Modified ε-constraint method for bi-objective optimization: Reduce computational complexity and increase efficiency
Subject Areas : Statistics
1 - Assistant Professor, Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Lahijan Branch, Lahijan, Iran.
Keywords: نقاط غیرمغلوب, روش &epsilon, -محدودیت, بهینه سازی چندهدفه,
Abstract :
One of the effective method for solving the multi-objective optimization problems is the ε-constraint method which, unlike the weighted sum method is able to find non-dominated points in non-convex parts of the non-dominated frontier. The main disadvantages of this method are finding similar non-dominated points for choosing different parameters and thus increasing the computational complexity of the algorithm and reducing its overall performance, which is not cost-effective in terms of time and cost. In this paper, a modified is made to ε-constraint method, which, due to the intelligence of the algorithm, the unnecessary areas that lead to the production of the same non-dominated points are eliminated from the beginning. Therefore, additional computational efforts are eliminated to produce the same non-dominated points. Discussions and details of the proposed method, with its algorithm, are presented and in the numerical examples section, the efficiency of the proposed method is compared with the ε-constraint method.
[1] L. He, A. M. Friedman, C. Bailey‐Kellogg. A divide‐and‐conquer approach to determine the Pareto frontier for optimization of protein engineering experiments. Proteins. Structure, Function, and Bioinformatics 80(3): 790-806 (2012)
[2] A. Chakraborty, A. A. Linninger. Plant-wide waste management. 1. Synthesis and multiobjective design. Industrial & engineering chemistry research 41(18): 4591-4604 (2002)
[3] M. Asteasuain, A. Bandoni, C. Sarmoria, A. Brandolin. Simultaneous process and control system design for grade transition in styrene polymerization. Chemical engineering science, 61(10), 3362-3378 (2006)
[4] A. Hugo, C. Ciumei, A. Buxton, E. N. Pistikopoulos. E nvironmental impact minimisation through material substitution: a multi-objective optimisation approach. In Computer Aided Chemical Engineering 14, 683-688 (2003)
[5] Y. L. Lim, P. Floquet, X. Joulia, S. D. Kim. Multiobjective optimization in terms of economics and potential environment impact for process design and analysis in a chemical process simulator. Industrial & engineering chemistry research. 38(12): 4729-4741 (1999)
[6] I. Das, J. E. Dennis. Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM journal on optimization. 8(3): 631-657 (1998)
[7] Y. Y. Haimes. On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE transactions on systems, man, and cybernetics, 1(3): 296-297 (1971)
[8] B. Pirouz, E. Khorram. A computational approach based on the ε-constraint method in multi-objective optimization problems. Adv. Appl. Stat 49: 453 (2016)
[9] M. Ehrenstein, G. Guillén-Gosálbez. Multiobjective Life Cycle Optimization of Hydrogen Supply Chains. In Hydrogen Supply Chains 389-404 (2018)
[10] T. Ganesan, P. Vasant, I. Litvinchev. Multiobjective Optimization of a Biofuel Supply Chain Using Random Matrix Generators in Deep Learning Techniques and Optimization Strategies in Big Data Analytics. IGI Global 206-232 (2020)
[11] K. Sreenu, S. Malempati. MFGMTS: Epsilon constraint-based modified fractional grey wolf optimizer for multi-objective task scheduling in cloud computing. IETE Journal of Research 65(2): 201-215 (2019)
[12] M. A. Tawhid, V. Savsani. ∊-constraint heat transfer search (∊-HTS) algorithm for solving multi-objective engineering design problems. Journal of computational design and engineering 5(1): 104-119 (2018)
[13] A. Ghane-Kanafi, E. Khorram. A new scalarization method for finding the efficient frontier in non-convex multi-objective problems. Applied Mathematical Modelling 39(23): 7483-7498 (2015)
[14] J. Borwein, A. S. Lewis. Convex analysis and nonlinear optimization: theory and examples. Springer Science & Business Media (2010)
[15] M. Ehrgott. Multicriteria optimization. Springer Science & Business Media (2006)
[16] G. Eichfelder. Adaptive scalarization methods in multiobjective optimization (436): Springer (2008)
[17] A. Messac, A. Ismail-Yahaya, C. A. Mattson. The normalized normal constraint method for generating the Pareto frontier. Structural and multidisciplinary optimization 25(2): 86-98 (2003)
[18] T. Evangelos. Multi-criteria decision making methods: a comparative study. Netherland: Kluwer Academic Publication (2000)
[19] P.C. Fishburn. Letter to the editor—additive utilities with incomplete product sets: application to priorities and assignments. Operations Research 15(3): 537-542 (1967)
[20] V. Chankong, Y. Y. Haimes. Multiobjective decision making: theory and methodology. Courier Dover Publications (2008)
[21] S. A. Vavasis. Complexity issues in global optimization: a survey, in Handbook of global optimization Springer. 27-41 (1995)
[22] Z. B. Zabinsky. Random search algorithms. Wiley Encyclopedia of Operations Research and Management Science (2010)
[23] A. A. Zhigljavsky. Theory of global random search. Springer Science & Business Media (65): (2012)
[24] B. Betrò, F. Schoen. Sequential stopping rules for the multistart algorithm in global optimisation. Mathematical Programming 38(3): 271-286 (1987)
[25] K. Deb, L. Thiele, M. Laumanns, E. Zitzler. Scalable test problems for evolutionary multiobjective optimization. Evolutionary Multiobjective Optimization. Theoretical Advances and Applications. 105-145 (2005)