Fuzzy multi objective transportation problem evolutionary algorithm approach
|
|
- Shona Watson
- 5 years ago
- Views:
Transcription
1 Journal of Physics: Conference Series PPER OPEN CCESS Fuzzy multi objective transportation problem evolutionary algorithm approach To cite this article: T Karthy and K Ganesan 08 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on /07/08 at 08:48
2 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 Fuzzy multi objective transportation problem evolutionary algorithm approach T Karthy and K Ganesan ssistant Professor, Department of Mathematics, SRM Institute of science and technology, Kattanulathur, Tamilnadu, India Professor, Department of Mathematics, SRM Institute of science and technology, Kattanulathur, Tamilnadu, India E.mail : arthy.t@tr.srmuniv.ac.in bstract: This paper deals with fuzzy multi objective transportation problem. n fuzzy optimal compromise solution is obtained by using Fuzzy Genetic lgorithm. numerical example is provided to illustrate the methodology.. Introduction: Fuzzy Transportation problem is a fuzzy optimization problem deals with transporting commodities from various sources to various destinations in such a way so that the total fuzzy transportation cost is minimum. When a fuzzy transportation problem involves more than one objective function the tas of finding one or more fuzzy optimal solution is nown as fuzzy multi objective transportation problem. For multiple conflicting fuzzy objectives, there cannot be a single fuzzy optimum solution which simultaneously optimizes all the fuzzy objectives. The resulting outcome is a set of fuzzy optimal solutions with varying degree of objective values. Hence it is better to compute the fuzzy compromise solution between two or more conflicting fuzzy objectives. In this article, we propose a fuzzy genetic algorithm approach for the solution of fuzzy multi objective transportation problems. In real life situations, supply, demand and unit transportation cost are uncertain. Hence idea of fuzzy sets was introduced by Zadeh [] in 965. Zimmerman [9] applied the fuzzy programming techniques to solve multi objective linear programming problems. C. Vayalashmi [3] solved the bi objective transportation problem using genetic algorithm and represented it by bipartite graphs. Waiel F. bd El- Wahed [8] applied fuzzy programming approach to determine the optimal compromise solution of a crisp multi objective transportation problem. For the balanced fuzzy multi objective transportation problem[7] T. leelavathy and et.al applied weighted sum of the objectives method and obtained the compromise solution by decision maer s preference. The rest of the paper is organized as follows: In section, we have discussed the basic concepts of triangular fuzzy number and their arithmetic operations. In section 3, we introduce the fuzzy multi objective transportation problem with cost coefficients, supplies and demands as triangular fuzzy numbers. In section 4, we define the basic concepts of fuzzy genetic algorithm. In section 5, a numerical example is provided to illustrate the efficiency of the proposed methodology.. PRELIMINRIES Content from this wor may be used under the terms of the Creative Commons ttribution 3.0 licence. ny further distribution of this wor must maintain attribution to the authors) and the title of the wor, journal citation and DOI. Published under licence by Ltd
3 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 Definition.: fuzzy set defined on the set of real numbers R is said to be a fuzzy number, if μ : R 0, has the following characteristics: its membership function [ ] i) μ is convex. ii) μ is normal. iii) is upper semi continuous iv) sup ) is bounded in R. Definition.: fuzzy number is a triangular fuzzy number denoted by = a, a, a ) a a a are real numbers and its membership function μ x ) where,, 3 μ x a, a x a a a a3 x x =, a x a a3 a 0,otherwise ) Definition.3: triangular fuzzy number = a, a, a ) ), )) of function of ), ) = a a 3 3 is given below and FR) can also be represented as a pair ar a r for 0 r which satisfies the following requirements: i) ar ) is a bounded monotonic increasing left continuous function. ii) a r) is a bounded monotonic decreasing left continuous function. iii) ar ) a r),0 r.. Raning of Triangular Fuzzy Numbers = a, a, a F R), the raning function R : F R) R by graded mean is defined by For every ) 3 3 a+ a + a3 R ) =.For any two triangular fuzzy number = a, a, a3) and B = b, b, b3) 4 in FR). We have the following comparison : ) i Bif andonlyif R R B. ii) Bif andonlyif R R B. iii) Bif andonlyif R = R B. iv) B 0 if andonlyif R R B = 0.
