Hybrid Constrained Evolutionary Algorithm for Numerical Optimization Problems

Year 2019, Volume: 48 Issue: 3, 931 - 950, 15.06.2019

Wali Khan MASHWANİ Alam ZAİB Özgür YENİAY Habib SHAH Naseer Mansoor TAİRAN Muhammad SULAİMAN

Abstract

Constrained optimization are naturally arises in many real-life applications, and is therefore gaining a constantly growing attention of the researchers.Evolutionary algorithms are not directly applied on constrained optimization problems. However, different constraint-handling techniques are incorporated in their framework to adopt it for dealing with constrained environments. This paper suggests an hybrid constrained evolutionary algorithm (HCEA) that employs two penalty functions simultaneously. The suggested HCEA has two versions namely HCEA-static and HCEA-adaptive. The performance of the HCEA-static and HCEA-adaptive algorithms are examined upon the constrained benchmark functions that are recently designed for the special session of the $2006$ IEEE Conference of Evolutionary Computation (IEEE-CEC'06). The experimental results of the suggested algorithms are much promising as compared to one of the recent constrained version of the JADE. The converging behaviour of the both suggested algorithms on each benchmark function is encouraging and promising in most cases.

Keywords

Constrained Functions, Evolutionary Computation(EC), Evolutionary Algorithm(EA) and Hybrid EAs

