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A hybrid model for supplier selection: integration of AHP and multi expression programming (MEP)


Abstract and Figures

Supplier evaluation and selection is a complicated process which deals with conflicting attributes such as quality, cost. To mitigate the computational complexity, intelligent-based techniques have gained much popularity. But the main shortcoming of the existing models in this regard is to be a black box system. In this paper, we aim to combine analytical hierarchy process with multi-expression programming to both introduce a new evolutionary approach in the field of supplier evaluation and selection and cope with the earlier problem. To show the validity of the model, statistical test was carried out. The finding showed that the proposed model is accurate and acceptable for using in the evaluation process.
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A hybrid model for supplier selection: integration of AHP
and multi expression programming (MEP)
Alireza Fallahpour
Ezutah Udoncy Olugu
Siti Nurmaya Musa
Received: 11 May 2015 / Accepted: 11 October 2015
The Natural Computing Applications Forum 2015
Abstract Supplier evaluation and selection is a compli-
cated process which deals with conflicting attributes such
as quality, cost. To mitigate the computational complexity,
intelligent-based techniques have gained much popularity.
But the main shortcoming of the existing models in this
regard is to be a black box system. In this paper, we aim to
combine analytical hierarchy process with multi-expression
programming to both introduce a new evolutionary
approach in the field of supplier evaluation and selection
and cope with the earlier problem. To show the validity of
the model, statistical test was carried out. The finding
showed that the proposed model is accurate and accept-
able for using in the evaluation process.
Keywords Supplier selection Black box
Multi-expression programming AHP Supply chain
1 Introduction
Supplier evaluation and selection is a critical issue for
achieving success in any manufacturing industry. Multi-
criteria decision making (MCDM) as the main approach of
decision-making theory has been successfully used to solve
this problem [1,2]. Due to the presence of conflicting
factors such as quality, cost, assessing and selecting the
proper suppliers is a very complex problem. Therefore,
numerous solo and integrated models have been presented
in this area.
One of the most attractive techniques for suppliers’ per-
formance evaluation is artificial intelligence (AI)-based
techniques [3,4]. Increasingly, academics are exploring
neural-based techniques such as artificial neural network
(ANN) [5] and adaptive neuro fuzzy inference system
(ANFIS) [6] asthe reliable approachesfor supplierevaluation
and selection. AI models as computer-aided techniques can
predict suppliers’ performance based on the historical data set.
One of the integrated neural-based methods which
recently received much attention is combination of ana-
lytical hierarchy process (AHP) and ANN for assessing
suppliers’ performance [5,7]. Although this model is
robust and accurate in performance evaluation, it has some
limitations. Although AHP is useful in decision making, it
cannot handle vagueness. In addition, ANN is a powerful
tool in pattern recognition, but it is unable to propose an
explicit mathematical model. In order to overcome the
aforementioned problems, this paper is aimed at integrating
fuzzy AHP and fuzzy preference programming (FPP) with
multi-expression programming (MEP).
The main contributions of this model are:
A new genetic-based model is introduced in the field of
supplier selection.
A genetic decision model on the basis of the relation-
ship of a set of input and output is developed in a
unique manner to forecast the performance.
A new pairwise comparison model for weight calculations
and performance values is performed for a MEP model.
Historical data set is used in assessment and modeling.
&Ezutah Udoncy Olugu
Alireza Fallahpour
Siti Nurmaya Musa
Department of Mechanical Engineering, Faculty of
Engineering, University of Malaya, Kuala Lumpur, Malaysia
Neural Comput & Applic
DOI 10.1007/s00521-015-2078-6
The rest of the model is presented as follows: Sect. 2
provides literature review related to supplier selection.
Section 3provides information about the techniques and
the proposed model. Case study is presented in Sect. 4.
Model performance evaluation is given in Sect. 5. Finally,
conclusion is presented in Sect. 6.
2 Literature
Since a proper supplier has crucial influence on the per-
formance of SCM, various models have been proposed in
this area. The literature reports that it can be categorized
into seven main parts such as multi-attribute decision
making (MADM) like TOPSIS, AHP, ANP, ; mathematical
modeling including linear programing, integer programing,
nonlinear modeling; data envelopment analysis (DEA);
fuzzy set theory (FST); artificial intelligence (AI) such as
ANFIS, ANN, SVM; statistical/probabilistic approaches;
hybrid techniques.
Each category possesses its own advantages and disad-
vantages. MADM is easy to use, but the results are almost
based on decision makers’ opinion. For example, different
weights could be given to the different criteria by the
experts. Mathematical programming technique is an accu-
rate model, but it is unable to take into account qualitative
criteria. In the mathematical models, finding the accurate
model for decision makers is so difficult. DEA method
does not use any assumption in efficiency evaluation, but it
is very sensitive to homogeneity. Most of the other cate-
gories do not consider the interactions among the various
factors and also cannot effectively consider risk and
uncertainty in estimating the supplier’s performance [3].