4 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 and. rithmetic Operations: In particular for any two fuzzy numbers = a, a, a ) B = b, b, b3), we define: ) i ddition ii) Subtraction : + B = a+ b, a + b, a3+ b3) : B = a b, a b, a3 b3) iii) Multiplication : * B = min ab, ab 3, a3b, a3b3), ab,max ab, ab 3, a3b, a3b3)) iv) Division : / B = min a / b, a / b, a / b, a / b ), a / b,max a / b, a / b, a / b, a / b )) FUZZY MULTI OBJECTIVE TRNSPORTTION PROBLEM 3. Mathematical formulation of Fuzzy Transportation Problem Consider a fuzzy multi objective transportation problem with m sources and n destinations. Let a i a i 0) be the fuzzy availability at source i and b j b j 0) be the fuzzy requirement at destination j. Let c be the fuzzy unit transportation cost from source i to destination j. Let x denote the number of fuzzy units to be transported from source i to destination j. Now the problem is to determine a feasible way of transporting which minimizes the total fuzzy transportation cost. Minimize z x) = c x i= j= subject to x = a, i =,,... m m i= m x = b, j =,,...,n j and x 0,for all i, j. n j= i n { } on both z x) and where ) ), ),..., z x = z x z x z x) is a vector of fuzzy objective functions and the superscript c are used to indicate the number of fuzzy objective functions. Without loss of a b i j c i j and a b. generality, it is assumed in the paper that 0, 0,,, 0,, i j i j i j Definition 3.: If the fuzzy objective functions are said to be conflicting, then there exists a fuzzy pareto optimal solution. Definition 3.: fuzzy solution is called fuzzy non dominated, fuzzy pareto optimal, fuzzy pareto efficient or non inferior, if none of the fuzzy objective functions can be improved in value without degrading some of the other fuzzy objective values. Definition 3.3: Fuzzy Pareto efficiency or fuzzy pareto optimality is a state of allocation of resources in which it is impossible to mae anyone individual better off without maing atleast one individual worse off. 3
5 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 Definition 3.4: If the fuzzy compromise solution satisfies the decision maer's preferences, then the solution is called the fuzzy preferred compromise solution. 4. Fuzzy Genetic lgorithm Fuzzy Genetic lgorithm consists of mainly three steps:. Fuzzy Selection. Fuzzy Crossover 3. Fuzzy Mutation Fuzzy Selection: Of the three methods, Fuzzy North West corner rule, fuzzy least cost method, fuzzy Vogel's approximation method we select FVM to obtain the initial fuzzy basic feasible solution. Fuzzy Crossover: There are different types of fuzzy crossover namely. Fuzzy single point Crossover - One fuzzy crossover point is selected, fuzzy allocation from the beginning to the fuzzy crossover point is copied from the first fuzzy parent solution, the rest is copied from the other fuzzy parent solution.. Fuzzy Two point Crossover - Two fuzzy crossover points are selected, fuzzy allocation from the beginning of the first fuzzy crossover point is copied from the first fuzzy parent, the part from the first to the second fuzzy crossover point is copied from the other fuzzy parent and the rest is copied from the first fuzzy parent again. 3. Fuzzy Uniform Crossover Fuzzy allocations are randomly copied from the fuzzy first or from the fuzzy second parent. Initial basic fuzzy feasible solutions are considered as the fuzzy parent solutions. By using Fuzzy Crossover operator we generate a second generation population of Fuzzy solutions from those Fuzzy parent solutions and we obtain Fuzzy child and Fuzzy child. In the problem illustrated, Fuzzy single point Crossover is used. Fuzzy Mutation: Fuzzy Mutation alters one or more gene values in a chromosome from its initial state. In mutation, the fuzzy solution may change entirely from the previous fuzzy solution. Hence fuzzy G can come to better fuzzy solution by using mutation. 5. Numerical Example Consider the balanced fuzzy multi objective transportation problem [7] 0,,),,3) = 0,,) 8,9,0) 7,8,9) 8,9,0) 6,7,8) 6,7,8),3,4) 3,4,5) 3,4,5) 5,6,7) =,3,4) 3,4,5) 4,5,6) 7,8,9) 5,6,7),,3),3,4) 3,4,5) 8,9,0) 9,0,) 4,5,6) 0,,) Fuzzy supplies: a = 0,3,5), a = 4,6,9), a 3 = 4,6,7) Fuzzy demands: b =,4,5), b =0,,), b 3 =,5,7), b 4 =4,5,7) Initial llocation 4
6 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 0,,3) 0,,) = 0,,) 0,0,0),,0) 0,0,0) 0,0,0) 4,5,7) ;,5,7) 0,0,0) =,4,5) 0,,) 0,3,5) 0,0,0),,) 0,0,0) 0,,0) 4,5,7) Fuzzy Parent : Z = 8, 53, 04), Z = 44, 9, 67) Fuzzy Parent : Z = 4, 7, 7), Z = 4, 56, 0) Fuzzy Single Point Crossover 0,,3) 0,,) = 0,,) 0,0,0),4,7) 0,0,0) ; 0,,0) 4,5,7) = 0,3,5) 0,,),,0) 0,0,0) 0,0,0) 0,3,5) 0,0,0) 4,,),5,7) 0,,) Fuzzy child : Z = 4,5, 93), Z = 44,9,53) Fuzzy child : Z =, 69, 43), Z = 6, 78, 73) Fuzzy Mutation 0,,3) 0,,) =,,) 0,0,0) 0,0,0),4,7) ;,5,7),,0) 0,0,0) 0,,) = 0,3,5) 0,0,0),,0) 0,0,0) 0,0,0) 0,,3) 0,0,0) 4,3,4),5,7) 0,0,0) Fuzzy child 3: Z =, 48, 86), Z = 30,84,55) Fuzzy child 4: Z = 8, 5, 0), Z = 44, 85, 55) fter Fuzzy Mutation, we have the better fuzzy optimal solution: Z =, 48, 86), Z = 0,,3) 0,,) 30,84,55) whose allocation is,,) 0,0,0) 0,0,0),4,7),5,7),,0) Conclusion: For the Bi objective fuzzy transportation problem solved by fuzzy Genetic lgorithm, the fuzzy compromised solution obtained is Z =, 48, 86), Z = 30,84,55) References: []. bdullah Kona, David W Coit and lice E Smith 006 Multi objective optimization using genetic algorithms: tutorial, Reliability Engineering and System Safety 9 pp
