Harmony search algorithm with differential evolution based control parameter co-evolution and its application in chemical process dynamic optimization

Abstract

A modified harmony search algorithm with co-evolutional control parameters (DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rate and pitch adjusting rate, are encoded as a symbiotic individual of an original individual (i.e., harmony vector). Harmony search operators are applied to evolving the original population. DE is applied to co-evolving the symbiotic population based on feedback information from the original population. Thus, with the evolution of the original population in DEHS, the symbiotic population is dynamically and self-adaptively adjusted, and real-time optimum control parameters are obtained. The proposed DEHS algorithm has been applied to various benchmark functions and two typical dynamic optimization problems. The experimental results show that the performance of the proposed algorithm is better than that of other HS variants. Satisfactory results are obtained in the application.

Keywords

harmony search / differential evolution optimization / co-evolution / self-adaptive control parameter / dynamic optimization

References

[1] GEEMZ W, KIMJ H, LOGANATHANG. A new heuristic optimization algorithm: harmony search [J]. Simulation, 2001, 76: 60-68

[2] HOSSEINIS D, SHIRAZIM A, GHOMIS M T F. Harmony search optimization algorithm for a novel transportation problem in a consolidation network[J]. Engineering Optimization, 2014, 46: 1538-1552

[3] RASTGOUA, MOSHTAGHJ. Improved harmony search algorithm for transmission expansion planning with adequacy-security considerations in the deregulated power system [J]. International Journal of Electrical Power & Energy Systems, 2014, 60: 153-164

[4] KALLIORASN A, LAGAROSN D, KARLAFTISM G. An improved harmony search algorithm for emergency inspection scheduling [J]. Engineering Optimization, 2014, 46: 1570-1592

[5] SHIVAIEM, AMELIM T. An implementation of improved harmony search algorithm for scenario-based transmission expansion planning [J]. Soft Computing, 2014, 18: 1615-1630

[6] MAHDAVIM, FESANGHARYM, DAMANGIRE. An improved harmony search algorithm for solving optimization problems [J]. Applied Mathematics and Computation, 2007, 188: 1567-1579

[7] OMRANM G, MAHDAVIM. Global-best harmony search [J]. Applied Mathematics and Computation, 2008, 198: 643-656

[8] PANQ-k, SUGANTHANP N, TASGETIRENM F, LIANGJ J. A self-adaptive global best harmony search algorithm for continuous optimization problems [J]. Applied Mathematics and Computation, 2010, 216: 830-848

[9] EIBENA E, HINTERDINGR, MICHALEWICZZ. Parameter control in evolutionary algorithms [J]. IEEE Transactions on Evolutionary Computation, 1999, 3: 124-141

[10] STORNR, PRICEK. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces [J]. Journal of Global Optimization, 1997, 11: 341-359

[11] QINA K, SUGANTHANP NSelf-adaptive differential evolution algorithm for numerical optimization [C]// Proceedings of 2005 IEEE International Conference on Evolutionary Computation., 20051785-1791

[12] LIX, HUC P, YANX F. Chaotic differential evolution algorithm based on competitive coevolution and its application to dynamic optimization of chemical processes [J]. Intelligent Automation and Soft Computing, 2013, 19: 85-98

[13] ZHUJ, YANX F, ZHAOW X. Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy [J]. Engineering Optimization, 2013, 45: 1205-1221

[14] FANQ Q, LÜZ M, YANX F, GUOM J. Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex [J]. Journal of Central South University, 2013, 20: 950-959

[15] RAYW H, SZEKELYJProcess optimization: With applications in metallurgy and chemical engineering [M], 1973New YorkWiley

[16] ROUBOSJ, de GOOIJERC, van STRATENG, van BOXTELA. Comparison of optimization methods for fed-batch cultures of hybridoma cells [J]. Bioprocess Engineering, 1997, 17: 99-102

[17] LEEJ, RAMIREZW F. Optimal fed-batch control of induced foreign protein production by recombinant bacteria [J]. AIChE Journal, 1994, 40: 899-907

[18] THOLUDURA, RAMIREZW F. Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm [J]. International Journal of Control, 1997, 68: 1115-1128

[19] ROUBOSJ v S v B A. An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance [J]. Journal of Biotechnology, 1999, 67: 173-187

[20] SARKARD, MODAKJ M. ANNSA: A hybrid artificial neural network/simulated annealing algorithm for optimal control problems [J]. Chemical Engineering Science, 2003, 58: 3131-3142

[21] ZHANGB, CHEND-z, ZHAOW-xiang. Iterative ant-colony algorithm and its application to dynamic optimization of chemical process [J]. Computers & Chemical Engineering, 2005, 29: 2078-2086

[22] YEOB. A modified quasilinearization algorithm for the computation of optimal singular control [J]. International Journal of Control, 1980, 32: 723-730

[23] RAJESHJ, GUPTAK, KUSUMAKARH S, JAYARAMANV K, KULKARNIB D. Dynamic optimization of chemical processes using ant colony framework [J]. Computers & Chemistry, 2001, 25: 583-595

[24] ASGARIS A, PISHVAIEM R. Dynamic optimization in chemical processes using region reduction strategy and control vector parameterization with an ant colony optimization algorithm [J]. Chemical Engineering & Technology, 2008, 31: 507-512