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Volumn 3, Issue 2, 2003, Pages 97-122

Efficient Differential Evolution algorithms for multimodal optimal control problems

Author keywords

Differential Evolution algorithms; Evolutionary algorithms; First order gradient algorithm; Iterative Dynamic Programming; Optimal control

Indexed keywords

DYNAMIC PROGRAMMING; ITERATIVE METHODS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS);

EID: 14344249577     PISSN: 15684946     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1568-4946(03)00007-3     Document Type: Article
Times cited : (104)

References (75)
  • 5
    • 0001327501 scopus 로고
    • αBB: A global optimization method for general constrained non-convex problems
    • I. Androulakis, C.D. Maranas, C.A. Floudas, αBB: A global optimization method for general constrained non-convex problems, J. Global Optim. 7 (1995) 337-363.
    • (1995) J. Global Optim. , vol.7 , pp. 337-363
    • Androulakis, I.1    Maranas, C.D.2    Floudas, C.A.3
  • 6
    • 84938590600 scopus 로고    scopus 로고
    • Deterministic global optimization in isothermal reactor network synthesis
    • W.R. Esposito, C.A. Floudas, Deterministic global optimization in isothermal reactor network synthesis, J. Global Optim. 22 (2002) 59-95.
    • (2002) J. Global Optim. , vol.22 , pp. 59-95
    • Esposito, W.R.1    Floudas, C.A.2
  • 8
    • 0003241007 scopus 로고
    • A controlled random search procedure for global optimization
    • L.C.W. Dixon, G.P. Zsego (Eds.), North-Holland Publishing, Amsterdam
    • W.L. Price, A controlled random search procedure for global optimization, in: L.C.W. Dixon, G.P. Zsego (Eds.), Toward Global Optimization 2, North-Holland Publishing, Amsterdam, 1978, pp. 71-84.
    • (1978) Toward Global Optimization , vol.2 , pp. 71-84
    • Price, W.L.1
  • 9
    • 0020792913 scopus 로고
    • Global optimisation by controlled random search
    • W.L. Price, Global optimisation by controlled random search, J. Optim. Theory Applic. 40 (3) (1983) 333-348.
    • (1983) J. Optim. Theory Applic. , vol.40 , Issue.3 , pp. 333-348
    • Price, W.L.1
  • 10
    • 0023436768 scopus 로고
    • Global optimization algorithms for CAD workstation
    • W.L. Price, Global optimization algorithms for CAD workstation, J. Optim. Theory Applic. 55 (1) (1987) 133-146.
    • (1987) J. Optim. Theory Applic. , vol.55 , Issue.1 , pp. 133-146
    • Price, W.L.1
  • 11
    • 0023420912 scopus 로고
    • Stochastic global optimization methods. I. Clustering methods
    • A.H.G. Rinnooy Kan, G.T. Timmer, Stochastic global optimization methods. I. Clustering methods, Math. Programming 39 (1987) 27-56.
    • (1987) Math. Programming , vol.39 , pp. 27-56
    • Rinnooy Kan, A.H.G.1    Timmer, G.T.2
  • 12
    • 0023419959 scopus 로고
    • Stochastic global optimization methods. II. Multilevel methods
    • A.H.G. Rinnooy Kan, G.T. Timmer, Stochastic global optimization methods. II. Multilevel methods, Math. Programming 39 (1987) 57-58.
    • (1987) Math. Programming , vol.39 , pp. 57-58
    • Rinnooy Kan, A.H.G.1    Timmer, G.T.2
  • 13
    • 0035505056 scopus 로고    scopus 로고
    • On success rates for controlled random search
    • E.M.T. Hendrix, P.M. Ortigosa, I. García, On success rates for controlled random search, J. Global Optim. 21 (3) (2001) 239-263.
    • (2001) J. Global Optim. , vol.21 , Issue.3 , pp. 239-263
    • Hendrix, E.M.T.1    Ortigosa, P.M.2    García, I.3
  • 14
    • 0000429265 scopus 로고    scopus 로고
    • Stochastic methods for practical global optimization
    • Z. Zabinsky, Stochastic methods for practical global optimization, J. Global Optim. 13 (4) (1998) 433-444.
    • (1998) J. Global Optim. , vol.13 , Issue.4 , pp. 433-444
    • Zabinsky, Z.1
  • 15
    • 0007557042 scopus 로고    scopus 로고
    • Convergence of simulated annealing algorithm for continuous global optimization
    • M. Locatelli, Convergence of simulated annealing algorithm for continuous global optimization, J. Global Optim. 18 (3) (2000) 219-233.
