دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Providing a new validation index to be used in interval type 2 fuzzy C-means (IT-2 FCM) algorithm
1
14
FA
I.
Mesgari
PhD in Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
imesgari@iust.ac.ir
Y
V. R.
Salamat
PhD Student, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran.
v_salamat@iust.ac.ir
N
B.
Minaei-Bidgoli
Associate Professor, Department of Computer Engineering, Iran University of Science and Technology, Tehran, Iran.
b_minaei@iust.ac.ir
N
One of the main issues in fuzzy clustering is to determine the number of clusters that should be available before clustering and selection of different values for the number of clusters will lead to different results. Then, different clusters obtained from different number of clusters should be validated with an index. But so far such an index has not been introduced for interval type-2 fuzzy C-means (IT-2 FCM), and when using this algorithm, common indices are used to determine the number of clusters, and these values are also considered constant and general. we will introduce an index to test the validity of these algorithms in this paper. Then, after an overview of clustering validation indices and related researches, the volatility of these indices for use in IT-2 FCM is shown. The results of the implementation of the proposed index on the four data sets show that by using the suggested index, the volatility and bugs of common indices have been fixed due to obtaining optimal interval. Using suggested index could have a significant effect on type-2 controllers (type-2 fuzzy logic systems) and improve forecast results and control in these systems.
Clustering Validation Index, Fuzzy Clustering, IT2 FCM.
http://jamlu.liau.ac.ir/article-1-1100-en.html
http://jamlu.liau.ac.ir/article-1-1100-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Solving a Fuzzy Fixed-Charge Transportation Problem by Meta-Heuristics with a New Encoding Scheme
15
35
FA
A.
Shabani
Department of Industrial Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran
atena_sh66@yahoo.com
N
R.
Tavakkoli-Moghaddam
Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
tavakoli@ut.ac.ir
Y
M.
Hajiaghaei-Keshteli
Department of Industrial Engineering, University of Science & Technology of Mazandaran, Behshahr, Iran
mostafahaji@gmail.com
N
A transportation problem is one of the most important issues in a supply chain, and one of its branches is a fixed-charge transportation problem (FCTP). The FCTP is an NP- problem and can be formulated as an integer programming model and solved. The purpose of this paper is to develop an effective and efficient method to solve this problem. Therefore, at first, this problem will be formulated by integer programming. Then, for solving this problem, various algorithms such as genetic algorithm, simulated annealing and firefly are used. A new solution presentation for the proposed algorithm is presented. By using these algorithms having the good performance such as time calculations, memory required for calculations, and the ability to find global optimal solution when you get a computer, several examples have been solved. In fact, initially, by using the Taguchi experimental design, parameters in algorithms are adjusted and set the best option for each of the determined parameters, and then the algorithm performance is examined. Finally, to make comparisons between the three proposed algorithms, several test problems in small and large sizes are produced. It is concluded that the objective function value and computational time in the genetic algorithm is less in order to obtain a near-optimal solution.
Fixed-charge transportation, Meta-heuristics, Fuzzy environment, Taguchi experimental design
http://jamlu.liau.ac.ir/article-1-1322-en.html
http://jamlu.liau.ac.ir/article-1-1322-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Multi-Objective Capacitated Facility Location Problem with Chance Constraint and Customer Preference and Solving it with Multi-Objective Evolutionary Algorithms
37
60
FA
N.
Zarrinpoor
Assistant Professor, Department of Industrial Engineering, Shiraz University of Technology, Shiraz, Iran.
zarrinpoor@sutech.ac.ir
Y
Facility location decisions are considered as the most important strategic decisions of organizations, and since they need large investment costs, changing in these decisions will be often impossible. Therefore, it seems necessary to decide about facility location with regard to the constraints and assumptions of real world in an optimal way. In this article, a facility location model is proposed from both the service provider’s point of view and customer’s perspective with the objective of minimizing the fixed cost and maximizing captured demands. The customer preference is considered in the model and based on it, customers choose facilities on the basis of the quality, travel time and service expense. With regard to the uncertain nature of customer’s demand in the real world and limited capacity of facilities, chance constraint is taken into account to the model which ensures the customer’s demand will be satisfied with a certain service level. Due to the NP-hard nature of the problem, a multi-objective harmony search (MOHS) algorithm and a non-dominated sorting genetic algorithm-II (NSGA-II) are proposed to solve the model. In order to calibrate the parameters of the proposed algorithms, the Taguchi method is utilized. The performance of proposed algorithms are compared in terms of different performance metrics such as error ratio, generational distance, spacing metric, diversification metric, number of Pareto-optimal solutions and computational time. Finally, the results are evaluated statistically by 2-sample t-test to determine if there is any significant difference among algorithms in any performance metric. The numerical results show that in total MOHS outperforms NSGA-II.