7 National Conference on Mathematical Techniques and its pplications NCMT 8) IOP Conf. Series: Journal of Physics: Conf. Series ) 0004 doi :0.088/ /000//0004 []. R Bellman and L Zadeh 970 Decision maing in a fuzzy environment, Management Sci. 7B4) pp 4-64 [3]. K Bharathi and C Vayalashmi 06 Optimization of Multi Objective Transportation Problem using Evolutionary lgorithms [4]. M P Biswal 99 Fuzzy programming technique to solve multi objective geometric programming problems, Fuzzy sets and Systems, 5 pp 67-7 [5]. D E Goldberg 989 Genetic lgorithms in search, Optimization and Machine Learning ddison Wesley Publishing company [6]. Kalyanmoy Deb 00 Multi objective optimization using Evolutionary lgorithm, John wiley & Sons, New Yor, US [7]. T Leelavathy and K Ganesan 06 Solution pproach to Multi Objective Fuzzy Transportation Problem, Global Journal of Pure and pplied Mathematics,, number, pp [8]. Waiel F.bd El- Wahed 00 multi objective transportation problem under fuzziness, Fuzzy sets and Systems 7 pp 7-33 [9]. H J Zimmermann 978 Fuzzy Programming and linear programming with several objective functions, Fuzzy Sets and Systems pp
A Comparative Study on Optimization Techniques for Solving Multi-objective Geometric Programming Problems
Applied Mathematical Sciences, Vol. 9, 205, no. 22, 077-085 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.205.42029 A Comparative Study on Optimization Techniques for Solving Multi-objective
More informationA Compromise Solution to Multi Objective Fuzzy Assignment Problem
Volume 113 No. 13 2017, 226 235 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu A Compromise Solution to Multi Objective Fuzzy Assignment Problem
More informationFuzzy Transportation Problems with New Kind of Ranking Function
The International Journal of Engineering and Science (IJES) Volume 6 Issue 11 Pages PP 15-19 2017 ISSN (e): 2319 1813 ISSN (p): 2319 1805 Fuzzy Transportation Problems with New Kind of Ranking Function
More informationZero Average Method to Finding an Optimal Solution of Fuzzy Transportation Problems
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-728, p-issn: 2319-76X. Volume 13, Issue 6 Ver. I (Nov. - Dec. 2017), PP 6-63 www.iosrjournals.org Zero verage Method to Finding an Optimal Solution of
More informationMulti-objective Optimization
Some introductory figures from : Deb Kalyanmoy, Multi-Objective Optimization using Evolutionary Algorithms, Wiley 2001 Multi-objective Optimization Implementation of Constrained GA Based on NSGA-II Optimization
More informationA Novel Approach for the Solution of Multi Objective Interval Transportation Problem
Journal of Physics: Conference Series PAPER OPEN ACCESS A Novel Approach for the Solution of Multi Objective Interval Transportation Problem To cite this article: G Ramesh et al 2018 J. Phys.: Conf. Ser.
More information2 Dept. of Computer Applications 3 Associate Professor Dept. of Computer Applications
International Journal of Computing Science and Information Technology, 2014, Vol.2(2), 15-19 ISSN: 2278-9669, April 2014 (http://ijcsit.org) Optimization of trapezoidal balanced Transportation problem
More informationSolving the Multiobjective Two Stage Fuzzy Transportation Problem by Zero Suffix Method
Solving the Multiobjective Two Stage Fuzzy Transportation Problem by Zero Suffix Method V.J. Sudhakar (Corresponding author) Department of Mathematics Adhiyamaan college of Engineering Hosur - 635 109,
More informationGenetic Algorithm for Finding Shortest Path in a Network
Intern. J. Fuzzy Mathematical Archive Vol. 2, 2013, 43-48 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 26 August 2013 www.researchmathsci.org International Journal of Genetic Algorithm for Finding
More informationUsing Ones Assignment Method and. Robust s Ranking Technique
Applied Mathematical Sciences, Vol. 7, 2013, no. 113, 5607-5619 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.37381 Method for Solving Fuzzy Assignment Problem Using Ones Assignment
More informationA compromise method for solving fuzzy multi objective fixed charge transportation problem
Lecture Notes in Management Science (2016) Vol. 8, 8 15 ISSN 2008-0050 (Print), ISSN 1927-0097 (Online) A compromise method for solving fuzzy multi objective fixed charge transportation problem Ratnesh
More informationAn Appropriate Method for Real Life Fuzzy Transportation Problems
International Journal of Information Sciences and Application. ISSN 097-55 Volume 3, Number (0), pp. 7-3 International Research Publication House http://www.irphouse.com An Appropriate Method for Real
More informationOptimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm
Optimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm N. Shahsavari Pour Department of Industrial Engineering, Science and Research Branch, Islamic Azad University,
More informationAdvanced Approximation Method for Finding an Optimal Solution of Unbalanced Fuzzy Transportation Problems
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 5307-5315 Research India Publications http://www.ripublication.com Advanced Approximation Method for Finding
More informationIJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 3, May
Optimization of fuzzy assignment model with triangular fuzzy numbers using Robust Ranking technique Dr. K. Kalaiarasi 1,Prof. S.Sindhu 2, Dr. M. Arunadevi 3 1 Associate Professor Dept. of Mathematics 2
More informationModified Procedure to Solve Fuzzy Transshipment Problem by using Trapezoidal Fuzzy number.