    • (2000) J. Global Optim. , vol.18 , Issue.3 , pp. 219-233
    • Locatelli, M.1
  • 22
    • 0008619798 scopus 로고    scopus 로고
    • A hybrid Genetic algorithm for non-convex function minimization
    • M.F. Hussain, K.S. Al-Sultan, A hybrid Genetic algorithm for non-convex function minimization, J. Global Optim. 11 (3) (1997) 313-324.
    • (1997) J. Global Optim. , vol.11 , Issue.3 , pp. 313-324
    • Hussain, M.F.1    Al-Sultan, K.S.2
  • 23
    • 0029768771 scopus 로고    scopus 로고
    • Re-evaluating Genetic algorithm performance under coordinate rotation of benchmark functions, a survey of some theoretical and practical aspects of Genetic algorithms
    • R. Salomon, Re-evaluating Genetic algorithm performance under coordinate rotation of benchmark functions, a survey of some theoretical and practical aspects of Genetic algorithms, BioSystems 39 (1996) 263-278.
    • (1996) BioSystems , vol.39 , pp. 263-278
    • Salomon, R.1
  • 24
    • 0142000477 scopus 로고    scopus 로고
    • Differential Evolution - A simple and efficient heuristic for global optimization over continuous spaces
    • R. Storn, Differential Evolution - a simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim. 11 (4) (1997) 341-359.
    • (1997) J. Global Optim. , vol.11 , Issue.4 , pp. 341-359
    • Storn, R.1
  • 26
    • 0026883116 scopus 로고    scopus 로고
    • Global optimisation approach to non-linear optimal control
    • O. Rosen, R. Luus, Global optimisation approach to non-linear optimal control, J. Optim. Theory Applic. 73 (3), 547-562.
    • J. Optim. Theory Applic. , vol.73 , Issue.3 , pp. 547-562
    • Rosen, O.1    Luus, R.2
  • 27
    • 15944397773 scopus 로고    scopus 로고
    • On global search for non-convex optimal control
    • I.M. Bomze, T. Csendes, R. Horst, P.M. Pardolos (Eds.), Kluwer Academic Publishers, Dordrecht
    • A. Strekalovsky, I. Vasiliev, On global search for non-convex optimal control, in: I.M. Bomze, T. Csendes, R. Horst, P.M. Pardolos (Eds.), Global Optimisation in Engineering Design, Kluwer Academic Publishers, Dordrecht, 1997, pp. 355-386.
    • (1997) Global Optimisation in Engineering Design , pp. 355-386
    • Strekalovsky, A.1    Vasiliev, I.2
  • 28
    • 0002327353 scopus 로고    scopus 로고
    • Deterministic global optimisation in non-linear optimal control problems
    • W.R. Esposito, Ch.A. Floudas, Deterministic global optimisation in non-linear optimal control problems, J. Global Optim. 17 (2000) 97-126.
    • (2000) J. Global Optim. , vol.17 , pp. 97-126
    • Esposito, W.R.1    Floudas, Ch.A.2
  • 29
    • 31244435059 scopus 로고    scopus 로고
    • A rigorous global optimization algorithm for problems with ordinary differential equations
    • I. Papamichail, C.L. Adjiman, A rigorous global optimization algorithm for problems with ordinary differential equations, J. Global Optim. 24 (2002) 1-33.
    • (2002) J. Global Optim. , vol.24 , pp. 1-33
    • Papamichail, I.1    Adjiman, C.L.2
  • 30
    • 0031316575 scopus 로고    scopus 로고
    • Application of stochastic global optimization algorithms to practical problems
    • M.M. Ali, C. Storey, A. Törn, Application of stochastic global optimization algorithms to practical problems, J. Optim. Theory Applic. 95 (3) (1997) 545-563.
    • (1997) J. Optim. Theory Applic. , vol.95 , Issue.3 , pp. 545-563
    • Ali, M.M.1    Storey, C.2    Törn, A.3
  • 31
    • 0001075482 scopus 로고    scopus 로고
    • Modified controlled random search algorithms
    • M.M. Ali, C. Storey, Modified controlled random search algorithms, Intern. J. Computer Math. 53, 229-235.
