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

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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.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, 306 Talbot Laboratory, University of Illinois, Urbana, IL, 61820, USA

    Bruce A. Conway

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  1. Bruce A. Conway
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Correspondence to Bruce A. Conway.

Additional information

The example of homotopy shown in Fig. 4 is due to my graduate research assistant (now Ph.D. recipient) Christopher Martin.

The Lyapunov orbit generation example of Sect. 6.1 is due to my post-doctoral researcher Mauro Pontani.

The B727 min-time to climb and the robot arm repositioning example of Sect. 6.2 are due to my graduate research assistant (and Ph.D. candidate) Pradipto Ghosh.

The motorized travelling salesman example of Sect. 6.2 is due to my graduate research assistant (now Ph.D. recipient) Christian Chilan.

The homicidal chauffeur example of Sect. 6.3 is due to my graduate research assistant (now Ph.D. recipient) Kazuhiro Horie.

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Conway, B.A. A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems. J Optim Theory Appl 152, 271–306 (2012). https://doi.org/10.1007/s10957-011-9918-z

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