Among the aforementioned techniques, predictive AI
models have been received much attention from the aca-
demics and practitioners. One of the benefits of AI methods
in contrast with other approaches is that they do not need
assumption in the decision-making process. Moreover, AI
methods provide predictive models based on the historical
data set. This feature is very useful for decision making [5].
Generally, the literature reports that AI techniques can
handle better with complexity and imprecision than pre-
vious approaches [8].
With respect to the literature, there are three main pre-
dictive AI-based models for supplier evaluation and
selection including: pure AI-based model (such as ANN-
based models, ANFIS-based model, SVM-based models,
and FIS-based models); DEA–AI models (such as DEA–
ANFIS) models.
Kuo et al. [9] proposed an intelligent supplier decision
support system which is able to consider both the quanti-
tative and qualitative criteria. The model enables decision
makers to deal with quantitative data such as profit and
productivity. Guneri et al. [6] proposed a predictive
ANFIS-based model in supplier selection in a textile
industry. A 1–10 numeric scale was applied to rate the
criteria. After collecting the data set, three most effective
criteria on the performance were selected and a predictive
ANFIS-based model was proposed to estimate the suppli-
ers’ performance. Golmohammadi [7] proposed a neural-
based structure for decision making and selecting the best
suppliers. After defining the evaluative criteria, using AHP
pairwise comparison the data set was collected. Then, the
collected AHP-based data set was divided into two parts
for training the ANN model and testing its prediction
ability. In order to improve the model, mathematical
models were defined for measuring each criterion. After-
wards, the same operation was done with the new collected
data set. Ozkan and Inal [10] improved the model proposed
by Golmohammadi [5] and presented an ANFIS-based
model for supplier selection. They highlighted that their
model is more accurate than the proposed neural network
model. Fallahpour et al. [11] combined DEA with ANFIS
to evaluate suppliers’ performance. They concluded that
the proposed integrated model is more accurate model
compared to other models. This paper is aimed at extend-
ing Golmohammadi’s model by combining AHP with
3 Methodology
In this part, an overview about AHP and MEP is given.
Then, the proposed model is explained.
3.1 Analytical hierarchy process (AHP)
Saati proposed AHP as a useful and flexible decision-
making model which can be used for both qualitative and
quantitative attributes. As the attributes are determined and
the weights are computed by pairwise comparison matrix,
similar procedure can be applied to calculate the weight of
the alternatives. The pairwise comparison matrix of alter-
natives is structured based on attribute. The result is a new
reciprocal square matrix for each criterion, with its corre-
sponding eigenvector. The procedure is repeated for all
attributes, and the number of each alternative and criterion
is obtained. Afterwards, the score of each alternative is
multiplied by the weight of the corresponding attribute. At
the end, all the numbers for an alternative are summed up
to find the overall score, and the final calculation results
show the importance of each alternative [12,13]. The
alternatives are then ranked according to their calculated
values. Generally, problems associated with AHP are split
into three parts [14]:
Neural Comput & Applic
1. Structuring the problem; evaluation of local priorities;
determination of global priorities. The main feature of
AHP is pairwise comparisons which enable decision
makers to obtain the best decision. Practically, AHP
includes the following steps:
2. Forming the defined attributes hierarchically.
3. Generating judgment matrix using pairwise
4. Computing a priority vector to weight the components
of the matrix.
5. Determining global priorities by gathering all local
priorities with the application of a simple weighted
6. At the end, the eigenvalue is performed to evaluate the
strength of the consistency ratio of the comparative
matrix and identify whether to accept the information.
In order to measure the rate of the criteria and suppliers’
performance, 1–9 scale (Saaty scale) is used (see Table 1).
The mathematical process starts by normalizing and
obtaining the relative weights for each matrix. The relative
weights are given by the right eigenvector (W) corre-
sponding to the largest eigenvalue (k
), as:
3.2 Multi-expression programming (MEP)
Oltean and Dumitrescu [15] presented MEP as an extension
of genetic programming (GP). MEP performs linear chro-
mosomes for solution encoding [16]. MEP is able to
encode multiple computer programs of a problem in a
single chromosome [16]. After checking the fitness of the
programs, the best one is selected to propose the chromo-
some. MEP is not as complex as other GP such as gene
expression programming (GEP). MEP begins by generating
a random population of individuals. MEP applies the fol-
lowing stages to create the best solution:
1. Choosing two parents using a binary tournament
procedure and recombining them with a fixed cross-
over probability;
2. Gaining two offspring by the recombination of two
3. Mutating the offspring and replacing the worst indi-
vidual in the current population with the best of them.