    • Intern. J. Computer Math. , vol.53 , pp. 229-235
    • Ali, M.M.1    Storey, C.2
  • 34
    • 0031168634 scopus 로고    scopus 로고
    • Dynamic optimization of batch reactors using adaptive stochastic algorithms
    • E.F. Carrasco, J.R. Banga, Dynamic optimization of batch reactors using adaptive stochastic algorithms, Ind. Eng. Chem. Res. 36 (1997) 2252-2261.
    • (1997) Ind. Eng. Chem. Res. , vol.36 , pp. 2252-2261
    • Carrasco, E.F.1    Banga, J.R.2
  • 36
    • 0025432467 scopus 로고
    • Optimal control by dynamic programming using systematic reduction grid size
    • R. Luus, Optimal control by dynamic programming using systematic reduction grid size, Int. J. Control 19 (1990) 995-1013.
    • (1990) Int. J. Control , vol.19 , pp. 995-1013
    • Luus, R.1
  • 37
    • 0025862808 scopus 로고
    • Multiplicity of solutions in using dynamic programming for optimal control
    • R. Luus, M. Galli, Multiplicity of solutions in using dynamic programming for optimal control, Hung. J. Ind. Chem. 19 (1991) 55-62.
    • (1991) Hung. J. Ind. Chem. , vol.19 , pp. 55-62
    • Luus, R.1    Galli, M.2
  • 38
    • 0028377729 scopus 로고
    • Global optimization of the bifunctional catalyst problem
    • R. Luus, B. Bojkov, Global optimization of the bifunctional catalyst problem, Can. J. Chem. Eng. 72 (1994) 160-163.
    • (1994) Can. J. Chem. Eng. , vol.72 , pp. 160-163
    • Luus, R.1    Bojkov, B.2
  • 39
    • 0026901422 scopus 로고
    • Multiplicity of solutions in the optimization of a bifuctional catalyst blend in a tubular reactor
    • R. Luus, J. Dittrich, F.J. Keil, Multiplicity of solutions in the optimization of a bifuctional catalyst blend in a tubular reactor, Can. J. Chem. Eng. 70 (1992) 780-785.
    • (1992) Can. J. Chem. Eng. , vol.70 , pp. 780-785
    • Luus, R.1    Dittrich, J.2    Keil, F.J.3
  • 40
    • 0026864223 scopus 로고
    • Use of random admissible values for control in Iterative Dynamic Programming
    • B. Bojkov, R. Luus, Use of random admissible values for control in Iterative Dynamic Programming, Ind. Eng. Chem. Res. 31 (1992) 1308-1314.
    • (1992) Ind. Eng. Chem. Res. , vol.31 , pp. 1308-1314
    • Bojkov, B.1    Luus, R.2
  • 41
    • 0000807789 scopus 로고
    • On the application of Iterative Dynamic Programming to Singular Optimal Control problems
    • R. Luus, On the application of Iterative Dynamic Programming to Singular Optimal Control problems, IEEE, Trans. Automatic Control 37 (11) (1992) 1802-1806.
    • (1992) IEEE, Trans. Automatic Control , vol.37 , Issue.11 , pp. 1802-1806
    • Luus, R.1
  • 42
    • 0031209508 scopus 로고    scopus 로고
    • Optimal control of final state constrained systems
    • W. Mekarapiruk, R. Luus, Optimal control of final state constrained systems, Can. J. Chem. Eng. 75 (1997) 806-811.
    • (1997) Can. J. Chem. Eng. , vol.75 , pp. 806-811
    • Mekarapiruk, W.1    Luus, R.2
  • 43
    • 0029310817 scopus 로고
    • Time optimal control of high dimensional systems by Iterative Dynamic Programming
    • B. Bojkov, R. Luus, Time optimal control of high dimensional systems by Iterative Dynamic Programming, Can. J. Chem. Eng. 73 (1995) 380-390.
    • (1995) Can. J. Chem. Eng. , vol.73 , pp. 380-390
    • Bojkov, B.1    Luus, R.2
  • 45
    • 0033954468 scopus 로고    scopus 로고
    • Optimal control by iterative dynamic programming and with deterministic and random candidates for control
    • W. Mekarapiruk, R. Luus, Optimal control by iterative dynamic programming and with deterministic and random candidates for control, Ind. Eng. Chem. Res. 39 (1) (2000) 84-91.
