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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 139036, 21 pages
Research Article

A Modified Hybrid Genetic Algorithm for Solving Nonlinear Optimal Control Problems

1Department of Applied Mathematics, Payame Noor University, Tehran 193953697, Iran
2Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad 9177948953, Iran

Received 4 September 2014; Accepted 30 January 2015

Academic Editor: Alain Vande Wouwer

Copyright © 2015 Saeed Nezhadhosein et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Here, a two-phase algorithm is proposed for solving bounded continuous-time nonlinear optimal control problems (NOCP). In each phase of the algorithm, a modified hybrid genetic algorithm (MHGA) is applied, which performs a local search on offsprings. In first phase, a random initial population of control input values in time nodes is constructed. Next, MHGA starts with this population. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by Linear interpolation (LI) or Spline interpolation (SI), using the curves obtained from the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA restarts with the new population constructed by above procedure and tries to improve the obtained solutions at the end of phase 1. We implement our proposed algorithm on 20 well-known benchmark and real world problems; then the results are compared with some recently proposed algorithms. Moreover, two statistical approaches are considered for the comparison of the LI and SI methods and investigation of sensitivity analysis for the MHGA parameters.