Number of the MEP genes per chromosome is constant
and determines the length of the chromosome. A terminal
(an element in the terminal set T) or a function symbol (an
element in the function set F) is encoded by each gene. A
gene that encodes a formulation consists of pointers toward
the function arguments. Function parameters always have
indices of lower values than the position of that function
itself in the chromosome. The first symbol in a chromo-
some must be a terminal symbol as stated by the proposed
representation scheme [17].
3.3 Methodology
This paper is aimed at proposing hybrid AHP–MEP model
to cope with the earlier-mentioned problems associated
with the previous intelligent-based model. To this end, the
following steps should be carried out (see Fig. 1):
Step 1 Collecting the importance of each criterion for
suppliers (alternatives) by pairwise comparison
(using AHP),
Step 2 Collecting the suppliers’ performance (scores) by
pairwise comparison (using AHP),
Step 3 Dividing the gathered data set into twofold for
training (pattern recognition) and testing
(prediction evaluation),
Table 1 Range for attributes measuring
Very poor (VP) 1 BWB2
Poor (P) 2 BWB3
Poor medium (PM) 3 BWB4
Medium (M) 4 BWB6
Medium good (MG) 6 BWB7
Good (G) 7 BWB8
Very good (VG) 8 BWB9
Fig. 1 Methodology of the model
Neural Comput & Applic
Step 4 Assessing the model using statistical test and
other AI-based models.
In order to evaluate the accuracy of the model, mean
square error (MSE) and mean absolute error (MAE) are
used in training and testing stages.
MAE ¼1
where h
and O
are, respectively, the real and predicted
performance scores for the ith performance, hiand oiare,
respectively, the average of the real and predicted perfor-
mance scores, and nis the number of suppliers.
4 Case study
To show the feasibility and application of the proposed
model, a real-life supplier selection problem from a textile
company of Iran is considered (the company name is not
disclosed for privacy reasons) which produces open-end
(OE) yarn. Its staff strength is 500. It works with 33 sup-
pliers to fill its daily order. Therefore, there is a great need
to evaluate the suppliers’ performance.
4.1 Determining the supplier selection criteria
The first echelon in evaluating the suppliers’ performance
includes determining and defining the evaluation attributes.
In this study, based on the literature and experts’ opinion,
five criteria were selected and applied to the textile factory.
The five criteria are quality, delivery, technology, cost, and
flexibility. Table 2shows the definition of each criterion.
4.2 Rating each attribute and suppliers’
performance score
As said earlier, AHP-based pairwise comparison is used to
gather the data set. Three experts have been selected to rate
the determined criteria and the suppliers’ performance. The
experts have PhD degree in long-fiber spinning, weft
knitting, and non-woven knitting. Each of them has more
than 10 years of experience in the textile industry. For this
research, they were asked to rate the selected criteria and
the suppliers’ performance based on the 1–9 Saaty scale
(Table 1). Next, pairwise comparison is performed for
obtaining suppliers’ performance scores. Table 3illustrates
the collected data set.
4.3 Training MEP (mathematical model)
and testing
The gathered data set was divided into twofolds for training
and testing (50 % for training and 50 % for testing). In the
training, MEP was run to find a computer program that
connects the criteria to the performance. The best model
was chosen considering the lowest statistical errors (shown
in Sect. 5).
4.3.1 Parameters of the predictive MEP-based algorithm,
the mathematical equation of the suppliers’
performance evaluation and statistical measures
in both the training and testing process
Since there is no exact rule to find the optimum parameters
in MEP (AI-based) techniques [21], for finding the best
structure of MEP several runs were conducted. Table 4
provides the best parameters of MEP predictive algorithm.
To find the optimized MEP-based model, there are some
important parameters which should be structured very well.
Table 2 Selection criteria for
evaluating the suppliers’
Criteria Definition
Quality The excellence ability of supplied materials to meet or exceed purchasers’ expectations. In
order to evaluate this criterion, quality certification and standards are very important
[18]. This attribute has positive impact on the suppliers’ efficiency, and with increasing
QM, the suppliers’ efficiency increases
Delivery (D) This looks at the on-time delivery. As this criterion increases, supplier’s performance is
Technology This mainly focuses on the range of material supplied and modernity of the machinery.
This factor has a direct relationship with efficiency
Cost (C) This covers the final cost of the goods and transportation [19]. A supplier is termed as ‘‘the
more efficient supplier’’ whose total cost is lower than other competing suppliers
Flexibility (F) Rate of response to change [20]. With increasing this attribute, the supplier’s performance
Neural Comput & Applic
P¼sin xTþxQ18:5ðÞþcos cos Ln xPxQ
þsin sin cos e
The remaining 50 % of the data set is used for evalu-
ating the predictive ability of the model. In the training, the
MSE, MAE, and Rare 0.002, 0.013, and 0.963, respec-
tively. In the testing stage, MSE, MAE, and R are 0.007,
0.043, and 0.912, respectively. Figure 2shows the accu-
racy of the model for both training and testing.
