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A Genetic Algorithm based Hybrid Approach to Solve Multi-objectiveInterval Assignment Problem by Estimation Theory
Objectives: In industrial organization and management science, Assignment Problem (AP) is most studied problem with multiple uncertain objectives; normally this uncertainty is represented by an interval. The main aim of this paper is to find a solution of such Multi-objective Interval Assignment Problem (MOIAP). Methods/Statistical analysis: This paper proposes a Genetic Algorithm (GA) based hybrid approach to solve MOIAP by using point and interval estimation theory. Estimation theory is used to manage such uncertainty with sampling. For that the samples are taken from the past data and find point estimation form the samples of each parameter to specified the range of interval with confidence level and this range is considered as an interval in AP. Findings: Traditional method like fuzzy, weighted min-max, goal programming is utilized by several researchers for find solution of MOIAP but here GA provided a proper analysis based solution. In this paper realistic example is provided to represents the solution effectiveness by estimation theory which shows that developed approach provide improved and analysis based solution compare to other approach.
Confidence Interval, Genetic Algorithm, Interval Estimation, Multi-objective Assignment Problem, Point Estimation.
- Pentico DW. Assignment problems: A golden anniversary survey. European Journal of Operational Research. 2007; 176(2):774–93.
- Oliveira C, Antunes CH. An interactive method of tackling uncertainty in interval multiple objective linear programming. Journal of Mathematical Sciences. 2009; 161(6):854–66.
- Ahmed B. On the efficiency of feasible solutions of a multi-criteria assignment problem. Open Operational Research Journal. 2008; 2:25–8.
- Majumdar J, Bhunia AK. Elitist genetic algorithm for assignment problem with imprecise goal. European Journal of Operational Research. 2007; 177(2):684–92.
- Majumdar S. Interval Linear Assignment Problems. Universal Journal of Applied Mathematics. 2013,1(1):14–6.
- Pereira J, Averbakh I. Exact and heuristic algorithms for the interval data robust assignment problem. Computers and Operations Research. 2011; 38(8):1153–63.
- Inuiguchi M, Kume Y. Goal programming problems with interval coefficients and target intervals. European Journal of Operational Research. 1991; 52(3):345–60.
- Inuiguchi M, Sakawa M. Minimax regret solution to linear programming problems with an interval objective function. European Journal of Operational Research. 1995; 86(3):526–36.
- Gabriel RB. Linear multiple objective problems with interval coefficients. Management Science. 1980; 26(7):694–706.
- Ida M. Efficient solution generation for multiple objective linear programming and uncertain coefficients. Proceedings of the 8th Bellman Continuum, Taiwan; 2000. p. 132–6.
- Ida M. Efficient solution generation for multiple objective linear programming based on extreme ray generation method. European Journal of Operational Research. 2005; 160(1):242–51.
- Ida M. Generation of efficient solutions for multiobjective linear programming with interval coefficients. Proceedings of the 35th SICE Annual Conference. International Session Papers SICE'96; 1996. p. 1041–4.
- Ida M. Interval multiobjective programming and mobile robot path planning. New Frontier in Computational Intelligence and its Applications; 2000. p. 313–22.
- Ida M. Necessary efficient test in interval multiobjective linear programming. Proceedings of the Eighth International Fuzzy Systems Association World Congress; 1999. p. 500–4.
- Ida M. Portfolio selection problem with interval coefficients. Applied Mathematics Letters. 2003; 16(5):709–13.
- Inuiguchi M, Sakawa M. Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test. Fuzzy Sets and Systems. 1996; 78(2):231–41.
- Chanas S, Kuchta D. Multiobjective programming in optimization of interval objective functions—A generalized approach. European Journal of Operational Research. 1996; 94(3):594–8.
- Sengupta A, Pal TK, Chakraborty D. Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems. 2001; 119(1):129–38.
- Oliveira C, Antunes CH. Multiple objective linear programming models with interval coefficients–An illustrated overview. European Journal of Operational Research. 2007; 181(3):1434–63.
- Hassanzadeh, Farhad, Nemati H, Sun M. Robust optimization for multiobjective programming problems with imprecise information. Procedia Computer Science. 2013; 17:357–64.
- Suprajitno H, Mohd IB. Linear programming with interval arithmetic. International Journal of Contemporary Mathematical Sciences. 2010; 5(7):323–32.
- Rivaz S, Yaghoobi MA. Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients. Central European Journal of Operations Research. 2013; 21(3):625–49.
- Kagade KL, Bajaj VH. Fuzzy method for solving multi-objective assignment problem with interval cost. Journal of Statistics and Mathematics. 2010; 1(1):1–9.
- Kai S, Yang L, Lu J, Zhi-ping F. An interval multiobject assignment method based on decision-maker's risk attitude. 2011 International Conference on Shanghai E-Business and E-Government (ICEE), China; 2011. p. 1–4.
- Salehi K. An approach for solving multi-objective assignment problem with interval parameters. Management Science Letters. 2014; 4(9):2155–60.
- Roussas G. Introduction to probability and statistical inference. Academic Press; 2003.
- Ross SM. Introduction to probability and statistics for engineers and scientists. Third Edition, Elsevier Academic Press; 2004.
- Khan AJ, Dash DK, EMV approach to solve multi-objective transportation problem under fuzzy conditions. International Journal of Mathematical Research and Science. 2013; 1(5):2347–3975.
- Tailor AR, Dhodiya JM. Genetic algorithm based hybrid approach to solve multi-objective assignment problem. International Journal of Innovative Research in Science, Engineering and Technology. 2016; 5(1):524–35.
- Farahani SSS, Nikzad M, Tabar MB, Naraghi MG, Javadian A. Multi-machine power system stabilizer adjustment using genetic algorithms. Indian Journal of Science and Technology. 2011 Aug; 4(8). DOI: 10.17485/ijst/2011/v4i8/30887.
- Hajmohammad MH, Salari M, Hashemi SA, Esfe MH. Optimization of stacking sequence of composite laminates for optimizing buckling load by neural network and genetic algorithm. Indian Journal of Science and Technology. 2013 Aug; 6(8). DOI: 10.17485/ijst/2013/v6i8/36346.
- Manoharan GV, Shanmugalakshmi R. Multi-objective firefly algorithm for multi-class gene selection. Indian Journal of Science and Technology. 2015 Jan; 8(1). DOI: 10.17485/ijst/2015/v8i1/52310.
- Sivanandam SN, Deepa SN. Introduction to genetic algorithms. Science and Business Media; 2007.
- Sahu A, Tapadar R. Solving the assignment problem using genetic algorithm and simulated annealing. IMECS; 2006. p. 762–5.
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