Local Search-Inspired Rough Sets for Improving Multiobjective Evolutionary Algorithm

Affiliation(s)

Department of Mathematics, Faculty of Science, Qassim University, Buraydah, Saudi Arabia.

Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shibin El-Kom, Egypt.

Department of Mathematics, Faculty of sciences, Taif University, Taif, Saudi Arabia.

Department of Mathematics, Faculty of Science, Qassim University, Buraydah, Saudi Arabia.

Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shibin El-Kom, Egypt.

Department of Mathematics, Faculty of sciences, Taif University, Taif, Saudi Arabia.

ABSTRACT

In this paper we
present a new optimization algorithm, and the proposed algorithm operates in
two phases. In the first one, multiobjective version of genetic algorithm is
used as search engine in order to generate approximate true Pareto front. This
algorithm is based on concept of co-evolution and repair algorithm for
handling nonlinear constraints. Also it maintains a finite-sized archive of
non-dominated solutions which gets iteratively updated in the presence of new
solutions based on the concept *e*-dominance. Then,
in the second stage, rough set theory is adopted as local search engine in
order to improve the spread of the solutions found so far. The results, provided
by the proposed algorithm for benchmark problems, are promising when compared
with exiting well-known algorithms. Also, our results suggest that our
algorithm is better applicable for solving real-world application problems.

Cite this paper

EL-Sawy, A. , Hussein, M. , Zaki, E. and Mousa, A. (2014) Local Search-Inspired Rough Sets for Improving Multiobjective Evolutionary Algorithm.*Applied Mathematics*, **5**, 1993-2007. doi: 10.4236/am.2014.513192.

EL-Sawy, A. , Hussein, M. , Zaki, E. and Mousa, A. (2014) Local Search-Inspired Rough Sets for Improving Multiobjective Evolutionary Algorithm.

References

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[2] Mousa, A.A. (2013) A New Stopping and Evaluation Criteria for Linear Multiobjective Heuristic Algorithms. Journal of Global Research in Mathematical Archives, 1, 1-11.

[3] Cai, Q.S., Zhang, D.F., Wu, B. and Leung, S.C.H. (2013) A Novel Stock Fore-Casting Model Based on Fuzzy Time Series and Genetic Algorithm. Procedia Computer Science, 18, 1155-1162.

http://dx.doi.org/10.1016/j.procs.2013.05.281

[4] Ni, H. and Wang, Y.Q. (2013) Stock Index Tracking by Pareto Efficient Genetic Algorithm. Applied Soft Computing, 13, 4519-4535.

http://dx.doi.org/10.1016/j.asoc.2013.08.012

[5] Straßburg, J., Gonzàlez-Martel, C. and Alexandrov, V. (2012) Parallel Genetic Algorithms for Stock Market Trading Rules. Procedia Computer Science, 9, 1306-1313.

[6] Xue, X.-W., Yao, M., Wu, Z.H. and Yang, J.H. (2013) Genetic Ensemble of Extreme Learning Machine. Neurocomputing, Accepted Manuscript. (In Press)

[7] Yang, J.D., Xu, H. and Jia, P.F. (2013) Effective Search for Genetic-Based Machine Learning Systems via Estimation of Distribution Algorithms and Embedded Feature Reduction Techniques. Neurocomputing, 113, 105-121.

http://dx.doi.org/10.1016/j.neucom.2013.01.014

[8] Yang, H.M., Yi, J., Zhao, J.H. and Dong, Z.Y. (2013) Extreme Learning Machine Based Genetic Algorithm and Its Application in Power System Economic Dispatch. Neurocomputing, 102, 154-162.

http://dx.doi.org/10.1016/j.neucom.2011.12.054

[9] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2005) A Solution to the Optimal Power Flow Using Genetic Algorithm. Journal of Applied Mathematics & Computation (AMC), 155, 391-405.