5 Performance evaluation
To assess the performance of the model, Smith [22] defined
the following circumstances:
If a model gives |R|[0.8, a strong correlation exists
between the predicted and real values.
If a model gives 0.2 \|R|\0.8, a correlation exists
between the predicted and real values.
If a model gives |R|\0.2, a weak correlation exists
between the predicted and real values.
In all conditions, the error values (e.g., MSE) should be
at the minimum [23]. The derived results show that the
MEP models provide very precise predictions for both the
training and testing data sets.
6 Conclusion
Suppliers’ performance evaluation as a common MCDM
problem has received much attention from academics and
practitioners. In today’s competitive world, companies
have concentrated on customer satisfaction and decreasing
price with long-term contracts with reliable suppliers.
Consequently, a robust and applicable method is needed to
ease monitoring suppliers’ performance for managers.
Over the recent decade, combining AHP with ANN has
gaining popularity. Although ANN is very powerful in
model prediction, its major drawback is the black box
system. Therefore, in this paper, a new evolutionary tech-
nique, namely MEP, was introduced to solve the earlier-
mentioned problem.
Generally, it could be concluded that the proposed
model (AHP–MEP) is very powerful and precise in sup-
pliers’ performance evaluation. The main limitation of the
proposed model is that while increasing the number of
criteria and alternative (supplier) the burden of computa-
tional complexity is increased.
Table 3 First data set
Inputs Output
Q D T P F Performance
3 6 3.5 4 1.5 0.05
3.5 3.5 6 6 1.5 0.05*
7 6 4.5 6 3 0.10*
6.5 6.5 6.5 6.5 5.5 0.11
5 4 5.5 4 5 0.11*
5 6 6 5.5 2.5 0.12
3.5 5 6 6.5 3.5 0.13*
5.5 4.5 6 4.5 7 0.15
5 6.5 3.5 3.5 8 0.16*
5.5 6.5 5.5 7 5.5 0.19
5 7 5.5 7 5.5 0.19*
2 6.5 2 8 4 0.22*
5.5 7.5 5.5 3.5 7.5 0.23
5 7 9 4.5 5 0.23*
4 4 7 6.5 6 0.25
6 6.5 8 4.5 5 0.27*
4 5.5 7 8 4 0.28
5 6.5 8 5 6 0.30*
7 8 7 4.5 2.5 0.34
6.5 7.5 6.0 6.5 3 0.36*
8.5 8 7.5 2.5 7.5 0.46
7 6.5 7 5 8 0.47*
7.5 6 7 5.5 8 0.49*
7.5 7.5 9 3 4.5 0.59
8.5 7 6.5 4 7 0.61
8 8 8.5 6 4 0.64
* These are the testing data set
Table 4 Optimal parameters of MEP
Parameters Setting
Population size 500–2000
Chromosome length 90 genes
Number of generations 500
Number of tournament 4
Crossover probability 0.5, 0.9
Crossover type Uniform
Mutation probability 0.01
Terminal set Problem input
Neural Comput & Applic
Acknowledgments This work is sponsored by Malaysian Ministry
of Higher Education High Impact Research (HIR-MOHE) Project
(UM.C/HIR/MOHE/ENG/01) and the University of Malaya Research
Grant Project (RP018C-13AET).
1. Fallahpour A, Moghassem A (2012) Evaluating applicability of
VIKOR method of multi-criteria decision making for parameters
selection problem in rotor spinning. Fibers Polym 13:802–808
2. Kuo R, Hsu C, Chen Y (2015) Integration of fuzzy ANP and
fuzzy TOPSIS for evaluating carbon performance of suppliers. Int
J Environ Sci Technol 1–14. doi:10.1007/s13762-015-0819-9
3. Vahdani B, Iranmanesh S, Mousavi SM, Abdollahzade M (2012)
A locally linear neuro-fuzzy model for supplier selection in
cosmetics industry. Appl Math Model 36:4714–4727
4. Fallahpour A, Olugu EU, Musa SN, Khezrimotlagh D, Wong KY
(2015) An integrated model for green supplier selection under
fuzzy environment: application of data envelopment analysis and
genetic programming approach. Neural Comput Appl 1–19.
