Information Technology Reference
In-Depth Information
0.3
Point A
Point B
Point C
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
1
2
3
4
5
6
7
8
9
10
Time (s)
Fig. 24 The position of the cart of the system of the parallel-double-inverted pendulum for design
points of the Pareto front of multi-objective hybrid of particle swarm optimization and the genetic
algorithm
8 Conclusions
In this work, a hybrid algorithm using GA operators and PSO formula was pre-
sented via using effectual operators, for example, traditional and multiple-crossover,
mutation and PSO formula. The traditional and multiple-crossover probabilities
were based upon fuzzy relations. Five prominent multi-objective test functions and
nine single-objective test functions were used to evaluate the capabilities of the
hybrid algorithm. Contrasting the results of the hybrid algorithm with other algo-
rithms demonstrates the superiority of the hybrid algorithm with regard to single
and multi-objective optimization problems. Moreover, the hybrid optimization
algorithm was used to obtain the Pareto front of non-commensurable objective
functions in designing parameters of linear state feedback control for a parallel-
double-inverted pendulum system. The con
icting objective functions of this
problem were the sum of settling time and overshoot of the cart and the sum of
settling time and overshoot of the
fl
first and second pendulums. The hybrid algorithm
could design the parameters of the controller appropriately in order to minimize
both objective functions simultaneously.
Acknowledgments The authors would like to thank the anonymous reviewers for their valuable
suggestions that enhance the technical and scienti
c quality of this paper.
Search WWH ::
Custom Search