A dynamic novel approach for bid/nobid decisionmaking
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Abstract
The process of bid/nobid decisionmaking is su bjected to uncertainty and influence of complex criteria. This paper proposed an application of the integration of rough sets (RS) and improved general regression neural network (GRNN) based on niche particle swarm optimization (NPSO) algorithm for tendering decision making. The decision table of RS and the attribution reduction was processed by MIBARK algorithm to simply the samples of GRNN. In order to improve the general regression neural network (GRNN) network performance, the niche particle swarm optimization (NPSO) was used to optimize the spread parameter σ of GRNN neural network, then a novel Bid/nobid decision model was established based on RS and NPSOGRNN neural network algorithm. The applicability of the proposed model was tested using real cases in Beijing. The results indicate that NPSOGRNN algorithm has an advantage such as in prediction accuracy and generalization ability. The proposed decision support system approach is useful to help manager to make better Bid/nobid decisions in uncertain construction markets, so they can take steps to prevent bid distress.
Keywords
Rough sets GRNN neural network Niche particle swarm optimization Bid/nobid decisionBackground
When a letter of call for bid has been received, construction manager must decide to submit a bid or not. For any construction firms, being able to make right bidding decision is very important. Biding or not is a very important activity for a contractor (Lin and Chen 2004; Mahdi and Alreshaid 2005; Irtishad 1990).
To aid managers in bid/no bid decisions making, many decision methods for bidding have been proposed to assist the construction managers making better decisionmaking in an uncertain biding environment. Many scholars have proposed techniques for bid decisionmaking. However, traditional models for bid decisionmaking tend to utilize quantitative tools, just as economic models, mathematical programming, etc. which managers in both theoretical and practical did not show interest in such models (Irtishad 1990). The complexity of the problem is so overwhelming that even the very experienced contracting managers feel that the bid/nobid decisions should have a better technique tool for archiving. ElMashaleh (2013) concluded key bidding variables that are considered by contractors when evaluating bids. Senior managers of contracting industry were interviewed to identify variables that affect biding and data envelopment analysis (DEA) developed to use in the tender decision. Boussabaine and Lewis (2003), proposed a novel tender decision method utility the artificial neural network (ANN) technique. A backpropagation ANN consisting of an input layer with 18 input nodes, two hidden layers and output layer with one node was developed. Chou et al. (2015) proposed an method for estimating project award prices utilizing artificial intelligence (AI)based bid/no bid technical as well as an auxiliary tool that contract managers can use to make bid/no bid decisionmaking. This research optimizing AI models that predict bid award amounts for bridge projects. Chou et al. (2013) developed a new bid/no bid decisionmaking strategy to support the decisionmaking that is based on a combined framework of the Fuzzy Analytical Hierarchy Process (FAHP) and regressionbased simulation. In a word, new methods of artificial intelligence(AI) have been widely used in tender decision with the increasing development of science and computer technology (Deng et al. 2015; Jiang et al. 2015). Among them, the BP artificial neural networks(ANN) algorithm has been extensive used, but the practical application of the algorithm has certain limitations due to it is easily trapped in local minima and the poor convergence performance. In view of some defects existing in the traditional bid/no bid forecast methods and the problem of insufficient predicted sample amount of historical data, this paper developed a novel approach integrating rough sets with GRNN neural network based on NPSO algorithm to bid/nobid decisions. It can not only overcoming the defects that the network is easy to fall into local minimum, poor convergence and etc., but also improve and optimize the generalization capability and performance of the network through NPSO GRNN neural network algorithm.