5. Golmohammadi D (2011) Neural network application for fuzzy
multi-criteria decision making problems. Int J Prod Econ
6. Gu
¨neri AF, Ertay T, Yu
¨Cel A (2011) An approach based on
ANFIS input selection and modeling for supplier selection
problem. Expert Syst Appl 38:14907–14917
7. Golmohammadi D, Creese RC, Valian H, Kolassa J (2009)
Supplier selection based on a neural network model using genetic
algorithm. IEEE Trans Neural Netw 20:1504–1519
8. Azadeh A, Saberi M, Anvari M (2011) An integrated artificial
neural network fuzzy C-means-normalization algorithm for per-
formance assessment of decision-making units: the cases of auto
industry and power plant. Comput Ind Eng 60:328–340
9. Kuo R, Hong S, Huang Y (2010) Integration of particle swarm
optimization-based fuzzy neural network and artificial neural
network for supplier selection. Appl Math Model 34:3976–3990
10. O
¨zkan G, I
˙nal M (2014) Comparison of neural network appli-
cation for fuzzy and ANFIS approaches for multi-criteria decision
making problems. Appl Soft Comput 24:232–238
11. Fallahpour A, Olugu EU, Musa SN, Khezrimotlagh D, Singh S
(2014) Supplier selection under fuzzy environment: a hybrid
model using KAM in DEA. In: Emrouznejad A, Banker R,
Doraisamy SM, Arabi B (eds) Recent developments in data
envelopment analysis and its applications, pp 342–348
12. Oztaysi B (2014) A decision model for information technology
selection using AHP integrated TOPSIS-Grey: the case of content
management systems. Knowl Based Syst 70:44–54
13. Deng X, Hu Y, Deng Y, Mahadevan S (2014) Supplier selection
using AHP methodology extended by D numbers. Expert Syst
Appl 41:156–167
14. Mikhailov L, Tsvetinov P (2004) Evaluation of services using a
fuzzy analytic hierarchy process. Appl Soft Comput 5:23–33
15. Oltean M, Dumitrescu D (2002) Multi expression programming,
16. Hossein A, Alavi A, Mollahasani A, Hossein Gandomi J, Boluori
Bazaz J (2012) Formulation of secant and reloading soil defor-
mation moduli using multi expression programming. Eng Com-
put 29:173–197
17. Alavi AH, Gandomi AH, Sahab MG, Gandomi M (2010) Multi
expression programming: a new approach to formulation of soil
classification. Eng Comput 26:111–118
18. C¸ elebi D, Bayraktar D (2008) An integrated neural network and
data envelopment analysis for supplier evaluation under incom-
plete information. Expert Syst Appl 35:1698–1710
19. Kuo RJ, Wang YC, Tien FC (2010) Integration of artificial neural
network and MADA methods for green supplier selection.
J Clean Prod 18:1161–1170
20. Lima FR, Junior L, Osiro LCR Carpinetti (2013) A fuzzy infer-
ence and categorization approach for supplier selection using
compensatory and non-compensatory decision rules. Appl Soft
Comput 13:4133–4147
21. Emrouznejad A, Shale E (2009) A combined neural network and
DEA for measuring efficiency of large scale datasets. Comput Ind
Eng 56:249–254
22. Smith GN (1986) Probability and statistics in civil engineering:
an introduction. Collins, London
23. Mostafavi ES, Mostafavi SI, Jaafari A, Hosseinpour F (2013) A
novel machine learning approach for estimation of electricity
demand: an empirical evidence from Thailand. Energy Convers
Manag 74:548–555
Fig. 2 Actual versus predicted suppliers’ performance scores using the GEP model atraining data, btesting
Neural Comput & Applic
... The MEP model, akin to the GEP model, enables the adjustment of diverse variables, as depicted in Fig. 3. According to previous research, the primary determinants of multi-expression programming are the function set, crossover likelihood, algorithm/code length, and the size and range of sub-populations [94]. When the total number of programs constitutes the population size, an Increase in the number of sub-populations and their respective sizes leads to a complex evaluation process and protracted computations. ...
... Their findings indicate that the amalgamation of LGP and MEP surpasses other neural network-based approaches in terms of performance. Comparatively, the operational process of the GEP is more intricate in comparison to the MEP mechanism [94]. While GEP and MEP have differing densities, with MEP being less dense [98], there are notable distinctions between the two. ...
... For example, the choice of population size was made depending on the computing resources available, the complexity of the problem, and previous knowledge of the problem area. The selection of chromosomal length is influenced by the problem's complexity, the need for accurate representation, and the balance of exploration and exploitation [94]. In order to choose crossover and mutation rates that were optimal for the particular issue area, empirical testing was used to establish these rates. ...
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This research used gene expression programming (GEP) and multigene expression programming (MEP) to determine the compressive strength (CS) of alkali-activated material (AAM) to compare and develop more reliable genetic algorithm-based prediction models. To learn more about how raw ingredients affect and interact with the CS of AAM, a SHapley Additive exPlanations (SHAP) analysis was conducted. A comprehensive dataset containing 676 points with fifteen influential parameters was formulated from the previously published literature. According to this study, considering the impact of 15 input variables, both genetic algorithms produced results close to the experimental CS (retrieved from the literature). When the performance of the GEP and MEP models were compared, it was found that the MEP model, with an R2 of 0.86, performed better than the GEP model, with an R2 of 0.82. The assessment of the statistical parameters of generated models revealed that the MEP model was more effective. Additionally, SHAP analysis revealed that slag content, followed by the specimen's age, sodium silicate, and curing temperature, showed a positive correlation with CS of AAM, which were the most important parameters. The results also revealed the importance of chemical contents, i.e., CaO, SiO2, Al2O3, of FA and slag on the CS of AAM. The built models might be used to compute the CS of AAMs with varying input parameter values, minimizing the effort, time, and cost of unnecessary lab tests. Furthermore, the outcomes of the SHAP study might help researchers and the industry determine the quantity or composition of raw ingredients when producing AAMs.