[10] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2009) Epsilon-Dominance Based Multiobjective Genetic Algorithm for Economic Emission Load Dispatch Optimization Problem. Electric Power Systems Research, 79, 1561-1567.

http://dx.doi.org/10.1016/j.epsr.2009.06.003

[11] AL-Matrafi, B.N. and Mousa, A.A. (2013) Optimization Methodology Based on Quantum Computing Applied to Fuzzy Practical Unit Commitment Problem. International Journal of Scientific & Engineering Research, 4, 1138.

[12] Galal, A.A., Mousa, A.A. and Al-Matrafi, B.N. (2013) Hybrid Ant Optimization System for Multiobjective Optimal Power Flow Problem Under Fuzziness. Journal of Natural Sciences and Mathematics, 6, 179-199.

[13] Deb, K. (2001) Multiobjective Optimization Using Evolutionary Algorithms. Wiley, Chichester.

[14] Schaffer, J.D. (1985) Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Grefenstette, J.J., et al., Eds., Genetic Algorithms and Their Applications, Proceedings of the 1st International Conference on Genetic Algorithms, Lawrence Erlbaum, Mahwah, 93-100.

[15] Horn, J., Nafpliotis, N. and Goldberg, D.E. (1994) A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: Grefenstette, J.J., et al., Eds., IEEE World Congress on Computational Intelligence, Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE Press, Piscataway, 82-87.

http://dx.doi.org/10.1109/ICEC.1994.350037

[16] Srinivas, N. and Deb, K. (1999) Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2, 221-248.

http://dx.doi.org/10.1162/evco.1994.2.3.221

[17] Deb, K., Agrawal, S., Pratab, A. and Meyarivan, T. (2000) A Fast Elitist Non-Dominated Sorting Genetic Algorithms for Multiobjective Optimization: NSGA II, KanGAL Report 200001. Indian Institute of Technology, Kanpur.

[18] Zitzler, E. and Thiele, L. (1998) Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Case Study. In: Eiben, A.E., Back, T., Schoenauer, M. and Schwefel, H.P., Eds., 5th International Conference on Parallel Problem Solving from Nature (PPSN-V), Springer, Berlin, 292-301.

http://dx.doi.org/10.1007/BFb0056872

[19] Zitzler, E., Laumanns, M. and Thiele, L. (2001) SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, EUROGEN 2001, Athens, 19-21 September 2001, 1-21.

[20] Knowles, J.D. and Corne, D.W. (1999) The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Multiobjective Optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, IEEE Press, Piscataway, 98-105.

[21] Knowles, J.D. and Corne, D.W. (2000) M-PAES: A Memetic Algorithm for Multiobjective Optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, IEEE Press, Piscataway, 325-332.

[22] Jimenez, F. and Verdegay, J.L. (1998) Constrained Multiobjective Optimization by Evolutionary Algorithm. Proceeding of the International ICSC Symposition on Engineering of Intelligent Systems (EIS’98), 266-271.

[23] Michalewiz, Z. (1996) Genetic Algorithms + Data Structures = Evolution Programs. 3rd Edition, Springer-Verlag, Berlin.

[24] Michalewicz, Z. and Schoenauer, M. (1996) Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 4, 1-32.

[25] EL-Sawy, A.A., Hussein, M.A., Zaki, E.S.M. and Mousa, A.A. (2014) An Introduction to Genetic Algorithms: A Survey A Practical Issues. International Journal of Scientific & Engineering Research, 5, 252-262.

[26] Fonseca, C.M. and Fleming, P.J. (1998) Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms: Part I: A Unified Formulation. IEEE Transactions on Systems and Cybernetics. Part A: Systems and Humans, 28, 26-37.

http://dx.doi.org/10.1109/3468.650319

[27] Harada, K., Sakuma, J., Isao, O. and Kobayashi, S. (2007) Constraint-Handling Method for Multi-Objective Function Optimization: Pareto Descent Repair Operator. Proceedings of the 4th International Conference on Evolutionary Multicriterion Optimization, Matsushima, 5-8 March 2007, 156-170.

