Abstract. Owing to the highly complicated nature and the escalating cost involved in construction claims, it is highly desirable for the parties to a dispute to know with some certainty how the case would be resolved if it were taken to court. The use of artificial neural networks can be a cost-effective technique to help to predict the outcome of construction claims, on the basis of characteristics of cases and the corresponding past court decisions. This paper presents the application of a split-step particle swarm optimization (PSO) model for training perceptrons to predict the outcome of construction claims in Hong Kong. The advantages of global search capability of PSO algorithm in the first step and local fast convergence of Levenberg-Marquardt algorithm in the second step are combined together. The results demonstrate that, when compared with the benchmark backward propagation algorithm and the conventional PSO algorithm, it attains a higher accuracy in a much shorter time

Kwok-Wing Chau

CiteSeerX

Lecture Notes in Artificial Intelligence, Vol. 4099, 2006, pp. 1211-1215 
A Split-Step PSO Algorithm in Predicting Construction 
Litigation Outcome 
Kwok-wing Chau 
Department of Civil and Structural Engineering, Hong Kong Polytechnic University, 
Hunghom, Kowloon, Hong Kong 
cekwchau@polyu.edu.hk 
Abstract. Owing to the highly complicated nature and the escalating cost 
involved in construction claims, it is highly desirable for the parties to a dispute 
to know with some certainty how the case would be resolved if it were taken to 
court. The use of artificial neural networks can be a cost-effective technique to 
help to predict the outcome of construction claims, on the basis of 
characteristics of cases and the corresponding past court decisions. This paper 
presents the application of a split-step particle swarm optimization (PSO) model 
for training perceptrons to predict the outcome of construction claims in Hong 
Kong. The advantages of global search capability of PSO algorithm in the first 
step and local fast convergence of Levenberg-Marquardt algorithm in the 
second step are combined together. The results demonstrate that, when 
compared with the benchmark backward propagation algorithm and the 
conventional PSO algorithm, it attains a higher accuracy in a much shorter time. 
1 Introduction 
It is highly desirable for the parties to a dispute to know with some certainty how the 
case would be resolved if it were taken to court. This would effectively help to 
significantly reduce the number of disputes that would need to be settled by the much 
more expensive litigation process. Artificial neural networks (ANN), in particular the 
feed forward back-propagation (BP) perceptrons, have been widely applied in 
different fields [1-2]. ANN can be a cost-effective technique to identify the hidden 
relationships among various interrelated factors and to mimic decisions that were 
made by the court. However, slow training convergence speed and easy entrapment in 
a local minimum are inherent drawbacks of the commonly used BP algorithm [3]. 
Levenberg-Marquardt (LM) optimization technique [4] is a commonly used ANN that 
has attained certain improvements such as convergence rates over the BP algorithm. 
Swarm intelligence is another recent SC technique that is developing quickly [5]. 
These SC techniques have been applied in construction problem and accomplished 
satisfactory results [6-7]. 
In this paper, a split-step PSO algorithm is employed to train multi-layer 
perceptrons for prediction of the outcome of construction litigation in Hong Kong. It 
is believed that, by combining the two algorithms, the advantages of global search 
This is the Pre-Published Version.
capability of PSO algorithm in the first step and local fast convergence of LM 
algorithm in the second step can be fully utilized to furnish promising results. 
2 Nature of Construction Disputes 
Prior to the actual construction process, the involving parties will attempt to sort out 
the conditions for claims and disputes through the contract documents. However, 
since a project usually involves thousands of separate pieces of work items to be 
integrated together to constitute a complete functioning structure, the potential for 
honest misunderstanding is extremely high. The legislation now in force requires that 
any disputes incurred have to be resolve successively by mediation, arbitration, and 
the courts [8]. 
3 Characteristics of PSO Algorithm 
Among other advantages, the more significant one is its relatively simple coding and 
hence low computational cost. One of the similarities between PSO and a genetic 
algorithm is the fitness concept and the random population initialization. However, 
the evolution of generations of a population of these individuals in such a system is by 