... Similar to the GEP model, the MEP model allows for the fitting of various factors. The range and size of sub-populations, algorithm/code length, cross-over likelihood, and function set are the key factors that control multi-expression programming [59]. A greater number of sub-populations and their corresponding subpopulation sizes result in complicated assessment and time-consuming calculation when the size of the population is the overall number of programs. ...
... In their comparison of the effectiveness of linear genetic programming (LGP) and MEP methodologies, Grosan and Abraham [62] discovered that the combination of LGP and MEP outperforms other neural network-based methods. Relatively, the GEP's working mechanism is more complicated than the MEP mechanism [59]. Although MEP is less dense than GEP [63], it differs from GEP (i) it is suitable to reuse code in MEP, (ii) the non-coding areas can be shown in any unfixed-location in the chromosomes, and (iii) the pointers to function arguments are explicitly encrypted in the MEP. ...
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This research intended to increase the understanding of using modern machine intelligence techniques, including multi-expression programming (MEP) and gene expression programming (GEP), for the compressive strength (CS) prediction of rice husk ash (RHA) concrete. In addition, SHapley Additive exExplanations (SHAP) analysis was made to study the impact and interaction of raw materials on the CS of RHA concrete. A comprehensive database of 192 points with six inputs (cement, specimen age, RHA, superplasticizer, water, and fine aggregate) was used for developing prediction models. This research determined that both GEP and MEP models for the CS prediction of RHA concrete yielded reliable results, which were in close agreement with the real CS. Comparing the performance of both GEP and MEP models, it was noted that MEP, with an R² of 0.89, outperformed the GEP model having an R² of 0.83. Additionally, SHAP analysis indicated that specimen age was the most vital measure, followed by cement, which positively correlated with CS of RHA. The overall effect of RHA was found to be more positive, suggesting RHA utilization in the optimal range of 75–100 kg/m³ in the RHA concrete mix. The use of prediction models and SHAP analysis will help the building industry assess material properties and raw material effects faster and more economical.
... Conversely, MEP introduces multiple genes, each encoding a sub-expression or component of the solution. These genes undergo genetic operations independently, allowing for greater exploration of the solution space and the generation of more diverse solutions [85]. ...
... In a manner analogous to that of the GEP model, the MEP model enables the fitting of a variety of factors. MEP is controlled by a number of essential criteria, the most important of which are the range and size of subpopulations, the length of the algorithm or code, the possibility of cross-over, and the function set [70]. When the size of the population is the same as the total number of programs, a more complex and time-consuming evaluation and computation is required due to the increased number of subpopulations and the corresponding sizes of those subpopulations. ...
Fiber-reinforced polymers (FRP) are widely utilized to improve the efficiency and durability of concrete structures, either through external bonding or internal reinforcement. However, the response of FRP-strengthened reinforced concrete (RC) members, both in field applications and experimental settings, often deviates from the estimation based on existing code provisions. This discrepancy can be attributed to the limitations of code provisions in fully capturing the nature of FRP-strengthened RC members. Accordingly, machine learning methods, including gene expression programming (GEP) and multi-expression programming (MEP), were utilized in this study to predict the flexural capacity of the FRP-strengthened RC beam. To develop data-driven estimation models, an extensive collection of experimental data on FRP-strengthened RC beams was compiled from the experimental studies. For the assessment of the accuracy of developed models, various statistical indicators were utilized. The machine learning (ML) based models were compared with empirical and conventional linear regression models to substantiate their superiority, providing evidence of enhanced performance. The GEP model demonstrated outstanding predictive performance with a correlation coefficient (R) of 0.98 for both the training and validation phases, accompanied by minimal mean absolute errors (MAE) of 4.08 and 5.39, respectively. In contrast, the MEP model achieved a slightly lower accuracy, with an R of 0.96 in both the training and validation phases. Moreover, the ML-based models exhibited notably superior performances compared to the empirical models. Hence, the ML-based models presented in this study demonstrated promising prospects for practical implementation in engineering applications. Moreover, the SHapley Additive exPlanation (SHAP) method was used to interpret the feature's importance and influence on the flexural capacity. It was observed that beam width, section effective depth, and the tensile longitudinal bars reinforcement ratio significantly contribute to the prediction of the flexural capacity of the FRP-strengthened reinforced concrete beam.