[28] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2006) IT-CEMOP: An Iterative Co-Evolutionary Algorithm for Multiobjective Optimization Problem with Nonlinear Constraints. Journal of Applied Mathematics & Computation, 183, 373-389.

http://dx.doi.org/10.1016/j.amc.2006.05.095

[29] Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello Coello, C.A., Caballero, R. and Molina, J. (2008) Improving Multi-Objective Evolutionary Algorithms by Using Rough Sets. In: Ligeza, A., Reich, S., Schaefer, R. and Cotta, C., Eds., Knowledge-Driven Computing: Knowledge Engineering and Intelligent Computations, Studies in Computational Intelligence, Vol. 102, Springer-Verlag, Berlin, 81-98.

[30] Laumanns, M., Thiele, L., Deb, K. and Zitzler, E. (2002) Archiving with Guaranteed Convergence and Diversity in Multi-Objective Optimization. GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, New York, 439-447.

[31] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2005) An Effective Genetic Algorithm Approach to Multiobjective Resource Allocation Problems (MORAPs). Journal of Applied Mathematics & Computation, 163, 755-768.

http://dx.doi.org/10.1016/j.amc.2003.10.057

[32] Murata, T., Ishibuchi, H. and Tanaka, H. (1996) Multiobjective Genetic Algorithm and Its Application to Flowshop Scheduling. Computers and Industrial Engineering, 30, 957-968.

http://dx.doi.org/10.1016/0360-8352(96)00045-9

[33] Binh, T.T. and Korn, U. (1997) MOBES: A Multi-Objective Evolution Strategy for Constrained Optimization Problems. Proceeding of the 3rd International Conference on Genetic Algorithm MENDEL, Brno, 176-182.

[34] Osyczka, A. and Kundu, S. (1995) A New Method to Solve Generalized Multicriteria Optimization Problems Using the Simple Genetic Algorithm. Structural Optimization, 10, 94-99.

[35] Tanaka, M., Watanabe, H., Furukawa, Y. and Tanino, T. (1995) GA-Based Decision Support System for Multi-Criteria Optimization. Proceeding of the International Conference on Systems, Man and Cybernetics, 2, 1556-1561.

[36] Deb, K., Pratap, A. and Moitra, S. (2000) Mechanical Component Design for Multiple Objectives Using Elitist Non-Dominated Sorting GA. Kangal Report No. 200002.

[37] Sarker, R., Abbass, H.A. and Karim, S. (2001) An Evolutionary Algorithm for Constrained Multiobjective Optimization Problems. 5th Australasia-Japan Joint Workshop, University of Otago, Dunedin, 19-21 November 2001, 1-10.

[38] Kirsch, U. (1981) Optimal Structural Design. McGraw-Hill Co., New York.

[1] Miettinen, K. (2002) Non-Linear Multiobjective Optimization. Kluwer Academic Publisher, Dordrecht.

[2] Mousa, A.A. (2013) A New Stopping and Evaluation Criteria for Linear Multiobjective Heuristic Algorithms. Journal of Global Research in Mathematical Archives, 1, 1-11.

[3] Cai, Q.S., Zhang, D.F., Wu, B. and Leung, S.C.H. (2013) A Novel Stock Fore-Casting Model Based on Fuzzy Time Series and Genetic Algorithm. Procedia Computer Science, 18, 1155-1162.

http://dx.doi.org/10.1016/j.procs.2013.05.281

[4] Ni, H. and Wang, Y.Q. (2013) Stock Index Tracking by Pareto Efficient Genetic Algorithm. Applied Soft Computing, 13, 4519-4535.

http://dx.doi.org/10.1016/j.asoc.2013.08.012

[5] Straßburg, J., Gonzàlez-Martel, C. and Alexandrov, V. (2012) Parallel Genetic Algorithms for Stock Market Trading Rules. Procedia Computer Science, 9, 1306-1313.

