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A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems

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  • Bruce A. Conway

    (University of Illinois)

Abstract

There has been significant progress in the development of numerical methods for the determination of optimal trajectories for continuous dynamic systems, especially in the last 20 years. In the 1980s, the principal contribution was new methods for discretizing the continuous system and converting the optimization problem into a nonlinear programming problem. This has been a successful approach that has yielded optimal trajectories for very sophisticated problems. In the last 15–20 years, researchers have applied a qualitatively different approach, using evolutionary algorithms or metaheuristics, to solve similar parameter optimization problems. Evolutionary algorithms use the principle of “survival of the fittest” applied to a population of individuals representing candidate solutions for the optimal trajectories. Metaheuristics optimize by iteratively acting to improve candidate solutions, often using stochastic methods. In this paper, the advantages and disadvantages of these recently developed methods are described and an attempt is made to answer the question of what is now the best extant numerical solution method.

Suggested Citation

  • Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9918-z
    DOI: 10.1007/s10957-011-9918-z
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    Cited by:

    1. David Ottesen & Ryan P. Russell, 2021. "Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 634-674, December.
    2. Sheng Zhang & En-Mi Yong & Wei-Qi Qian & Kai-Feng He, 2019. "A Variation Evolving Method for Optimal Control Computation," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 246-270, October.
    3. Alena Vagaská & Miroslav Gombár & Ľuboslav Straka, 2022. "Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice," Energies, MDPI, vol. 15(6), pages 1-22, March.
    4. N. Koeppen & I. M. Ross & L. C. Wilcox & R. J. Proulx, 2019. "Fast Mesh Refinement in Pseudospectral Optimal Control," Papers 1904.12992, arXiv.org.
    5. Miguel G. Villarreal-Cervantes, 2017. "Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 628-657, May.
    6. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    7. Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
    8. Mauro Pontani, 2021. "Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 545-574, December.
    9. Calvin Kielas-Jensen & Venanzio Cichella & David Casbeer & Satyanarayana Gupta Manyam & Isaac Weintraub, 2021. "Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 899-916, December.

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