This article investigates the fluid dynamics and heat transfer properties in a trapezoidal enclosure containing a heated cylindrical object. It involves the interaction of multiple physical processes such as the magnetic field, thermal radiation, porous materials, and aqueous copper oxide nanoparticles. The governing partial differential equations are analyzed numerically through the continuous Galerkin finite element algorithm. The analysis takes into account various physical parameter factors, including the Richardson number (0–5), the Hartmann number (5−40), the Darcy number (0.001−0.1), thermal radiation parameter (0.5−2), and nanoparticle volume concentration (0.01−0.1). The physical mechanism of thermal and mass transfer in the enclosure caused by various factors is fully explored. In addition, the multiple expression programming (MEP) technique is implemented to report a comparative analysis of flow profiles and thermal distribution. The findings demonstrated that at low Ri, the primary flow within the cavity is driven by the shear friction generated by the moving walls. The growing importance of radiative heat transfer reduces the effectiveness of convective heat transfer, resulting in a decline in the average Nusselt number with R. The heat transfer rate rises up to 27.7% as ϕ augments; however, its value declines by 9.37% against Ha. The expected results obtained by the MEP approach are very consistent with the numerical ones. There is no doubt that the new MEP concept provides a valuable tool for researchers to predict the heat transfer behavior of any data set in cavities of different shapes. It is expected to provide new idea for the development of efficient cooling systems and the improvement of energy efficiency in various engineering applications.
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Supplier evaluation plays a critical role in a successful supply chain management. Hence, the evaluation and selection of the right suppliers have become a central decision of manufacturing business activities around the world. Consequently, numerous individual and integrated methods have been presented to evaluate and select suppliers. The current literature shows that hybrid artificial intelligence (AI)-based models have received much attention for supplier evaluation. Integrated data envelopment analysis–artificial neural network (DEA–ANN) is one of the combined methods that have recently garnered great attention from academics and practitioners. However, DEA–ANN model has some drawbacks, which make some limitation in the evaluation process. In this study, we aim at improving the previous DEA–AI models by integrating the Kourosh and Arash method as a robust model of DEA with a new AI approach namely genetic programming (GP) to overcome the shortcomings of previous DEA–AI models in supplier selection. Indeed, in this paper, GP provides a robust nonlinear mathematical equation for the suppliers’ efficiency using the determined criteria. To validate the model, adaptive neuro-fuzzy inference system as a powerful tool was used to compare the result with GP-based model. In addition, parametric analysis and unseen data set were used to validate the precision of the model.
Conference Paper
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In today’s competitive world, supplier selection is contemporary issue to business success for the manufacturing industry. Robust techniques are required to evaluate and select the most qualified suppliers. Regarding to the literature, the hybrid data envelopment analysis-artificial intelligence (DEA-AI) models are the effective models to assess the suppliers’ performance. This paper proposes an integrated Kourosh and Arash Model (KAM) in DEA, and Adaptive Fuzzy Inference System (ANFIS) as a powerful prediction tool to estimate the supplier efficiency scores. This hybrid model consists of two parts. First part applies KAM to determine the besttechnical efficiency score for each supplier, while the second part utilizes the suppliers’ performance score for training ANFIS to estimate the new suppliers’ performance. The proposed model is validated using data from a cosmetic manufacturing company.
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Optimum spinning machine parameters selection among available alternatives with different significances is a difficult task in textile industry. To overcome disadvantages associated with statistical methods that are used in such kind of problems, multi-criteria decision making approaches (MCDM) were employed by researchers. TOPSIS, AHP-TOPSIS and ELECTRE are three popular techniques in spinning problems. VIKOR, the Serbian name; Vlse Kriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution is a novel approach that has priority over other MCDM methods in terms of precision in final ranking. In this study, selecting the appropriate doffing tube components and its adjustment for 30Ne rotor spun yarn that is intended to be used for weft-knitted fabric will be provided by this approach. Yarn samples were spun considering three variables namely, the distance between the nozzle and rotor, the extractive nozzle and the draw-off tube. Feasible alternatives were ranked on the basis of the yarn quality parameters by the VIKOR and the best alternative for increasing weft-knitting machine efficiency was introduced. According to the final ranking, the spinning condition in which the sample was spun using a spiral nozzle, a doffing tube without a torque stop and a closer setting had the highest performance.
This study proposes an innovative hybrid approach for the estimation of the long-term electricity demand. A new prediction equation was developed for the electricity demand using an integrated search method of genetic programming and simulated annealing, called GSA. The annual electricity demand was formulated in terms of population, gross domestic product (GDP), stock index, and total revenue from exporting industrial products of the same year. A comprehensive database containing total electricity demand in Thailand from 1986 to 2009 was used to develop the model. The generalization of the model was verified using a separate testing data. A sensitivity analysis was conducted to investigate the contribution of the parameters affecting the electricity demand. The GSA model provides accurate predictions of the electricity demand. Furthermore, the proposed model outperforms a regression and artificial neural network-based models.