[6] Xue, X.-W., Yao, M., Wu, Z.H. and Yang, J.H. (2013) Genetic Ensemble of Extreme Learning Machine. Neurocomputing, Accepted Manuscript. (In Press)

[7] Yang, J.D., Xu, H. and Jia, P.F. (2013) Effective Search for Genetic-Based Machine Learning Systems via Estimation of Distribution Algorithms and Embedded Feature Reduction Techniques. Neurocomputing, 113, 105-121.

http://dx.doi.org/10.1016/j.neucom.2013.01.014

[8] Yang, H.M., Yi, J., Zhao, J.H. and Dong, Z.Y. (2013) Extreme Learning Machine Based Genetic Algorithm and Its Application in Power System Economic Dispatch. Neurocomputing, 102, 154-162.

http://dx.doi.org/10.1016/j.neucom.2011.12.054

[9] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2005) A Solution to the Optimal Power Flow Using Genetic Algorithm. Journal of Applied Mathematics & Computation (AMC), 155, 391-405.

[10] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2009) Epsilon-Dominance Based Multiobjective Genetic Algorithm for Economic Emission Load Dispatch Optimization Problem. Electric Power Systems Research, 79, 1561-1567.

http://dx.doi.org/10.1016/j.epsr.2009.06.003

[11] AL-Matrafi, B.N. and Mousa, A.A. (2013) Optimization Methodology Based on Quantum Computing Applied to Fuzzy Practical Unit Commitment Problem. International Journal of Scientific & Engineering Research, 4, 1138.

[12] Galal, A.A., Mousa, A.A. and Al-Matrafi, B.N. (2013) Hybrid Ant Optimization System for Multiobjective Optimal Power Flow Problem Under Fuzziness. Journal of Natural Sciences and Mathematics, 6, 179-199.

[13] Deb, K. (2001) Multiobjective Optimization Using Evolutionary Algorithms. Wiley, Chichester.

[14] Schaffer, J.D. (1985) Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Grefenstette, J.J., et al., Eds., Genetic Algorithms and Their Applications, Proceedings of the 1st International Conference on Genetic Algorithms, Lawrence Erlbaum, Mahwah, 93-100.

[15] Horn, J., Nafpliotis, N. and Goldberg, D.E. (1994) A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: Grefenstette, J.J., et al., Eds., IEEE World Congress on Computational Intelligence, Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE Press, Piscataway, 82-87.

http://dx.doi.org/10.1109/ICEC.1994.350037

[16] Srinivas, N. and Deb, K. (1999) Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2, 221-248.

http://dx.doi.org/10.1162/evco.1994.2.3.221

[17] Deb, K., Agrawal, S., Pratab, A. and Meyarivan, T. (2000) A Fast Elitist Non-Dominated Sorting Genetic Algorithms for Multiobjective Optimization: NSGA II, KanGAL Report 200001. Indian Institute of Technology, Kanpur.

[18] Zitzler, E. and Thiele, L. (1998) Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Case Study. In: Eiben, A.E., Back, T., Schoenauer, M. and Schwefel, H.P., Eds., 5th International Conference on Parallel Problem Solving from Nature (PPSN-V), Springer, Berlin, 292-301.

http://dx.doi.org/10.1007/BFb0056872

[19] Zitzler, E., Laumanns, M. and Thiele, L. (2001) SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, EUROGEN 2001, Athens, 19-21 September 2001, 1-21.

[20] Knowles, J.D. and Corne, D.W. (1999) The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Multiobjective Optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, IEEE Press, Piscataway, 98-105.

[21] Knowles, J.D. and Corne, D.W. (2000) M-PAES: A Memetic Algorithm for Multiobjective Optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, IEEE Press, Piscataway, 325-332.

[22] Jimenez, F. and Verdegay, J.L. (1998) Constrained Multiobjective Optimization by Evolutionary Algorithm. Proceeding of the International ICSC Symposition on Engineering of Intelligent Systems (EIS’98), 266-271.