The organize of this paper is structured as: Introduction of bid/no bid decisions making are presented in section “Background”. The basics of NPSO and GRNN methodology are introduced. The framework and key algorithms are proposed, and the flowchart of proposed NPSO GRNN approach is designed in section “Methods”. Data analysis, model implementation and some comparisons are put forward to demonstrate the developed approach in section “Data analysis and model implementation”. Results and discussion are listed in section “Results and discussion”. Our conclusions and expectations are summarized in section “Conclusions”.
Methods
GRNN model
The fourlayer structure of GRNN network is as follow: the input layer, the pattern layer, the summation layer and the output layer. Let the input vector is: \(X = \left[ {x_{1} ,x_{2} , \ldots x_{n} } \right]^{T}\), output vector is: \(Y = \left[ {y_{1} ,y_{2} , \ldots y_{k} } \right]^{T}\).
The input neurons nodes are equal to input vector dimension in the learning sample, each node which is a simple distribution unit directly takes the input vectors into the pattern layer.
X is input variable for the network, and \(X_i\) = the ith neuron correlated learning samples, σ represents spread parameter.
Equation (2) is exponent summation of all output of nodes in the pattern layer, the connection weights for each model layer and neurons is 1, the conversion formula is \(SD = \sum\nolimits_{i = 1}^{n} {P_{i} }\).
Equation (3) is a weighted exponent summation of all pattern layer’s neurons, the neurons connection weights of the ith node in the pattern layer and the jth molecule in the summation layer is the jth unit in the ith output samples, the conversion formula is \(S_{N_j} = \sum\nolimits_{i = 1}^{n} {y_{ij}P_i} \quad j = 1,2, \ldots ,k\).
Finally, the output neuron may provide the desired results, that is \(\hat{y}_{i} = \frac{S_{N_j}}{S_D}\quad j = 1,2, \ldots ,k\).2.2. Niche Particle Swarm Optimization (NPSO).
PSO was first introduced in 1995 by the American social psychologist Kennedy and electrical engineers Eberhart. In the PSO algorithm, we think each individual as particles without mass and volume in D dimensional search space and flight with a certain speed (Li et al. 2009).
Algorithm could be progressed with two core operations:
(1) If the particles \(x_{i}\) enter into the range of sub particle swarm \(S_{j}\), expressed as \(\left. {\left\ {x_{i}  x_{{s_{j} ,i}} } \right.} \right\ \le R_{{s_{j} }}\), then the particles will be assimilated by this NPS.
(2) If \(S_{j}\) and \(S_{k}\)’s range are intersected, that is \(\left. {\left\ {x_{i}  x_{{s_{j} ,i}} } \right.} \right\ \le \left {\left. {R_{{s_{j} }}  R_{{s_{k} }} } \right} \right.\), then the two subPS will be united into one.
NPSOGRNN steps for bid/nobid decisions
Seven steps were employed to build the simulation model for bid/nobid decisions, as follows:
Step 1 population initialization and parameter initialization settings, the particle size is N, c _{1} is cognitive factor and c _{2} is social factor, iteration termination condition.
Step 4 Taking the study samples and particles into the GRNN neural network.
Step 5 Calculate the fitness value of each particle and retains optimal fitness and individual, check whether it comes the optimized conditions, if it reaches the error accuracy, then end. Otherwise, go to the next niche groups of particles to optimize, the current global extreme optimal of the particle populations’ optimal solution is the spread parameter of GRNN neural network.
Step 6 If the optimal value is not found, then form a new group space for the best individual niche groups of each particle retention, redefine individual niche populations, repeat steps (4).
Step 7 Optimized by the niche particle swarm optimization, when algorithm terminates, the position of the extreme points of the global is the smooth factor values of GRNN neural network for bid/nobid decision model, then substitute it into GRNN neural network model to learn. In a word, it can be used for solving the prediction model.
Data analysis and model implementation
Variables
Reduction
Rough set theory is a data analysis theory put forward by a polish mathematician Z.Pawlak in 1982. Let \(X \subseteq U\) and \(R\) as an equivalence relation. When \(X\) repents for some basic categories ‘union and we said \(X\) can be defined for \(R\) (Definable R), otherwise, \(X\) cannot be defined for \(R\) (Indefinable R). Definable set \(R\) can also be defined as accurate set (Exact Sets R), and indefinable R set can be called as Inexact Sets or Rough set. When there is an equivalence relation \(R \in ind(K)\), and \(X\) represents for \(R\) accurate set, precise set \(X \subseteq U\) is called of collection accurate set of K; As for any \(R \in ind(K)\), \(X\) is called rough set for \(R\), \(X\) is rough set of K.
Variables processed by reduction
Reduction results
Target  Variable 