International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: 2321 4767 P-ISSN: 2321-4759 Volume 4 Issue 6 August. 216 PP-3-34 Modified Procedure to Solve Fuzzy Transshipment Problem by
More informationα-pareto optimal solutions for fuzzy multiple objective optimization problems using MATLAB
Advances in Modelling and Analysis C Vol. 73, No., June, 18, pp. 53-59 Journal homepage:http://iieta.org/journals/ama/ama_c α-pareto optimal solutions for fuzzy multiple objective optimization problems
More informationALGORITHMIC APPROACH TO UNBALANCED FUZZY TRANSPORTATION PROBLEM. A. Samuel 1, P. Raja 2
International Journal of Pure and Applied Mathematics Volume 113 No. 5 2017, 553-561 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v113i5.3
More informationNew Approaches to Find the Solution for the Intuitionistic Fuzzy Transportation Problem with Ranking of Intuitionistic Fuzzy Numbers
New Approaches to Find the Solution for the Intuitionistic Fuzzy Transportation Problem with Ranking of Intuitionistic Fuzzy Numbers Sagaya Roseline 1, Henry Amirtharaj 2 Assistant Professor, Department
More informationCHAPTER 2 LITERATURE REVIEW
22 CHAPTER 2 LITERATURE REVIEW 2.1 GENERAL The basic transportation problem was originally developed by Hitchcock (1941). Efficient methods of solution are derived from the simplex algorithm and were developed
More informationFuzzy Variable Linear Programming with Fuzzy Technical Coefficients
Sanwar Uddin Ahmad Department of Mathematics, University of Dhaka Dhaka-1000, Bangladesh sanwar@univdhaka.edu Sadhan Kumar Sardar Department of Mathematics, University of Dhaka Dhaka-1000, Bangladesh sadhanmath@yahoo.com
More informationSolving Fuzzy Sequential Linear Programming Problem by Fuzzy Frank Wolfe Algorithm
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume 3, Number (07), pp. 749-758 Research India Publications http://www.ripublication.com Solving Fuzzy Sequential Linear Programming Problem
More informationAn Evolutionary Algorithm for the Multi-objective Shortest Path Problem
An Evolutionary Algorithm for the Multi-objective Shortest Path Problem Fangguo He Huan Qi Qiong Fan Institute of Systems Engineering, Huazhong University of Science & Technology, Wuhan 430074, P. R. China
More informationISSN: [Keswani* et al., 7(1): January, 2018] Impact Factor: 4.116
IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY AUTOMATIC TEST CASE GENERATION FOR PERFORMANCE ENHANCEMENT OF SOFTWARE THROUGH GENETIC ALGORITHM AND RANDOM TESTING Bright Keswani,
More informationMulti-objective Optimization
Jugal K. Kalita Single vs. Single vs. Single Objective Optimization: When an optimization problem involves only one objective function, the task of finding the optimal solution is called single-objective
More informationMulti objective linear programming problem (MOLPP) is one of the popular
CHAPTER 5 FUZZY MULTI OBJECTIVE LINEAR PROGRAMMING PROBLEM 5.1 INTRODUCTION Multi objective linear programming problem (MOLPP) is one of the popular methods to deal with complex and ill - structured decision
More informationOptimizing Octagonal Fuzzy Number EOQ Model Using Nearest Interval Approximation Method
Optimizing Octagonal Fuzzy Number EOQ Model Using Nearest Interval Approximation Method A.Farita Asma 1, C.Manjula 2 Assistant Professor, Department of Mathematics, Government Arts College, Trichy, Tamil
More informationRevision of a Floating-Point Genetic Algorithm GENOCOP V for Nonlinear Programming Problems
4 The Open Cybernetics and Systemics Journal, 008,, 4-9 Revision of a Floating-Point Genetic Algorithm GENOCOP V for Nonlinear Programming Problems K. Kato *, M. Sakawa and H. Katagiri Department of Artificial
More informationFuzzy Optimal Transportation Problems by Improved Zero Suffix Method via Robust Rank Techniques
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 3, Number 4 (2013), pp. 303-311 Research India Publications http://www.ripublication.com Fuzzy Optimal Transportation Problems
More informationA MODIFICATION OF FUZZY TOPSIS BASED ON DISTANCE MEASURE. Dept. of Mathematics, Saveetha Engineering College,
International Journal of Pure and pplied Mathematics Volume 116 No. 23 2017, 109-114 ISSN: 1311-8080 (printed version; ISSN: 1314-3395 (on-line version url: http://www.ijpam.eu ijpam.eu MODIFICTION OF
More informationOptimal Solution of a Mixed type Fuzzy Transportation Problem
Intern. J. Fuzzy Mathematical Archive Vol. 15, No. 1, 2018, 83-89 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 20 March 2018 www.researchmathsci.org DOI: http://dx.doi.org/10.22457/ijfma.v15n1a8
More informationGOAL GEOMETRIC PROGRAMMING PROBLEM (G 2 P 2 ) WITH CRISP AND IMPRECISE TARGETS
Volume 4, No. 8, August 2013 Journal of Global Research in Computer Science REVIEW ARTICLE Available Online at www.jgrcs.info GOAL GEOMETRIC PROGRAMMING PROBLEM (G 2 P 2 ) WITH CRISP AND IMPRECISE TARGETS
More informationThe MOMC Method: a New Methodology to Find. Initial Solution for Transportation Problems
Applied Mathematical Sciences, Vol. 9, 2015, no. 19, 901-914 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121013 The MOMC Method: a New Methodology to Find Initial Solution for Transportation
More informationA New pivotal operation on Triangular Fuzzy number for Solving Fully Fuzzy Linear Programming Problems
International Journal of Applied Mathematical Sciences ISSN 0973-0176 Volume 9, Number 1 (2016), pp. 41-46 Research India Publications http://www.ripublication.com A New pivotal operation on Triangular
More informationKEYWORDS Fuzzy numbers, trapezoidal fuzzy numbers, fuzzy Vogel s approximation method, fuzzy U-V distribution method, ranking function.