    • (2000) Ind. Eng. Chem. Res. , vol.39 , Issue.1 , pp. 84-91
    • Mekarapiruk, W.1    Luus, R.2
  • 46
  • 47
    • 0029228155 scopus 로고
    • Genetic algorithm approach for optimal control problems with linearity appearing controls
    • H. Sewald, R.R. Kumar, Genetic algorithm approach for optimal control problems with linearity appearing controls, J. Guidance, Control and Dyn. 18 (1) (1995) 177-182.
    • (1995) J. Guidance, Control and Dyn. , vol.18 , Issue.1 , pp. 177-182
    • Sewald, H.1    Kumar, R.R.2
  • 48
    • 0041939633 scopus 로고    scopus 로고
    • Numerical computational method using Genetic algorithms for the optimal control problem with terminal constraints and free parameters
    • Y. Yamashita, M. Shima, Numerical computational method using Genetic algorithms for the optimal control problem with terminal constraints and free parameters, Non-linear Anal., Theory, Meth. And Applic. 30 (4) (1997) 2285-2290.
    • (1997) Non-linear Anal., Theory, Meth. and Applic. , vol.30 , Issue.4 , pp. 2285-2290
    • Yamashita, Y.1    Shima, M.2
  • 49
    • 0029522015 scopus 로고
    • An Evolutionary Program for a class of continuous optimal control problems
    • IEEE, Piscataway
    • S. Smith, An Evolutionary Program for a class of continuous optimal control problems, in: Proceedings of the IEEE Conference on Evolutionary Computation, vol. 1, IEEE, Piscataway, 1995, pp. 418-422.
    • (1995) Proceedings of the IEEE Conference on Evolutionary Computation , vol.1 , pp. 418-422
    • Smith, S.1
  • 53
    • 15944385445 scopus 로고    scopus 로고
    • Optimal control of greenhouse climate using a short time climate model and evolutionary algorithms
    • A. Munack, H.J. Tantau (Eds.), IFAC Workshop, Hannover, Germany
    • H. Pohlheim, A. Heißner, Optimal control of greenhouse climate using a short time climate model and evolutionary algorithms, in: A. Munack, H.J. Tantau (Eds.), Preprints Mathematical and Control Applications in Agriculture and Horticulture, IFAC Workshop, Hannover, Germany, 1997, pp. 113-118.
    • (1997) Preprints Mathematical and Control Applications in Agriculture and Horticulture , pp. 113-118
    • Pohlheim, H.1    Heißner, A.2
  • 54
    • 0033993192 scopus 로고    scopus 로고
    • A combined Genetic algorithm-shooting method approach to solving optimal control problems
    • Y.C. Sim, S.B. Leng, V. Subramanian, A combined Genetic algorithm-shooting method approach to solving optimal control problems, Int. J. Syst. Sci. 31(1) (2000) 83-89.
    • (2000) Int. J. Syst. Sci. , vol.31 , Issue.1 , pp. 83-89
    • Sim, Y.C.1    Leng, S.B.2    Subramanian, V.3
  • 55
    • 0032893519 scopus 로고    scopus 로고
    • An evolutionary strategy for fed-bacth bioreactor optimization: Concepts and performance
    • J.A. Roubos, G. Van Straten, A.J.B. Van Boxtel, An evolutionary strategy for fed-bacth bioreactor optimization: concepts and performance, J. Biotechnol. 67 (1999) 173-187.
    • (1999) J. Biotechnol. , vol.67 , pp. 173-187
    • Roubos, J.A.1    Van Straten, G.2    Van Boxtel, A.J.B.3
  • 56
    • 11744332007 scopus 로고    scopus 로고
    • A new Evolution Strategy and its application to solving optimal control problems
    • M.M.A. Hashem, K. Watanabe, K. Izumi, A new Evolution Strategy and its application to solving optimal control problems, JSME Int. J., Ser. C, 41 (3) (1998) 406-412.
    • (1998) JSME Int. J., Ser. C , vol.41 , Issue.3 , pp. 406-412
    • Hashem, M.M.A.1    Watanabe, K.2    Izumi, K.3
  • 57
    • 0031339730 scopus 로고    scopus 로고
    • Optimal control and optimal time location problems of differential-algebraic systems by differential evolution
    • F.S. Wang, J.P. Chiou, Optimal control and optimal time location problems of differential-algebraic systems by differential evolution, Ind. Eng. Chem. Res. 36 (1997) 5348-5357.