Facility Location, Capacity constraint, Customer preference, Chance constraint, Multi-objective harmony search, NSGA-II
http://jamlu.liau.ac.ir/article-1-982-en.html
http://jamlu.liau.ac.ir/article-1-982-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
A New Mathematical Model for Haplotype Inference from Genotypes by Parsimony Criterion
61
77
FA
R.
Feizabadi
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
feizabadireza1@gmail.com
N
M.
Bagherian
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
mbagherian@guilan.ac.ir
Y
The haplotype inference is one of the most important issues in the field of bioinformatics. It is because of its various applications in the diagnosis and treatment of inherited diseases such as diabetes, Alzheimer's and heart disease, which has provided a competition for researchers in presentation of mathematical models and design of algorithms to solve this problem. Despite the existence of a robust literature, a need is still felt for providing new or improved methods because of the NP-hard nature of the problem. Haplotype inference is expressed by different criteria. Parsimony is one of the most important criteria here, and the problem in this study is examined with this criterion. Haplotype inference by parsimony criterion solving methods are divided into two categories: exact and approximate. The exact methods often formulate this problem as an integer programming model. Recently, in an article an exact model, HI Base- 10, for haplotype inference has been proposed, which first corresponds a number to each haplotype and genotype, and then forms the model based on these numbers. As a result of this action, it does not impose any variable and constraint corresponding to heterozygous sites in the model. In this paper, we correspond numbers to the genotype in a different approach and form a mixed binary model based on these numbers. As a result of this conversion, the new model has fewer variables than the HI Base- 10, and it doesn’t have integer variable. In addition, in the new model, there is no variable and constraint corresponding to homozygous sites, and they are assigned to heterozygous sites. In addition, the value of the model is determined considering the large number of homozygous sites compared with heterozygous sites.
Bioinformatics, Haplotype inference, Integer programming, Parsimony, Genotype
http://jamlu.liau.ac.ir/article-1-1515-en.html
http://jamlu.liau.ac.ir/article-1-1515-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Presentation of the Human Resource Performance Assessment Model using Fuzzy Inference System (FIS)
79
95
FA
H.
Rezaee Kelidbari
Faculty of Management and Accounting, Rasht Branch, Islamic Azad University, Rasht, Iran
hrezaee41@yahoo.com
Y
Human resource performance assessment is an important part of human resource management and the core of performance management. However, reports of performance appraisals by supervisors are usually archived in employee records, and this often questions the credibility of assessors and the evaluation process. In terms of management, in the process of evaluating performance, valuable time needed to achieve the goals of the organization is spent on non-productive activities. In addition, choosing the way to evaluate performance is also an important issue that plays a vivid role in performance evaluation. In this paper, using a fuzzy inference system consisting of two dimensions of field performance and a duty function, evaluation of employee performance is performed. For this purpose, after extracting the initial criteria of performance evaluation from theoretical foundations, using the Fuzzy Delphi technique and with the opinion of experts, the criteria were evaluated. The research experts include human resources managers of various departments of a public organization in the Guilan province and human resources managers of the headquarters of the same organization, totaling 20 members. Then, using the Fuzzy Delphi method, 5 field performance indices and 3 functional performance indicators were identified as the final performance evaluation indicators. Next, the existing rules between the dimensions of performance appraisal and human resource performance, field performance indicators and field performance, and finally, performance and duty performance indicators were defined according to the experts' opinion. In this research, the programming of the rules of the fuzzy inference system was carried out in the MATLAB software, and the method was summed up using the Mamdani method. Finally, with the implementation of the limit test, the validity of the model was verified and confirmed. The results show that the presented model is a valuable method in evaluating employees’ performance.
Performance Evaluation, Manpower, Fuzzy Inference System, Duty Function, Background Function
http://jamlu.liau.ac.ir/article-1-1585-en.html
http://jamlu.liau.ac.ir/article-1-1585-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Modeling and Solving Single-Allocation p-Hub Maximal Covering Location Problem with Gradual Coverage
97
119
FA
F.
Moeen Moghadas
Department of Mathematics, University of Bojnord, Bojnord, Iran
f.moeen@ub.ac.ir
Y
S.
