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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)271-306
Number of pages36
JournalJournal of Optimization Theory and Applications
Issue number2
StatePublished - Feb 2012


  • Dynamical system
  • Evolutionary optimization
  • Numerical optimization
  • Optimization

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems'. Together they form a unique fingerprint.

Cite this