References

• Abraham, Ajith, Grosan, Crin and Ishibuchi, Hisao,Hybrid Evolutionary Algorithms, Stud- ies in Computational Intelligence, Springer, 2007.
• Abdel-Basset, Mohamed, Wang, Gai-Ge, Kumar Sangaiah, Arun and Rushdy, Ehab., Krill herd algorithm based on cuckoo search for solving engineering optimization problems, Mul- timedia Tools and Applications, 1-24,2017.
• Alam, Khug, Mashwani, Wali Khan and Asim, Muhammad,Hybrid Biography Based Opti- mization Algorithm for Optimization Problems, Gomal University Journal of Research,33(1), 134-142, 2017.
• Asim, Muhammad, Mashwani, Wali Khan and Jan, M.A., Hybrid Genetic Firefly Algorithm for Global Optimization Problems, Sindh University Research Journal, 49(4), 899-906, 2017.
• Asim, Muhammad, Mashwani, Wali Khan, Jan, Muhammad Asif and Iqbal, Javed, De- rivative Based Hybrid Genetic Algorithm: A Preliminary Experimental Results, Punjab University Journal of Mathematics, Vol. 49(2), pp. 89-99, 2017.
• Asim, Muhammad, Mashwani, Wali Khan, Yeniay, Ozgur, Jan, Muhammad Asif, Hussian, Hazrat and Wang, Gai-Ge, Hybrid Genetic Algorithms for Global Optimization Problems, Hacettepe Journal of Mathematics and Statistics, 47 (3), 539 - 551, 2018.
• Blaha, Brian and Wunsch, Don, Evolutionary programming to optimize an assembly program, Proceedings of the 2002 Congress on Evolutionary Computation, CEC02, 2, 19011903, 2002.
• Bentouati,Bachir, Saliha, Chettih, El-Sehiemy, Ragab A. andWang, Gai-Ge, Elephant Herd- ing Optimization for Solving Non-convex Optimal Power Flow Problem,Journal of Electrical and Electronics Engineering, 10, 31-40, 2017.
• Coello Coello, Carlos, Use of a self-adaptive penalty approach for engineering optimization problems, Computers in Industry, 41(2), 113127, 2000.
• Chen, Q., Liu, B., Zhang, Q., Liang, J. J., Suganthan, P. N., Qu, B.Y. , Problem Definition and Evaluation Criteria for CEC 2015 Special Session and Competition on Bound Con- strained Single-Objective Computationally Expensive Numerical Optimization, Technical Report, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Technical Report, Nanyang Technological University, Singapore, Nov, 2014.
• Chiong, Raymond, Weise, Thomas and Michalewicz, Zbigniew (Editors), Variants of Evo- lutionary Algorithms for Real-World Applications, ISBN 3642234232, Springer, 2012.
• Cagnoni, Stefano, Poli, Riccardo, Smith, George D., Corne, David, Oates, Martin, Hart, Emma, Lanzi, Pier L., Egbert J, Willem, Li, Yun, Paechter, Ben, Fogarty, Terence C. Real- World Applications of Evolutionary Computing, Springer-Verlag Lecture Notes in Computer Science, Berlin, 2000.
• Chen, Su Huan, Wu, Jie and Chen, Yu Dong, Interval optimization for uncertain structures, Finite Elements in Analysis and Design, 40(11), 13791398, 2004.
• Datta, Rituparna and Deb, Kalyanmoy,Evolutionary Constrained Optimization,Infosys Sci- ence Foundation Series in Applied Sciences and Engineering, ISSN: 2363-4995, Springer, 2015.
• Eidehall, Andreas and Petersson, Lars Threat assessment for general road scenes using Monte Carlo sampling, IEEE Intelligent Transportation Systems Conference, 2006.
• Eiben, A.E. and Smith, James E., Introduction to Evolutionary Computing: Natural Com- puting Series, Springer-Verlag Berlin Heidelberg, 2015.
• Engelbrecht, Andries P., Computational Intelligence An Introduction,Second Edition, John Wiley, 2007.
• El-Mihoub, Tarek A., Hopgood, Adrian A., Nolle, Lars and Battersby, Alan, Hybrid Genetic Algorithms: A Review, Engineering Letters, 13(2), 124-137, 2006.
• Floudas, Christodoulos A., Pardalos, Panos M., Adjiman, Claire, Esposito, William R., Gums, Zeynep H., Harding, Stephen T., Klepeis, John L., Meyer, Clifford A., and Schweiger, Carl A., Handbook of test problems in local and global optimization, Vol. 33. Springer Science & Business Media, 2013.
• Fogel, Lawrence J., Walsh, Alvin J. and Owens, Michael J., Artificial Intelligence through Simulated Evolution, John Wiley, 1966.
• Fogel, Lawrence J., Intelligence through Simulated Evolution: Forty Years of Evolutionary Programming, John Wiley, 1999.
• Farmani, R. and Wright, J. A., Self-Adaptive Fitness Formulation for Constrained Opti- mization, IEEE Transactions on Evolutionary Computation, 7, 445-455, 2003.
