چكيده
Optimal control problems, due to nonlinear behaviors, complex constraints, and the presence of multiple local optima, are regarded as one of the most important topics in optimization
theory. This dissertation aims to improve numerical accuracy and computational
efficiency in solving such problems by proposing a numerical framework based on chaotic
behavior and evolutionary algorithms. In the first stage of this research, after applying direct
discretization to optimal control problems and transforming them into a nonlinear programming
formulation, four chaotic strategies are designed and evaluated, including Logisticbased
Global Chaotic Search (L-GCS), Logistic-based Local Chaotic Search (L-LCS), Hybrid
Chaotic Gradient Search (HCGS), and Modified Chaotic Gradient Optimization (MCGO).
Numerical results obtained from a set of benchmark problems show that incorporating the
logistic map alongside gradient-based search improves computational accuracy and optimizes
convergence behavior.
In the continuation of this research, a hybrid approach based on Particle Swarm Optimization
with chaotic initialization is developed. This mechanism not only provides adequate
diversity in the search space but also significantly reduces the probability of premature convergence.
Comparative results and statistical analyses using Friedman and Dunn–Holm tests
demonstrate that the proposed hybrid algorithm achieves statistically significant superiority
over the standard Particle Swarm Optimization algorithm and other gradient-based solution
methods in terms of accuracy, numerical stability, and convergence speed.
Overall, the numerical results presented in this dissertation indicate that combining
chaotic behavior with metaheuristic algorithms enhances the numerical solution performance
of nonlinear optimal control problems with respect to accuracy, stability, and convergence.