Applications (IJERA ISSN: 2248-9622 www.ijera.com Method For Solving The Transportation Problems Using Trapezoridal Numbers Kadhirvel.K, Balamurugan.K Assistant Professor in Mathematics,T.K.Govt.Arts College,
More informationII. MULTI OBJECTIVE NON- LINEAR PROGRAMMING
Solving Fuzzy Multi Objective Non-linear Programming Problem Using Fuzzy Programming Technique P.Durga Prasad Dash, Rajani B. Dash Shishu Ananta Mahavidyalaya, Balipatna, Khurda,Odisha,India Department
More informationBI-OBJECTIVE EVOLUTIONARY ALGORITHM FOR FLEXIBLE JOB-SHOP SCHEDULING PROBLEM. Minimizing Make Span and the Total Workload of Machines
International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN 2249-6955 Vol. 2 Issue 4 Dec - 2012 25-32 TJPRC Pvt. Ltd., BI-OBJECTIVE EVOLUTIONARY ALGORITHM FOR FLEXIBLE JOB-SHOP
More informationA New Approach for Solving Unbalanced. Fuzzy Transportation Problems
International Journal of Computing and Optimization Vol. 3, 2016, no. 1, 131-140 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijco.2016.6819 A New Approach for Solving Unbalanced Fuzzy Transportation
More informationFuzzy type-2 in Shortest Path and Maximal Flow Problems
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 6595-6607 Research India Publications http://www.ripublication.com Fuzzy type-2 in Shortest Path and Maximal
More informationUsing Goal Programming For Transportation Planning Decisions Problem In Imprecise Environment
Australian Journal of Basic and Applied Sciences, 6(2): 57-65, 2012 ISSN 1991-8178 Using Goal Programming For Transportation Planning Decisions Problem In Imprecise Environment 1 M. Ahmadpour and 2 S.
More informationSub-Trident Ranking Using Fuzzy Numbers
International Journal of Mathematics nd its pplications Volume, Issue (016), 1 150 ISSN: 7-1557 vailable Online: http://ijmaain/ International Journal 7-1557 of Mathematics pplications nd its ISSN: International
More informationDifferent Algorithmic Approach for Type 2 Fuzzy Shortest Path Problem on a Network
Intern. J. Fuzzy Mathematical rchive Vol. 7, No., 205, 27-33 ISSN: 2320 3242 (P), 2320 3250 (online) Published on 22 January 205 www.researchmathsci.org International Journal of Different lgorithmic pproach
More informationInternational Journal of Scientific & Engineering Research, Volume 6, Issue 3, March ISSN
nternational Journal of Scientific & Engineering Research, Volume 6, ssue, March-5 SSN 9-558 Fuzzy Hungarian Method for Solving ntuitionistic Fuzzy Assignment Problems K. Prabakaran and K. Ganesan ABSTRACT-
More informationA NEW METHOD FOR SOLVING TWO VEHICLE COST VARYING FUZZY TRANSPORTATION PROBLEM
ISSN: 0975-766X CDEN: IJPTFI Available nline through esearch Article www.ptonline.com A NEW METHD F SLVING TW VEHICLE CST VAYING FUZZY TANSPTATIN PBLEM D.Kalpanapriya* and D.Anuradha Department of Mathematics
More informationIncorporation of Scalarizing Fitness Functions into Evolutionary Multiobjective Optimization Algorithms
H. Ishibuchi, T. Doi, and Y. Nojima, Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms, Lecture Notes in Computer Science 4193: Parallel Problem Solving
More informationSolving A Nonlinear Side Constrained Transportation Problem. by Using Spanning Tree-based Genetic Algorithm. with Fuzzy Logic Controller
Solving A Nonlinear Side Constrained Transportation Problem by Using Spanning Tree-based Genetic Algorithm with Fuzzy Logic Controller Yasuhiro Tsujimura *, Mitsuo Gen ** and Admi Syarif **,*** * Department
More informationOn JAM of Triangular Fuzzy Number Matrices
117 On JAM of Triangular Fuzzy Number Matrices C.Jaisankar 1 and R.Durgadevi 2 Department of Mathematics, A. V. C. College (Autonomous), Mannampandal 609305, India ABSTRACT The fuzzy set theory has been
More informationA Study on Triangular Type 2 Triangular Fuzzy Matrices
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 4, Number 2 (2014), pp. 145-154 Research India Publications http://www.ripublication.com A Study on Triangular Type 2 Triangular
More informationA method for solving unbalanced intuitionistic fuzzy transportation problems
Notes on Intuitionistic Fuzzy Sets ISSN 1310 4926 Vol 21, 2015, No 3, 54 65 A method for solving unbalanced intuitionistic fuzzy transportation problems P Senthil Kumar 1 and R Jahir Hussain 2 1 PG and
More informationMULTI-OBJECTIVE PROGRAMMING FOR TRANSPORTATION PLANNING DECISION
MULTI-OBJECTIVE PROGRAMMING FOR TRANSPORTATION PLANNING DECISION Piyush Kumar Gupta, Ashish Kumar Khandelwal, Jogendra Jangre Mr. Piyush Kumar Gupta,Department of Mechanical, College-CEC/CSVTU University,Chhattisgarh,
More informationEvolutionary Algorithm for Embedded System Topology Optimization. Supervisor: Prof. Dr. Martin Radetzki Author: Haowei Wang
Evolutionary Algorithm for Embedded System Topology Optimization Supervisor: Prof. Dr. Martin Radetzki Author: Haowei Wang Agenda Introduction to the problem Principle of evolutionary algorithm Model specification
More informationSaudi Journal of Business and Management Studies. DOI: /sjbms ISSN (Print)
DOI: 10.21276/sjbms.2017.2.2.5 Saudi Journal of Business and Management Studies Scholars Middle East Publishers Dubai, United Arab Emirates Website: http://scholarsmepub.com/ ISSN 2415-6663 (Print ISSN
More informationNew Methodology to Find Initial Solution for. Transportation Problems: a Case Study with Fuzzy Parameters
Applied Mathematical Sciences, Vol. 9, 2015, no. 19, 915-927 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121018 New Methodology to Find Initial Solution for Transportation Problems:
More informationEvolutionary Algorithms: Lecture 4. Department of Cybernetics, CTU Prague.