Bid/nobid decision making (\(U\))  Project demand degree (\(U_{1}\)) 
Project uncertainty (\(U_{2}\))  
Strength of firm (\(U_{3}\))  
Strategic target fulfillment (\(U_{4}\))  
Technical risk (\(U_{5}\))  
Cost risk (\(U_{6}\))  
Preferred contractor (\(U_{7}\))  
Special competitors (\(U_{8}\)) 
Simulating
Due to the impact of the variables considered are most difficultly quantitative descried, experts grading method was used. This method requires the respondents to grade the degree of importance of 8 variables that affect the tender decision making. Every variable is graded according to a 15 Likert scale, which “1” indicates not important, less and small etc., and “5” indicates most important, more and great etc.

Project demand degree: (less ~ more) corresponding (1~5)

Project uncertainty: (small ~ great) corresponding (1~5)

Strategic target fulfillment: (no meet ~ meet) corresponding (1~5)
Results and discussion
This study proposed a novel approach of process bid/nobid decision prediction while considering uncertainties and interdependencies among attribute and subattribute. Eight quantitative and qualitative factors having major impact on tending decision were identified by RS. Through investigation and analysis of the main features of tending cases in Beijing, strength of firm, project requirements, strategic target fulfillment, project uncertainty, cost risk, technical risk, preferred contractor and special competitors were as inputs of GRNN neural network, tender decision was as output. We take the above eight variables impacting bid/nobid decision as input of NPSOGRNN neural network, tendering demand as output, And take 20 cases of 2015 as the network data of training sample and the network data of prediction test samples. A computer program has been developed for training and predicting process utilizing MATLAB. Setting the size of particles in particle swarm niche N = 30, cognitive factors \(c_{1}\) = 2 and social factors \(c_{2}\) = 2. Iteration termination condition is training error of 104 or the maximum number of iterations 100.
In formula (9), \(y_{i}\) indict actual value, \(\hat{y}_{i}\) indict calculated value.
Sample distribution by tender need
Bid.  \(U_{1}\)  \(U_{2}\)  \(U_{3}\)  \(U_{4}\)  \(U_{5}\)  \(U_{6}\)  \(U_{7}\)  \(U_{8}\)  Tender decision 

1  0.8000  0.4400  0.2000  0.2000  0.2000  0.5667  0.400  0.7559  Stronger 
2  0.8000  0.4400  0.2000  0.2000  0.2000  0.5667  0.4400  0.7559  Strongest 
3  0.2000  0.2000  0.8000  0.8000  0.2000  0.4333  0.5600  0.3500  Stronger 
4  0.8000  0.4400  0.2000  0.8000  0.8000  0.5000  0.4400  0.7559  Weaker 
5  0.3912  0.5360  0.8000  0.5000  0.8000  0.5667  0.4400  0.8000  Moderate 
6  0.8000  0.4400  0.2000  0.6500  0.8000  0.6000  0.3200  0.7559  Weaker 
7  0.3912  0.5360  0.8000  0.3500  0.2000  0.4667  0.4400  0.8000  Strongest 
8  0.2000  0.2000  0.8000  0.8000  0.2000  0.2667  0.6800  0.5000  Strongest 
9  0.8000  0.4400  0.2000  0.8000  0.6000  0.7667  0.2000  0.7559  Weaker 
10  0.8000  0.4400  0.2000  0.2000  0.4000  0.5333  0.4400  0.7559  Weaker 
11  0.2743  0.2720  0.2000  0.3500  0.2000  0.6333  0.3200  0.7559  Weaker 
12  0.3912  0.5360  0.8000  0.3500  0.2000  0.4667  0.4400  0.8000  Stronger 
13  0.2000  0.2000  0.8000  0.8000  0.2000  0.2667  0.6800  0.5000  Stronger 
14  0.3912  0.5360  0.8000  0.5000  0.8000  0.5667  0.4400  0.8000  Moderate 
…  …  …  …  …  …  …  …  …  … 
38  0.4124  0.4400  0.5000  0.5000  0.2000  0.6667  0.3200  0.7559  Weakest 
Comparison results of identification performance based on different methods
Indexes  GRNN  BP  RSGRNN  NPSOGRNN  RSNPSOGRNN 

Training accuracy (%)  88.46  89.33  96.33  96.67  98.33 
Training error (%)  2.71  2.76  1.76  1.82  1.56 
Training MSE  0.1035  0.1104  0.0421  0.04017  0.0112 
Testing accuracy (%)  86.00  86.01  92.00  92.15  94.00 
Testing error (%)  4.53  4.49  2.51  2.46  2.12 
Testing MSE  0.2013  0.1895  0.08014  0.07127  0.01879 
Simulation time (s)  28.27  28.36  21.76  25.15  21.07 
Conclusions
Aiming at aiding bid/nobid decision making, this paper introduced a novel identification model through integration of rough sets(RS) and GRNN, with NPSO algorithm to optimize the smooth factor GRNN neural network and improve the prediction accuracy and convergence of networks. This method comprehensively considers various parameters that affect the tender decision. Rough sets(RS) were used to reduce the factors. MIBARK algorithm is applied in attribution reduction to simplify the network input dimension number. Furthermore, the NPSO algorithm is proposed to realize the optimization of GRNN parameters. A simulation example is provided and some comparisons with other ANN algorithms are carried out. The results show that the model proposed in this paper exhibits fairly good prediction accuracy in the same test sample, that is, the value of MSE is only 0.0112.The results of examples show that using NPSOGRNN neural network prediction model for Bid/nobid decision prediction is reasonable and feasible. NPSOGRNN neural network model offers a novel model and method to predict Bid/nobid decision.
Notes
Authors’ contributions
HS carried out the RS and NPSOGRNN neural network algorithm studies, participated in the sequence alignment and drafted the manuscript. HY collected the data needed and made the data processing in this research. LW carried out the design of the study and performed the statistical analysis. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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