cooperation and competition among the individuals themselves. The capability of 
stochastic PSO algorithm, in determining the global optimum with high probability 
and fast convergence rate, has been demonstrated in other cases [9-10]. PSO can be 
readily adopted to train the multi-layer perceptrons as an optimization technique. 
4 Training of Perceptrons by PSO 
Without loss of generality, a three-layered preceptron is considered in the following. 
W[1] and W[2] represent the connection weight matrix between the input layer and the 
hidden layer, and that between the hidden layer and the output layer, respectively. 
During training of the preceptron, the i-th particle is denoted by Wi = {W[1], W[2]} 
whilst the velocity of particle i is denoted by Vi. The position representing the 
previous best fitness value of any particle is denoted by Pi whilst the best matrix 
among all the particles in the population is recorded as Pb. Let m and n represent the 
index of matrix row and column, respectively, the following equation represents the 
computation of the new velocity of the particle based on its previous velocity and the 
distances of its current position from the best experiences both in its own and as a 
group. 
)],(),([),(),( ][][][][ nmWnmPrnmVnmV ji
j
i
j
i
j
i −+= α  
)],(),([ ][][ nmWnmPs ji
j
b −+ β  
(1) 
where j = 1, 2; m = 1, …, Mj; n= 1, …, Nj; Mj and Nj are the row and column sizes of 
the matrices W, P, and V; r and s are positive constants; α and β are random numbers 
in the range from 0 to 1. In the context of social behavior, the cognition part 
)],(),([ ][][ nmWnmPr ji
j
i −α  denotes the private thinking of the particle itself 
whilst the social part )],(),([ ][][ nmWnmPs ji
j
b −β  represents the collaboration 
among the particles as a group. The new position is then determined based on the new 
velocity as follows: 
][][][ j
i
j
i
j
i VWW +=  (2) 
The fitness of the i-th particle is determined in term of an output mean squared 
error of the neural networks as follows: 
∑ ∑
= =
⎥
⎦
⎤
⎢
⎣
⎡
−=
S
k
O
l
iklkli WptS
Wf
1 1
2)}({1)(  
(3) 
where f is the fitness value, tkl is the target output; pkl is the predicted output based on 
Wi; S is the number of training set samples; and, O is the number of output neurons. 
5 The Study 
The system is applied to study and predict the outcome of construction claims in 
Hong Kong. The data from 1991 to 2000 are organized case by case and the dispute 
characteristics and court decisions are correlated. Through a sensitivity analysis, 13 
case elements that seem relevant in courts’ decisions are identified. They are, namely, 
type of contract, contract value, parties involved, type of plaintiff, type of defendant, 
resolution technique involved, legal interpretation of contract documents, 
misrepresentation of site, radical changes in scope, directed changes, constructive 
changes, liquidated damages involved, and late payment.  
Some of the 13 case elements can be expressed in binary format; for example, the 
input element ‘liquidated damages involved’ receives a 1 if the claim involves 
liquidated damages or a 0 if it does not. However, some elements are defined by 
several alternatives; for example, ‘type of contract’ could be remeasurement contract, 
lump sum contract, or design and build contract. These elements with alternative 
answers are split into separate input elements, one for each alternative. Each 
alternative is represented in a binary format, such as 1 for remeasurement contract and 
0 for the others if the type of contract is not remeasurement. In that case, only one of 
these input elements will have a 1 value and all the others will have a 0 value. In this 
way, the 13 elements are converted into an input layer of 30 neurons, all expressed in 
binary format. Table 1 shows examples of the input neurons for cases with different 
types of contract. The court decisions are also organized in an output layer of 6 
neurons expressed in binary format corresponding to the 6 elements: client, contractor, 
engineer, sub-contractor, supplier, and other third parties.  
In total, 1105 sets of construction-related cases were available, of which 550 from 
years 1991 to 1995 were used for training, 275 from years 1996 to 1997 were used for 
testing, and 280 from years 1998 to 2000 were used to validate the network results 
with the observations. It is ensured that the data series chosen for training and 
validation comprised balanced distribution of cases. 
Table 1. Examples of the input neurons for cases with different types of contract 
Cases  
Input neuron Remeasurement Lump sum Design and 
build 
Type of contract -
remeasurement 
1 0 0 
Type of contract - lump 
sum 
0 1 0 
Type of contract – design 
and build 
0 0 1 
 