Roobin
Department of Mathematics, University of Bojnord, Bojnord, Iran
roobin.safiyeh@gmail.com
N
P-hub maximal covering location problem is one of the most commonly used location- allocation problems. In this problem, the goal is to determine the best location for the hubs such that the covered demand is maximized by considering the predefined coverage radius. In classical hub problems, if the distance between the origin and destination is less than this radius, coverage is possible; otherwise the demand between the two points will not be covered. In this paper, the problem of p-hub maximal covering is investigated with gradual coverage. First, the concept of gradual coverage and its developed functions is examined and then, a new mathematical model is presented for the problem. Also, in order to calculate the appropriate upper bound for the problem, the Lagrangian relaxation method is used and a heuristic method and a genetic algorithm are used to solve it. Finally, the results of using these methods are compared with the results of GAMS software. This comparison shows that the new model presented for gradual coverage and the new covering parameter have more suitable results in comparison with the coverage model and function in the literature of the subject. Also, applying Lagrangian relaxation will provide a suitable upper bound for the problem. The heuristic method yields better computational results in less time, and the genetic algorithm provides more coverage with less computational time compared to solving examples with the GAMS software, especially for larger test instances.
Hub Maximal Covering Location Problem, gradual Coverage, Lagrangean Relaxation, Heuristic Algorithm, Genetic Algorithm
http://jamlu.liau.ac.ir/article-1-1613-en.html
http://jamlu.liau.ac.ir/article-1-1613-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Fuzzy Mathematical Programming Model for Designing Sustainable Supply Chain: A Comparative Study
121
149
FA
M.
aghajani
Department of Industrial Management, University of Mazandaran, Babolsar, Iran
mo_aghajani@yahoo.com
N
A.
Safaei Ghadikolaei
Department of Industrial Management, University of Mazandaran, Babolsar, Iran.
ab.safaei@umz.ac.ir
Y
H.
Aghajani
Department of Industrial Management, University of Mazandaran, Babolsar, Iran.
aghagani@umz.ac.ir
N
M.
Valipour Khatir
Department of Industrial Management, University of Mazandaran, Babolsar, Iran
valipourkhatir@umz.ac.ir
N
In this paper, a fuzzy mathematical programming model is proposed for designing a sustainable multi-product, multi-stage supply chain (including, purchase, production and distribution) under the competition and uncertainty conditions. The sustainability measures in each of the sustainability dimensions were extracted using earlier conducted research as well as the SCOR model and then were localized using the Delphi method. The obtained fuzzy model is converted to a crisp one by using Jimenez model. The solving approach is based on the Triple Bottom line model and the Nested model. As each model has its own characteristics, in order to determine the relations between the indices and the importance of each indicator and its application, the DANP and DEMATEL methods were used respectively. In order to indicate the efficiency of the model and the solution approach, a real example is presented in refractory products industry, and finally the obtained results are analyzed and compared based on the two models and suggestions are presented.
TBL Model, Nested Model, Competition, Uncertainty, SCOR Model, DANP Method, DEMATEL Method
http://jamlu.liau.ac.ir/article-1-1731-en.html
http://jamlu.liau.ac.ir/article-1-1731-en.pdf
دانشگاه آزاد اسلامی واحد لاهیجان
Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University
2251-7286
2251-9807
15
4
2019
1
1
Symmetric Rank-One Method for Solving Large-Scale Optimization Problems
151
170
FA
F.
Modarres Khiyabani
Department of Mathematics, Islamic Azad University, Tabriz Branch, Tabriz, Iran
f.modarres@iaut.ac.ir
Y
B.
Daneshian
Department of Mathematics, Islamic Azad University, Tehran Center Branch, Tehran, Iran
bdaneshian@yahoo.com
N
The search for finding the local minimization in unconstrained optimization problems and a fixed point of the gradient system of ordinary differential equations are two close problems. Limited-memory algorithms are widely used to solve large-scale problems, while Rang Kuta's methods are also used to solve numerical differential equations. In this paper, using the concept of sub-space method and fixed-step length and integration of line-search and trust-region techniques, an ODE-based hybrid method is proposed for solving large-scale optimization problems. Since the line-search methods may require more iteration for convergence, while Trust-region methods also require a lot of iteration to solve the constrained sub problem, a new class of methods is proposed in this way, which combines the best features of trust-region and line-search methods. The main feature of the proposed method is that the linear equation system is solved only once in order to obtain the experimental step.
Unconstrained optimization, Ordinary differential equations, Limited memory methods, Line-search, Trust-region
http://jamlu.liau.ac.ir/article-1-1511-en.html
http://jamlu.liau.ac.ir/article-1-1511-en.pdf