Evolutionary Algorithms: Lecture 4 Jiří Kubaĺık Department of Cybernetics, CTU Prague http://labe.felk.cvut.cz/~posik/xe33scp/ pmulti-objective Optimization :: Many real-world problems involve multiple
More informationA Novel Method to Solve Assignment Problem in Fuzzy Environment
A Novel Method to Solve Assignment Problem in Fuzzy Environment Jatinder Pal Singh Neha Ishesh Thakur* Department of Mathematics, Desh Bhagat University, Mandi Gobindgarh (Pb.), India * E-mail of corresponding
More informationFuzzy multi objective linear programming problem with imprecise aspiration level and parameters
An International Journal of Optimization and Control: Theories & Applications Vol.5, No.2, pp.81-86 (2015) c IJOCTA ISSN:2146-0957 eissn:2146-5703 DOI:10.11121/ijocta.01.2015.00210 http://www.ijocta.com
More informationA new approach for solving cost minimization balanced transportation problem under uncertainty
J Transp Secur (214) 7:339 345 DOI 1.17/s12198-14-147-1 A new approach for solving cost minimization balanced transportation problem under uncertainty Sandeep Singh & Gourav Gupta Received: 21 July 214
More informationMulti-Objective Sorting in Light Source Design. Louis Emery and Michael Borland Argonne National Laboratory March 14 th, 2012
Multi-Objective Sorting in Light Source Design Louis Emery and Michael Borland Argonne National Laboratory March 14 th, 2012 Outline Introduction How do we handle multiple design goals? Need to understand
More informationFuzzy Inspired Hybrid Genetic Approach to Optimize Travelling Salesman Problem
Fuzzy Inspired Hybrid Genetic Approach to Optimize Travelling Salesman Problem Bindu Student, JMIT Radaur binduaahuja@gmail.com Mrs. Pinki Tanwar Asstt. Prof, CSE, JMIT Radaur pinki.tanwar@gmail.com Abstract
More informationA Computational Study on the Number of. Iterations to Solve the Transportation Problem
Applied Mathematical Sciences, Vol. 8, 2014, no. 92, 4579-4583 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46435 A Computational Study on the Number of Iterations to Solve the Transportation
More informationDifferent strategies to solve fuzzy linear programming problems
ecent esearch in Science and Technology 2012, 4(5): 10-14 ISSN: 2076-5061 Available Online: http://recent-science.com/ Different strategies to solve fuzzy linear programming problems S. Sagaya oseline
More informationLecture
Lecture.. 7 Constrained problems & optimization Brief introduction differential evolution Brief eample of hybridization of EAs Multiobjective problems & optimization Pareto optimization This slides mainly
More informationA GENETIC ALGORITHM APPROACH TO OPTIMAL TOPOLOGICAL DESIGN OF ALL TERMINAL NETWORKS
A GENETIC ALGORITHM APPROACH TO OPTIMAL TOPOLOGICAL DESIGN OF ALL TERMINAL NETWORKS BERNA DENGIZ AND FULYA ALTIPARMAK Department of Industrial Engineering Gazi University, Ankara, TURKEY 06570 ALICE E.