[23] Michalewiz, Z. (1996) Genetic Algorithms + Data Structures = Evolution Programs. 3rd Edition, Springer-Verlag, Berlin.

[24] Michalewicz, Z. and Schoenauer, M. (1996) Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 4, 1-32.

[25] EL-Sawy, A.A., Hussein, M.A., Zaki, E.S.M. and Mousa, A.A. (2014) An Introduction to Genetic Algorithms: A Survey A Practical Issues. International Journal of Scientific & Engineering Research, 5, 252-262.

[26] Fonseca, C.M. and Fleming, P.J. (1998) Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms: Part I: A Unified Formulation. IEEE Transactions on Systems and Cybernetics. Part A: Systems and Humans, 28, 26-37.

http://dx.doi.org/10.1109/3468.650319

[27] Harada, K., Sakuma, J., Isao, O. and Kobayashi, S. (2007) Constraint-Handling Method for Multi-Objective Function Optimization: Pareto Descent Repair Operator. Proceedings of the 4th International Conference on Evolutionary Multicriterion Optimization, Matsushima, 5-8 March 2007, 156-170.

[28] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2006) IT-CEMOP: An Iterative Co-Evolutionary Algorithm for Multiobjective Optimization Problem with Nonlinear Constraints. Journal of Applied Mathematics & Computation, 183, 373-389.

http://dx.doi.org/10.1016/j.amc.2006.05.095

[29] Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello Coello, C.A., Caballero, R. and Molina, J. (2008) Improving Multi-Objective Evolutionary Algorithms by Using Rough Sets. In: Ligeza, A., Reich, S., Schaefer, R. and Cotta, C., Eds., Knowledge-Driven Computing: Knowledge Engineering and Intelligent Computations, Studies in Computational Intelligence, Vol. 102, Springer-Verlag, Berlin, 81-98.

[30] Laumanns, M., Thiele, L., Deb, K. and Zitzler, E. (2002) Archiving with Guaranteed Convergence and Diversity in Multi-Objective Optimization. GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, New York, 439-447.

[31] Osman, M.S., Abo-Sinna, M.A. and Mousa, A.A. (2005) An Effective Genetic Algorithm Approach to Multiobjective Resource Allocation Problems (MORAPs). Journal of Applied Mathematics & Computation, 163, 755-768.

http://dx.doi.org/10.1016/j.amc.2003.10.057

[32] Murata, T., Ishibuchi, H. and Tanaka, H. (1996) Multiobjective Genetic Algorithm and Its Application to Flowshop Scheduling. Computers and Industrial Engineering, 30, 957-968.

http://dx.doi.org/10.1016/0360-8352(96)00045-9

[33] Binh, T.T. and Korn, U. (1997) MOBES: A Multi-Objective Evolution Strategy for Constrained Optimization Problems. Proceeding of the 3rd International Conference on Genetic Algorithm MENDEL, Brno, 176-182.

[34] Osyczka, A. and Kundu, S. (1995) A New Method to Solve Generalized Multicriteria Optimization Problems Using the Simple Genetic Algorithm. Structural Optimization, 10, 94-99.

[35] Tanaka, M., Watanabe, H., Furukawa, Y. and Tanino, T. (1995) GA-Based Decision Support System for Multi-Criteria Optimization. Proceeding of the International Conference on Systems, Man and Cybernetics, 2, 1556-1561.

[36] Deb, K., Pratap, A. and Moitra, S. (2000) Mechanical Component Design for Multiple Objectives Using Elitist Non-Dominated Sorting GA. Kangal Report No. 200002.

[37] Sarker, R., Abbass, H.A. and Karim, S. (2001) An Evolutionary Algorithm for Constrained Multiobjective Optimization Problems. 5th Australasia-Japan Joint Workshop, University of Otago, Dunedin, 19-21 November 2001, 1-10.

[38] Kirsch, U. (1981) Optimal Structural Design. McGraw-Hill Co., New York.