Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling. (English) Zbl 1198.90184

Summary: The goal of this paper is to present a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region for long-term cascaded hydroelectric system scheduling. The introduced chaotic maps improve the global optimal capability of CPSO algorithm. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for implementing the maximum of objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on a practical hydro-system.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


90B35 Deterministic scheduling theory in operations research
90C59 Approximation methods and heuristics in mathematical programming
37N35 Dynamical systems in control
Full Text: DOI


[1] Ott, E., Chaos in dynamical systems, (1993), Cambridge university press · Zbl 0792.58014
[2] Zhang, T.; Wang, H.; Wang, Z., Mutative scale chaos optimization algorithm and its application, Control decis, 14, 3, 285-288, (1999)
[3] Hu, Y.; Li, Y.C.; Yu, J.X.; Chao, H.D., Steeped-up chaos optimization algorithm and its application, J syst eng, 17, 1, 41-44, (2002)
[4] Lu, Z.; Shieh, L.S.; Chen, G.R., On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization, Chaos solitons & fractals, 18, 819-827, (2003) · Zbl 1068.93053
[5] Yang, J.J.; Zhou, J.Z.; Wu, W.; Liu, F., A chaos algorithm based on progressive optimality and tabu search algorithm, IEEE proc 4th int conf Mach learn cybernet, 2977-2981, (2005)
[6] Tavazoei, M.S.; Haeri, M., Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms, Appl math comput, 187, 1076-1085, (2007) · Zbl 1114.65335
[7] Yang, D.X.; Li, G.; Cheng, G.D., On the efficiency of chaos optimization algorithms for global optimization, Chaos solitons & fractals, 34, 1366-1375, (2007)
[8] Li, B.; Jiang, W., Optimation of complex functions by chaos search, Int J cybernet syst, 29, 4, 409-419, (1998) · Zbl 1012.90068
[9] Kennedy, J.; Eberhan, R.J., Particle swarm optimization, IEEE int conf neural netw, 4, 1942-1948, (1995)
[10] Shi, Y.H.; Eberhart, R.A., Modified particle swarm optimizer, IEEE proc cong evol comput, 69-73, (1998)
[11] Shi, Y.H.; Eberhart, R.A., Empirical study of particle swarm optimization, IEEE proc cong evol comput, 1945-1950, (1999)
[12] Angeline, P.J., Evolutionary optimization versus particle swarm optimization: philosophy and performance differences, Evolution programming VII, (1998), Springer
[13] Meng, H.J.; Zheng, P.; Wu, R.Y.; Hao, X.J., A hybrid particle swarm algorithm with embedded chaotic search, IEEE conf cybernet intelligent syst, 367-371, (2004)
[14] Liu, B.; Wang, L.; Jin, Y.H.; Tang, F.; Huang, D.X., Improved particle swarm optimization combined with chaos, Chaos solitons & fractals, 25, 5, 1261-1271, (2005) · Zbl 1074.90564
[15] Jiang, C.W.; Etorre, B.; Jiang, J., A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment, Energy conv manag, 46, 2689-2696, (2005)
[16] Liu, B.; Wang, L.; Jin, Y.H.; Tang, F.; Huang, D.X., Directing orbits of chaotic systems by particle swarm optimization, Chaos solitons & fractals, 29, 454-461, (2006) · Zbl 1147.93314
[17] He, Q.; Wang, L.; Liu, B., Parameter estimation for chaotic systems by particle swarm optimization, Chaos solitons & fractals, 34, 654-661, (2007) · Zbl 1152.93504
[18] Xiang, T.; Liao, X.F.; Wong, K.W., An improved particle swarm optimization algorithm combined with piecewise linear chaotic map, Appl math comput, 190, 1637-1645, (2007) · Zbl 1122.65363
[19] Coelho, L.S.; Mariani, V.C.; Li, Y.G., A novel chaotic particle swarm optimization approach using henon map and implicit filtering local search for economic load dispatch, Chaos solitons & fractals, 39, 2, 510-518, (2009)
[20] Coelho, L.S., A quantum particle swarm optimizer with chaotic mutation operator, Chaos solitons & fractals, 37, 1409-1418, (2008)
[21] May, R., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467, (1976) · Zbl 1369.37088
[22] Parlitz, U.; Ergezinger, S., Robust communication based on chaotic spreading sequences, Phys lett A, 5, 146-150, (1994)
[23] Akritas, P.; Antoniou, I.; Ivanov, V.V., Identification and prediction of discrete chaotic maps applying a Chebyshev neural network, Chaos solitons & fractals, 11, 337-344, (2000) · Zbl 1115.68469
[24] Liao, X.; Li, X.; Peng, J.; Chen, G., A digital secure image communication scheme based on the chaotic Chebyshev map, Int J commun syst, 17, 437-445, (2004)
[25] Alvarez, G., Security problems with a chaos-based deniable authentication scheme, Chaos solitons & fractals, 26, 7-11, (2005) · Zbl 1077.94019
[26] He D, He C, Jiang LG, Zhu HW, Hu GR. A chaotic map with infinite collapses. Proc IEEE tencon, vol. III. Kuala Lumpur, Malaysia 2000;9:95-9.
[27] He, D.; He, C.; Jiang, L.G.; Zhu, H.W.; Hu, G.R., Chaotic characteristics of a one-dimensional iterative map with infinite collapses, IEEE trans circ syst, 48, 7, 900-906, (2001) · Zbl 0993.37033
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