource details are stored as FACTS in a database.

These are then coded as a set of cost parameters in

the two-dimensional genetic model developed for

the research investigation; and

Procedural knowledge in which resource combina-tions are modelled as a stochastic process expressed

in terms of the genetic operators (crossover, muta-

tion, and reproduction) within the multidimen-

sional genetic model.

By utilizing knowledge at the above two levels, the

GA system generates the cost profile for various

options (combination of the assigned resources) as an

output. The project manager or user is also able to

investigate other options so as to be well informed of

the consequences of taking a particular action. The

results demonstrate that a hybrid GA system is a

potential reusable component for resource-optimiza-

tion problems in various types of construction

projects.

The application has the following limitations in its

present form:

The representation of decision-making parametersin the genetic model is limited to two attributes:

cost and duration. However, there is scope to

expand on, and increase the number of project

evaluation parameters to include: project location

factors, economic forecasts of the project, project

risk factors and other investment decision-making

parameters.

The GA output is used to populate the task-scheduling database table object manually, so that

the project management system can interface with

the GA results. There is a need to automate the

update functions of the database so that the GA

output can be used to automatically update the

database. Further work could also investigate the

possible application of eXtensible Mark-up Lan-

guage (XML) to extract display and/or interpret

GA output data in various formats based on user

preferences in a web-enabled distributed project

management environment.

CONCLUSION

This paper discussed the application of a hybrid GA to

resource optimization and management. It described

the formulation of a genetic model that addresses the

specific problems of combinatorial optimization in

managing construction resources. A suitable two-

dimensional data structure for the problem was also

investigated. The GA interacts with a database and

extracts the detail project and resource attributes for

use in quantitative computations and combinatorial

optimization. This approach of integrating GA

with project databases is quite novel and adopting GA

in this manner makes it a true global optimization

technique.

The study focused on the efficiency and behaviour of

GA system as component(s) of a DSS. Our approach

has been to examine resource assignment and optimi-

zation as a generic problem. The following observations

were made:

GAs can be effectively integrated into the evolvingDSSs for resource optimization and management,

and in solving other engineering problems. The

study demonstrates that with adequate design of

Figure 8 Proportion of the output within

the range of 85100% of the best

solution.



data structures a GA system can be a reusable

component for resource assignment problems in

various types of construction projects. Integrating a

hybrid GA that incorporates resource economic

and productivity factors would enhance the

development of more robust DSS. This helps to

overcome the major limitations of current optimi-

zation techniques such as linear programming.

The output do not necessarily constitute the overallbest solution in all cases but nevertheless, the speed

of computation has been demonstrably very

impressive as this supersedes any attempt to

evaluate similar combinatorial trials manually. This

suggests that the main advantage of a GA is that it

guarantees a good solution over a large complex

search space within a short time. GA should

therefore be applied only to appropriate problems.

The basic assumption at this stage of model devel-opment and testing is that each selected resource in

the GA satisfies resource availability requirements.

Although resource availability constraint is verified

or relaxed by the user, further work is needed to

incorporate greedy algorithms that sifts the

resources to ensure that this fundamental assump-

tion is not violated by any resource(s) in the solu-

tions generated by the GA.

The result of the system validation shows that GA

systems are very efficient tools for complex combina-

torial searches over a highly multimodal space. The

tests also reveal that although GA systems are capable

of converging at optimal solutions within a very short

time, they also exhibit some chaotic characteristics such

as a complete absence of the optimal solution in a

generation of results. However, such chaotic behaviours

are often observed in other complex nonlinear dynamic

systems. In addition a GA must have enough search

space to minimize degradation of its performance.

The major contribution of this work is that it extends

the simple GA model by: (a) designing a GA that

processes two-dimensional string objective functions,

and (b) integrates with organizational databases in

solving the multidimensional problem of resource

management. This means that resource productivity

factors can be independently updated and maintained

in the database and dynamically extracted for function

and combinatorial optimization by the GA even in a

distributed environment. With this functionality for

analytical evaluations, the hybrid GA exploits the

power of the genetic operators in search and optimiza-

tion over a large search space. The interaction with the

project database(s) ensures that the knowledge of the

tasks and assigned resources from which the analytical

results are computed is distinctly separated from the

coded information on the genetic model that is subjec-

ted to the actions of the genetic operators. Thus the

resource optimization problem is addressed here in a

generic context while available task and resource

attributes are used to populate the project database.

Furthermore, the GA results can be propagated to

other database table objects for integration with project

management systems such as MS Project (Ugwu,

1999). This enhances distributed collaborative project

management.

The study reported in this paper has shown that

GAs have huge potential generic applications in

resource optimization in construction engineering and

management, and that it is best suited for large and

complex search problems. Most of the current works

concentrate on developing GAs that optimize one-

dimensional string functions. This has very limited

application in solving real life multidimensional prob-

lems such as resource selection and optimization. It is

therefore recommended that further work be directed

towards developing improved data structures that

would facilitate solutions to such problems. Further

research is also required to address the chaotic

behaviours of GAs, and investigate its applications

for decision support in other areas of engineering

design and management. This will be a major step

towards realizing its industrial applications in the

architecture, engineering and construction sector.

ACKNOWLEDGEMENT

This research was conducted as a PhD programme

funded by the Faculty of the Built Environment, South

Bank University London, SW8 2JZ, UK. The authors

also wish to acknowledge the useful comments and

suggestions from the anonymous reviewers of this

paper.

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