    • (1997) Ind. Eng. Chem. Res. , vol.36 , pp. 5348-5357
    • Wang, F.S.1    Chiou, J.P.2
  • 58
    • 0033544450 scopus 로고    scopus 로고
    • Hybrid method of evolutionary algorithms for static and dynamic optimisation problems with applications to a fed-batch fermentation process
    • J.P. Chiou, F.S. Wang, Hybrid method of evolutionary algorithms for static and dynamic optimisation problems with applications to a fed-batch fermentation process, Comput. Chem. Eng. 23 (1999) 1277-1291.
    • (1999) Comput. Chem. Eng. , vol.23 , pp. 1277-1291
    • Chiou, J.P.1    Wang, F.S.2
  • 59
    • 0343262717 scopus 로고    scopus 로고
    • Dynamic optimisation of continuous polymer reactor using a modified differential evolution algorithm
    • M.H. Lee, Ch. Han, K.S. Chang, Dynamic optimisation of continuous polymer reactor using a modified differential evolution algorithm, Ind. Eng. Chem. Res. 38 (1999) 4825-4831.
    • (1999) Ind. Eng. Chem. Res. , vol.38 , pp. 4825-4831
    • Lee, M.H.1    Han, Ch.2    Chang, K.S.3
  • 61
    • 0042163579 scopus 로고    scopus 로고
    • An Introduction to Differential Evolution
    • D. Corne, M. Dorigo, F. Glover (Eds.), McGraw-Hill, New York
    • K.V. Price, An Introduction to Differential Evolution, in: D. Corne, M. Dorigo, F. Glover (Eds.), New Ideas in Optimization, McGraw-Hill, New York, 1999.
    • (1999) New Ideas in Optimization
    • Price, K.V.1
  • 63
    • 0029713262 scopus 로고    scopus 로고
    • Minimizing the real functions of the ICEC'96 contest by Differential Evolution
    • Nagoya
    • R. Storn, K. Price, Minimizing the real functions of the ICEC'96 contest by Differential Evolution, in: IEEE Conference on Evolutionary Computation, Nagoya, 1996, pp. 842-844.
    • (1996) IEEE Conference on Evolutionary Computation , pp. 842-844
    • Storn, R.1    Price, K.2
  • 64
    • 0033115654 scopus 로고    scopus 로고
    • Systems design by constraint adaptation and differential evolution
    • R. Storn, Systems design by constraint adaptation and differential evolution, IEEE Trans. Evol. Comput. 3 (1) (1999) 22-34.
    • (1999) IEEE Trans. Evol. Comput. , vol.3 , Issue.1 , pp. 22-34
    • Storn, R.1
  • 66
    • 0001307871 scopus 로고
    • Direct and indirect methods for trajectory optimization
    • O. von Stryk, R. Bulirsch, Direct and indirect methods for trajectory optimization, Annal. Oper. Res. 37 (1992) 357-373.
    • (1992) Annal. Oper. Res. , vol.37 , pp. 357-373
    • Von Stryk, O.1    Bulirsch, R.2
  • 69
    • 0023826312 scopus 로고
    • Control parametrization: A unified approach to optimal control problems with general constraints
    • C.J. Goh, K.L. Teo, Control parametrization: a unified approach to optimal control problems with general constraints, Automatica 24 (1) (1988) 3-18.
    • (1988) Automatica , vol.24 , Issue.1 , pp. 3-18
    • Goh, C.J.1    Teo, K.L.2
  • 71
    • 0003140039 scopus 로고
    • Predictive models for the Breeder Genetic Algorithm. I. Continuous parameter optimization
    • H. Mühlenbein, D. Schlierkamp-Voosen, Predictive models for the Breeder Genetic Algorithm. I. Continuous parameter optimization, Evol. Comput. 1 (1) (1993) 25-49.
    • (1993) Evol. Comput. , vol.1 , Issue.1 , pp. 25-49
    • Mühlenbein, H.1    Schlierkamp-Voosen, D.2
  • 75
    • 0032096190 scopus 로고    scopus 로고
    • Enhancement of the global convergence of using iterative dynamic programming to solve optimal control problems
    • L.J. Shiaw, Ch. Hwang, Enhancement of the global convergence of using iterative dynamic programming to solve optimal control problems, Ind. Eng. Chem. Res. 38 (6) (1998) 2469-2478.
    • (1998) Ind. Eng. Chem. Res. , vol.38 , Issue.6 , pp. 2469-2478
    • Shiaw, L.J.1    Hwang, Ch.2


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