Previous studies have proven that enterprises addressing green supply chain management problem may produce an apparent improvement to their stockholder interests. According to the report of Kearney (Carbon Disclosure Project: supply chain report 2010. CDP, London, 2010), more than 80 % of the carbon emissions are generated from the suppliers’ activities in a company’s performance. Many members of the project claimed that they will reassess their suppliers as soon as possible. Therefore, to combine the carbon management issue and supplier evaluating problem turns to be a very crucial work. Therefore, this study intends to develop a framework of the supplier evaluating process for carbon management by integrating fuzzy ANP and fuzzy TOPSIS approaches. Thirteen criteria of carbon management under four dimensions were identified by literature review and modified according to the opinion of seven experts in the environmental department. The model result in a case company shows that three of the most important criteria are “carbon governance,” “carbon policy” and “carbon reduction targets.” The proposed hybrid methodology has great ability to explain the vagueness of decision maker’s expression and better discrimination power to evaluate suppliers in carbon management.
Fuzzy set theory has been used as an approach to deal with uncertainty in the supplier selection decision process. However, most studies limit applications of fuzzy set theory to outranking potential suppliers, not including a qualification stage in the decision process, in which non-compensatory types of decision rules can be used to reduce the set of potential suppliers. This paper presents a supplier selection decision method based on fuzzy inference that integrates both types of approaches: a non-compensatory rule for sorting in qualification stages and a compensatory rule for ranking in the final selection. Fuzzy inference rules model human reasoning and are embedded in the system, which is an advantage when compared to approaches that combine fuzzy set theory with multicriteria decision making methods. Fuzzy inference combined with a fuzzy rule-based classification method is used to categorize suppliers in qualification stages. Classes of supplier performance can be represented by linguistic terms, which allow decision makers to deal with subjectivity and to express qualification requirements in linguistic formats. Implementation of the proposed method and techniques were analyzed and discussed using an illustrative case. Three defuzzification operators were used in the final selection, yielding the same ranking. Factorial design was applied to test consistency and sensitivity of the inference rules. The findings reinforce the argument that including stages of qualification based on fuzzy inference and categorization makes this method especially useful for selecting from a large set of potential suppliers and also for first time purchase.
In this study, Adaptive Neuro-Fuzzy Inference System (ANFIS) is used for multi-criteria decision making in supplier evaluation and selection problem. The contemporary supply-chain management is looking for both quantitative and qualitative measures other than just getting the lowest price. After evaluating a number of distinct suppliers, determining the reliable suppliers by ANFIS model with better approximation will support decision makers. To this end, ANFIS is evaluated for different data sets with the attributes of the suppliers and their scores that are gathered from a previous study conducted for the same problem under the name of Neural Network (NN) application for fuzzy multi-criteria decision-making model. In the proposed ANFIS model built for determining supplier score, linear regression analysis (R-value) and Mean Square Error (MSE) were 0.8467 and 0.0134, respectively, while they were 0.7733 and 0.0193 for NN for fuzzy. ANFIS gives better results according to MSEs. Hence, it is determined that ANFIS algorithm can be used in multi-criteria decision making problems for supplier evaluation and selection with more precise and reliable results.
Supplier selection is an important issue in supply chain management (SCM), and essentially is a multi-criteria decision-making problem. Supplier selection highly depends on experts' assessments. In the process of that, it inevitably involves various types of uncertainty such as imprecision, fuzziness and incompleteness due to the inability of human being's subjective judgment. However, the existing methods cannot adequately handle these types of uncertainties. In this paper, based on a new effective and feasible representation of uncertain information, called D numbers, a D-AHP method is proposed for the supplier selection problem, which extends the classical analytic hierarchy process (AHP) method. Within the proposed method, D numbers extended fuzzy preference relation has been involved to represent the decision matrix of pairwise comparisons given by experts. An illustrative example is presented to demonstrate the effectiveness of the proposed method.
Content Management System (CMS) is an information system that allows publishing, editing, modifying content over internet through a central interface. By the evolution of Internet and related communication technologies, CMS has become a key information technology (IT) for organizations to communicate with its internal and exterior environment. Just like any other IT projects, the selection of CMS consists of various tangible and intangible criteria which contain uncertainty and incomplete information. In this paper the selection of CMS among available alternatives is regarded as a multi criteria decision making problem. A decision model which consists of seven criteria and four alternatives is built, AHP (Analytic Hierarchy Process) integrated Grey-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is proposed, and applied in a Turkish foreign trade company. In the proposed model, the weights of the criteria are determined by AHP method and the alternatives are evaluated by Grey-TOPSIS. Due to the uncertainties, grey numbers are used for evaluations of the alternatives. One at a time sensitivity analysis is also provided in order to monitor the robustness of the method to the changes in the weights of evaluation criteria. Besides, the effects of using different distance functions, such as Manhattan, Euclidian and Minkowski distance functions on the results are examined.