More informationSimulation of rotation and scaling algorithm for numerically modelled structures
IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Simulation of rotation and scaling algorithm for numerically modelled structures To cite this article: S K Ruhit et al 2018 IOP
More informationA Strategy to Solve Mixed Intuitionistic Fuzzy Transportation Problems by BCM
Middle-East Journal of Scientific Research 25 (2): 374-379, 207 SSN 990-9233 DOS Publications, 207 DO: 0.5829/idosi.mesr.207.374.379 A Strategy to Solve Mixed ntuitionistic Fuzzy Transportation Problems
More informationA NEW APPROACH FOR FUZZY CRITICAL PATH METHOD USING OCTAGONAL FUZZY NUMBERS
Volume 119 No. 13 2018, 357-364 ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu A NEW APPROACH FOR FUZZY CRITICAL PATH METHOD USING OCTAGONAL FUZZY NUMBERS D. STEPHEN DINAGAR 1 AND
More informationReference Point Based Evolutionary Approach for Workflow Grid Scheduling
Reference Point Based Evolutionary Approach for Workflow Grid Scheduling R. Garg and A. K. Singh Abstract Grid computing facilitates the users to consume the services over the network. In order to optimize
More informationGenetic algorithm based hybrid approach to solve fuzzy multi objective assignment problem using exponential membership function
DOI 10.1186/s40064-016-3685-0 RESEARCH Open Access Genetic algorithm based hybrid approach to solve fuzzy multi objective assignment problem using exponential membership function Jayesh M. Dhodiya * and
More informationUsing Genetic Algorithm to Find the Optimal Shopping Policy for 1-out-of-n Active-Redundancy Series Systems under Budget Constraint
Computer and Inmation Science; Vol. 7, No. 3; 2014 ISSN 1913-8989 E-ISSN 1913-8997 Published by Canadian Center of Science and Education Using Genetic Algorithm to Find the Optimal Shopping Policy 1-out-of-n
More informationGrid Scheduling Strategy using GA (GSSGA)
F Kurus Malai Selvi et al,int.j.computer Technology & Applications,Vol 3 (5), 8-86 ISSN:2229-693 Grid Scheduling Strategy using GA () Dr.D.I.George Amalarethinam Director-MCA & Associate Professor of Computer
More informationOperations in Fuzzy Labeling Graph through Matching and Complete Matching
Operations in Fuzzy Labeling Graph through Matching and Complete Matching S. Yahya Mohamad 1 and S.Suganthi 2 1 PG & Research Department of Mathematics, Government Arts College, Trichy 620 022, Tamilnadu,
More informationA Fuzzy Logic Controller Based Dynamic Routing Algorithm with SPDE based Differential Evolution Approach
A Fuzzy Logic Controller Based Dynamic Routing Algorithm with SPDE based Differential Evolution Approach Debraj De Sonai Ray Amit Konar Amita Chatterjee Department of Electronics & Telecommunication Engineering,
More informationMultiobjective Formulations of Fuzzy Rule-Based Classification System Design
Multiobjective Formulations of Fuzzy Rule-Based Classification System Design Hisao Ishibuchi and Yusuke Nojima Graduate School of Engineering, Osaka Prefecture University, - Gakuen-cho, Sakai, Osaka 599-853,
More informationHAAR HUNGARIAN ALGORITHM TO SOLVE FUZZY ASSIGNMENT PROBLEM
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 7 2017, 58 66 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu HAAR HUNGARIAN
More informationGlobal Optimization of a Magnetic Lattice using Genetic Algorithms
Global Optimization of a Magnetic Lattice using Genetic Algorithms Lingyun Yang September 3, 2008 Global Optimization of a Magnetic Lattice using Genetic Algorithms Lingyun Yang September 3, 2008 1 / 21
More informationCHAPTER 6 REAL-VALUED GENETIC ALGORITHMS
CHAPTER 6 REAL-VALUED GENETIC ALGORITHMS 6.1 Introduction Gradient-based algorithms have some weaknesses relative to engineering optimization. Specifically, it is difficult to use gradient-based algorithms
More informationNCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems
: Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems Shinya Watanabe Graduate School of Engineering, Doshisha University 1-3 Tatara Miyakodani,Kyo-tanabe, Kyoto, 10-031,
More informationFuzzy Transportation by Using Monte Carlo method
Advances in Fuzzy Mathematics. ISSN 0973-533X Volume 12, Number 1 (2017), pp. 111-127 Research India Publications http://www.ripublication.com Fuzzy Transportation by Using Monte Carlo method Ashok S.Mhaske
More informationA Genetic Algorithm for Graph Matching using Graph Node Characteristics 1 2
Chapter 5 A Genetic Algorithm for Graph Matching using Graph Node Characteristics 1 2 Graph Matching has attracted the exploration of applying new computing paradigms because of the large number of applications
More informationImproving interpretability in approximative fuzzy models via multi-objective evolutionary algorithms.