Sensitivity analysis is performed to determine the best architecture, with variations 
in the number of hidden layers and number of hidden neurons. The final perceptron 
has an input layer with thirty neurons, a hidden layer with fifteen neurons, and output 
layer with six neurons. In the PSO-based perceptron, the number of population is set 
to be 40 whilst the maximum and minimum velocity values are 0.25 and -0.25 
respectively. 
Table 2. Comparison of prediction results for various perceptrons 
Training Validation  
Algorithm Coefficient of 
correlation 
Prediction rate Coefficient of 
correlation 
Prediction rate 
BP-based 0.956 0.69 0.953 0.67 
PSO-based 0.987 0.81 0.984 0.80 
LM 0.964 0.70 0.957 0.68 
Split-step 0.990 0.84 0.987 0.83 
6 Analysis and Discussions 
The performance of the split-step multi-layer ANN is evaluated in comparison with 
the benchmarking standard BP-based network, a PSO-based network and a LM 
network. In order to provide a fair and common initial ground for comparison purpose, 
the training process of the BP-based perceptron or LM network commences from the 
best initial population of the corresponding PSO-based perceptron or split-step 
network. Table 2 shows comparisons of the results of network for various perceptrons. 
It can be observed that the split-step algorithm performs the best in terms of 
prediction accuracy. It is noted that testing cases of the split-step PSO-based network 
are able to give a successful prediction rate higher than 80%, which is much higher 
than by pure chance. It is believed that, if the involving parties to a construction 
dispute become aware with some certainty how the case would be resolved if it were 
taken to court, the number of disputes could be reduced significantly. 
7 Conclusions 
In this paper, a perceptron based on a split-step PSO algorithm is employed for 
prediction of outcomes of construction litigation on the basis of the characteristics of 
the individual dispute and the corresponding past court decisions. The results show 
that the split-step PSO-based perceptron outperforms the other commonly used 
optimization techniques in prediction of outcomes of construction litigation, in terms 
of both convergence and accuracy. The final network presented in this study is 
recommended as an approximate prediction tool for the parties in dispute, since the 
rate of prediction is higher than 80%, which is much higher than chance. It is, of 
course, recognized that there are limitations in the assumptions used in this study. 
Other factors that may have certain bearing such as cultural, psychological, social, 
environmental, and political factors have not been considered here. 
References 
1. Chau, K.W., Cheng, C.T.: Real-Time Prediction of Water Stage with Artificial Neural 
Network Approach. Lecture Notes in Artificial Intelligence, 2557 (2002) 715-715 
2. Cheng, C.T., Chau, K.W., Sun, Y.G., Lin, J.Y.: Long-term Prediction of Discharges in 
Manwan Reservoir using Artificial Neural Network Models. Lecture Notes in Computer 
Science 3498 (2005) 1040-1045 
3. Rumelhart, D.E., Widrow, B., Lehr, M.A.: The Basic Ideas in Neural Networks. 
Communications of the ACM 37(3) (1994) 87-92 
4. Hagan, M.T., Menhaj, M.B.: Training Feedforward Networks with the Marquardt 
Algorithm. IEEE Transactions on Neural Networks 5(6) (1994) 989-993 
5. Kennedy, J., Eberhart, R.: Particle Swarm Optimization. Proceedings of the 1995 IEEE 
International Conference on Neural Networks. Perth (1995) 1942-1948 
6. Arditi, D., Oksay, F.E., Tokdemir, O.B.: Predicting the Outcome of Construction 
Litigation Using Neural Networks. Computer-Aided Civil and Infrastructure Engineering 
13(2) (1998) 75-81 
7. Chau, K.W.: Predicting Construction Litigation Outcome using Particle Swarm 
Optimization. Lecture Notes in Artificial Intelligence 3533 (2005) 571-578 
8. Chau, K.W.: Resolving Construction Disputes by Mediation: Hong Kong Experience. Journal 
of Management in Engineering, ASCE 8(4) (1992) 384-393 
9. Kennedy, J.: The Particle Swarm: Social Adaptation of Knowledge. Proceedings of the 1997 
International Conference on Evolutionary Computation. Indianapolis (1997) 303-308 
10. Clerc, M., Kennedy, J.: The Particle Swarm—Explosion, Stability, and Convergence in a 
Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation 6(1) 
(2002) 58-73 


A Split-Step PSO Algorithm in Predicting Construction Litigation Outcome

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A8016B73C18287FD170799324EC3CA17?doi=10.1.1.1045.3693&rep=rep1&type=pdf

A Split-Step PSO Algorithm in Predicting Construction Litigation Outcome

Abstract

Similar works

Full text

Available Versions

CiteSeerX