• Geng, Xiutang, Xu, Jin, Xiao, Jianhua and Pan, Linqiang, A simple simulated annealing algorithm for the maximum clique problem, Information Sciences, 177, 22, 50645071, 2007.
• Homaifar, Abdollah, Qi, Charlene X. and Lai, Steven H., Constrained optimization via genetic algorithms, Simulation, 62, 242-254, 1994.
• Kennedy, James and Eberhart, Russell C., Particle swarm optimization, in Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948, November, 1995.
• Khanum, Rashida Adeeb, Jan, Muhammad Asif, Mashwani, Wali Khan, Tairan, Naseer Mansoor, Khan, Hidayat Ullah and Shah, Habib, On the hybridization of global and local search methods, Journal of Intelligent & Fuzzy Systems, 35(3), 3451-3464, 2018.
• Lawler, Eugene L. and Wood, D. E., Branch-and-Bound Methods: A Survey, Journal Op- eration Research, 14, 4, 699-719, Institute for Operations Research and the Management Sciences, Linthicum, Maryland, USA, 1996.
• Liu, H., Cai, Z., and Wang, Y., Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization, Applied Soft Comput- ing,10(2), 629-640, 2010.
• Liang, J. J., Qu, B-Y., Suganthan, P. N., Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization, Technical Report 201311, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Technical Report, Nanyang Technological University, Singapore, December, 2013.
• Liang, J. J., Qu, B. Y., Suganthan, P. N. and Chen, Q., Problem Definitions and Evaluation Criteria for the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization, Technical Report, Computational Intelligence Laboratory, Zhengzhou Univer- sity, Zhengzhou, China and Technical Report, Nanyang Technological University, Singapore, November, 2014.
• Liang, J. J., Runarsson, T. P., Mezura-Montes, E., Clerc, M., Suganthan, P. N., Coello Coello, C. A. and Deb, K., Problem definitions and evaluation criteria for the CEC 2006 spe- cial session on constrained real-parameter optimization, Technical Report, Nanyang Tech- nological University, Singapore, 2006.
• Lin, Mingjie and Wawrzynek, John, Improving FPGA placement with dynamically adaptive stochastic tunneling, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 29, 12, 18581869, 2010.
• Mezura-Montes, Efrén and Coello Coello, Carlos, A simple multimembered evolution strategy to solve constrained optimization problems, IEEE Transactions on Evolutionary Computa- tion, 9(1), 117, 2005
• Machta, Jon Strengths and weaknesses of parallel tempering, Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 80, 5, 2009.
• Mallipeddi, Rammohan, Das, S., Suganthan, P.N., Ensemble of Constraint Handling Tech- niques for Single Objective Constrained Optimization, In: Datta R., Deb K. (eds) Evolu- tionary Constrained Optimization. Infosys Science Foundation Series, Springer, New Delhi, 2015.
• Mallipeddi, Rammohan and Suganthan, P.N., Ensemble of Constraint Handling Techniques, in IEEE Transactions on Evolutionary Computation, 14(4), 561-579, 2010.
• Mashwani, Wali Khan and Salhi, Abdellah,Multiobjective Memetic Algorithm Based on Decomposition, Applied Soft Computing, No 21, 221-243, 2014.
• Mashwani, Wali Khan and Salhi, Abdellah, Multiobjective Evolutionary Algorithm Based on Multimethod with Dynamic Resources Allocation Strategy, Applied Soft Computing Journal, Vol 39, 292-309, 2016.
• Mashwani, Wali Khan, Salhi, Abdellah, Yeniay, Ozgur, Hussian, Hazrat, Jan, Muhmmad Asif, Hybrid non-dominated sorting genetic algorithm with adaptive operators selection, Applied Soft Computing, vol 56, 1-18, 2017.
• Mashwani, Wali Khan, Salhi, Abdellah, Yeniay, Ozgur and Khanum, R.A and Jan, Muham- mad Asif, Hybrid Adaptive Evolutionary Algorithm Based on Decomposition, Applied Soft Computing, Volume 57, 363378, 2017.
• Mashwani, Wali Khan,Salhi, Abdel, Jan, Muhammad Asif, Khanum, R.A. and Su- laiman, M., Impact Analysis of Crossovers in Multiobjective Evolutionary Algorithm, Sci.Int.(Lahore), 27(6), 4943-4956, 2015.
• Mashwani, Wali Khan and Salhi, Abdellah, A Decomposition Based Hybrid Multiobjec- tive Evolutionary Algorithm with Dynamic Resources Allocation, Applied Soft Computing, 12(9), 2765-2780, 2012.
• Pan, Changcheng, Xu, Chen and Li, Guo, Differential evolutionary strategies for global op- timization, Shenzhen Daxue Xuebao (Ligong Ban), Journal of Shenzhen University Science and Engineering, 25(2), 211-215, 2008.