Improving interpretability in approximative fuzzy models via multi-objective evolutionary algorithms. Gómez-Skarmeta, A.F. University of Murcia skarmeta@dif.um.es Jiménez, F. University of Murcia fernan@dif.um.es
More informationIrregular Bipolar Fuzzy Graphs
Inernational Journal of pplications of Fuzzy Sets (ISSN 4-40) Vol ( 0), 9-0 Irregular ipolar Fuzzy Graphs Sovan Samanta ssamantavu@gmailcom Madhumangal Pal mmpalvu@gmailcom Department of pplied Mathematics
More informationGenetic Algorithms Variations and Implementation Issues
Genetic Algorithms Variations and Implementation Issues CS 431 Advanced Topics in AI Classic Genetic Algorithms GAs as proposed by Holland had the following properties: Randomly generated population Binary
More informationC 1 Modified Genetic Algorithm to Solve Time-varying Lot Sizes Economic Lot Scheduling Problem
C 1 Modified Genetic Algorithm to Solve Time-varying Lot Sizes Economic Lot Scheduling Problem Bethany Elvira 1, Yudi Satria 2, dan Rahmi Rusin 3 1 Student in Department of Mathematics, University of Indonesia,
More informationTotal Semi - µ Strong (Weak) Domination in Intuitionistic Fuzzy Graph
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 5 Ver. V (Sep. - Oct.2016), PP 37-43 www.iosrjournals.org Total Semi - µ Strong (Weak) Domination in Intuitionistic
More informationMechanical Component Design for Multiple Objectives Using Elitist Non-Dominated Sorting GA
Mechanical Component Design for Multiple Objectives Using Elitist Non-Dominated Sorting GA Kalyanmoy Deb, Amrit Pratap, and Subrajyoti Moitra Kanpur Genetic Algorithms Laboratory (KanGAL) Indian Institute
More informationFuzzy Set, Fuzzy Logic, and its Applications
Sistem Cerdas (TE 4485) Fuzzy Set, Fuzzy Logic, and its pplications Instructor: Thiang Room: I.201 Phone: 031-2983115 Email: thiang@petra.ac.id Sistem Cerdas: Fuzzy Set and Fuzzy Logic - 1 Introduction
More informationShortest Path Problem in Network with Type-2 Triangular Fuzzy Arc Length
J. Appl. Res. Ind. Eng. Vol. 4, o. (207) 7 Journal of Applied Research on Industrial Engineering www.journal-aprie.com Shortest Path Problem in etwork with Type-2 Triangular Fuzzy Arc Length Ranjan Kumar
More informationScholars Journal of Physics, Mathematics and Statistics
Scholars Journal of Physics, Mathematics and Statistics Sch. J. Phys. Math. Stat. 2014; 1(2):53-60 Scholars cademic and Scientific Publishers (SS Publishers) (n International Publisher for cademic and
More informationAdaptive Crossover in Genetic Algorithms Using Statistics Mechanism
in Artificial Life VIII, Standish, Abbass, Bedau (eds)(mit Press) 2002. pp 182 185 1 Adaptive Crossover in Genetic Algorithms Using Statistics Mechanism Shengxiang Yang Department of Mathematics and Computer
More informationBipolar Fuzzy Line Graph of a Bipolar Fuzzy Hypergraph
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 13, No 1 Sofia 2013 Print ISSN: 1311-9702; Online ISSN: 1314-4081 DOI: 10.2478/cait-2013-0002 Bipolar Fuzzy Line Graph of a
More informationMultiobjective Job-Shop Scheduling With Genetic Algorithms Using a New Representation and Standard Uniform Crossover
Multiobjective Job-Shop Scheduling With Genetic Algorithms Using a New Representation and Standard Uniform Crossover J. Garen 1 1. Department of Economics, University of Osnabrück, Katharinenstraße 3,
More informationPROGRESSIVE STRUCTURAL TOPOLOGY OPTIMIZATION BY VARIABLE CHROMOSOME LENGTH GENETIC ALGORITHM
PROGRESSIVE STRUCTURAL TOPOLOGY OPTIMIZATION BY VARIABLE CHROMOSOME LENGTH GENETIC ALGORITHM Abstract Il Yong KIM 1 * Olivier DE WECK 2 1 Dept. of Mechanical and Materials Engineering, Queen s University,
More informationAutomata Construct with Genetic Algorithm
Automata Construct with Genetic Algorithm Vít Fábera Department of Informatics and Telecommunication, Faculty of Transportation Sciences, Czech Technical University, Konviktská 2, Praha, Czech Republic,
More informationA New approach for Solving Transportation Problem
Journal for Research Volume 03 Issue 01 March 2017 ISSN: 2395-7549 A New approach for Solving Transportation Problem Manamohan Maharana Lecturer Department of Mathematics M.P.C. (Jr.) College, Baripada,
More informationGT HEURISTIC FOR SOLVING MULTI OBJECTIVE JOB SHOP SCHEDULING PROBLEMS
GT HEURISTIC FOR SOLVING MULTI OBJECTIVE JOB SHOP SCHEDULING PROBLEMS M. Chandrasekaran 1, D. Lakshmipathy 1 and P. Sriramya 2 1 Department of Mechanical Engineering, Vels University, Chennai, India 2
More informationCost Minimization Fuzzy Assignment Problem applying Linguistic Variables
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 6 2017, 404 412 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Cost Minimization
More informationA method for unbalanced transportation problems in fuzzy environment
Sādhanā Vol. 39, Part 3, June 2014, pp. 573 581. c Indian Academy of Sciences A method for unbalanced transportation problems in fuzzy environment 1. Introduction DEEPIKA RANI 1,, T R GULATI 1 and AMIT
More informationMulti-Objective Optimization Using Genetic Algorithms
Multi-Objective Optimization Using Genetic Algorithms Mikhail Gaerlan Computational Physics PH 4433 December 8, 2015 1 Optimization Optimization is a general term for a type of numerical problem that involves
More informationPreprint Stephan Dempe, Alina Ruziyeva The Karush-Kuhn-Tucker optimality conditions in fuzzy optimization ISSN
Fakultät für Mathematik und Informatik Preprint 2010-06 Stephan Dempe, Alina Ruziyeva The Karush-Kuhn-Tucker optimality conditions in fuzzy optimization ISSN 1433-9307 Stephan Dempe, Alina Ruziyeva The
More informationSolving Fuzzy Travelling Salesman Problem Using Octagon Fuzzy Numbers with α-cut and Ranking Technique
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volume 2, Issue 6 Ver. III (Nov. - Dec.26), PP 52-56 www.iosrjournals.org Solving Fuzzy Travelling Salesman Problem Using Octagon
More information