• Salhi, Abdellah and Fraga, Eric S., Nature-Inspired Optimisation Approaches and the New Plant Propagation Algorithm, Proceedings of the ICeMATH2011, K2-1 to K2-8, 2011.
• Shah, Habib, Tairan, Nasser, Ghazali, Rozaida, Yeniay, Ozgur and Mashwani, Wali Khan, Hybrid Honey Bees Meta-Heuristic For Benchmark Data Classification, Exploring Critical Approaches of Evolutionary Computation, IGI Global Publisher, 2019
• Shah, Habib, Tairan, Nasser, Mashwani, Wali Khan, Ahmad Al-Sewari, Abdulrahman, Jan, Muhammad Asif and Badshah, Gran, Hybrid Global Crossover Bees Algorithm for Solving Boolean Function Classification Task. International Conference on Intelligent Computing ICIC (3), 467-478, 2017.
• Sharma, Jyoti and Singhal, Ravi Shankar,Genetic Algorithm and Hybrid Genetic Algorithm for Space Allocation Problems-A Review, International Journal of Computer Applications, 95(4), 33-37, 2014.
• Sulaiman, Muhammad, Salhi, Abdelah, Khan, Asfandyar,Muhammad, Shakoor and Mash- wani, Wali Khan, On the Theoretical Analysis of the Plant Propagation Algorithms, Math- ematical Problems in Engineering, Volume 2018.
• Sulaiman, Muhammad, Salhi, Abdellah, Mashwani, Wali Khan and Rashidi, Muhammad M., A Novel Plant Propagation Algorithm: Modifications and Implementation, Science International, 28(1), 201-209, 2016.
• Sulaiman, Muhammad and Salhi, Abdella, A Seed-based Plant Propagation Algorithm: The Feeding Station Model, The Scientific World Journal, 1-16, 2015
• Sulaiman, Muhammad, Salhi, Abdella, Selamoglu, Birsen Irem, Kirikchi, Omar Bahaaldin, A Plant Propagation Algorithm for Constrained Engineering Optimisation Problems, Math- ematical problems in engineering, 1-10, 2014.
• Storn, Rainer M. and Price, Kenneth,Differential Evolution: A Simple and Efficient Heuris- tic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11(4), 341-359, 1997.
• Shah, Tayaba,Jan, Muhammad Asif, Mashwani, Wali Kahan and Wazir, Hamza, Adap- tive differential evolution for constrained optimization problems, Science Int.(Lahore), 3(28) 41044108, 2016.
• Veltman, M., Algebraic techniques, Computer Physics Communications, 3, 7578, September, 1972.
• Vetschera, Rudolf, A general branch-and-bound algorithm for fair division problems, Journal Computers and Operations Research, 37(12), 2121-2130, December, 2010.
• Wang, Gai-Ge, Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems, Memetic Computing, 2016.
• Wang, Gai-Ge, Deb, Suash, Zhao, Xinchao and Cui, Zhihua, A new monarch butterfly optimization with an improved crossover operator, Operational Research, 2016.
• Wang, Gai-Ge, Deb, Suash and Coelho, Leandro Elephant Herding Optimization, 2015.
• Wang, Gai-Ge, Deb, Suash and Coelho, Leandro,Earthworm optimization algorithm: a bio- inspired metaheuristic algorithm for global optimization problems, International Journal of Bio-Inspired Computation, 2015.
• Wu, Chenhan, Ant colony multilevel path optimize tactic based on information consistence optimize, International Conference on “Computer Application and System Modeling, 1, 533536, November, 2010.
• Wazir, Hamza, Jan, Muhammad Asif, Mashwani, Wali Khan and Shah, Tayyaba, A Penalty Function Based Differential Evolution Algorithm for Constrained Optimization, The Nu- cleus Journal, 53(1), 155-161, 2016
• Wang, Gai-Ge, Gandomi, Amir, Alavi, Amir and Gong, Dunwei, A comprehensive review of krill herd algorithm: variants, hybrids and applications Artificial Intelligence Review, 2017.
• Wang,Yong, Liu, Hui, Cai, Zixing and Zhou, Yuren, An orthogonal design based constrained evolutionary optimization algorithm Engineering Optimization, 39 (6): 715736, 2007.
• Wang, Y, Cai, Z, Zhou, Y, Zeng, W., An adaptive trade-off model for constrained evolu- tionary optimization, IEEE Transactions on Evolutionary Computation,12(1): 8092, 2008.
• Wang, Yong and Cai, Zixing,A hybrid multi-swarm particle swarm optimization to solve con- strained optimization problems, Frontiers of Computer Science in China, 3(1),38-52, 2009.
• Wang, Yong, Cai, Zixing, Zhou, Yuren and Zeng, Wei, An adaptive trade-off model for constrained evolutionary optimization, IEEE Transactions on Evolutionary Computation, 12(1), 8092,2018.
• Yu, Jianbo, Xi, Lifeng and Wang, Shijin, An improved particle swarm optimization for evolving feed forward artificial neural networks, Neural Processing Letters, vol. 26, no. 3, pp. 217231, 2007.