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ef
ciency of the hybrid of particle swarm optimization and genetic algorithm
optimization with regard to addressing both single-objective and multi-objective
optimization problems.
Keywords Particle swarm optimization
Genetic algorithm optimization
Single-
objective problems
Multi-objective problems
State feedback control
Parallel-
double-inverted pendulum system
1 Introduction
Optimization is the selection of the best element from some sets of variables with a
long history dating back to the years when Euclid conducted research to gain the
minimum distance between a point and a line. Today, optimization has an extensive
application in different branches of science, e.g. aerodynamics (Song et al.
2012
),
robotics (Li et al.
2013
; Cordella et al.
2012
), energy consumption (Wang et al.
2014
), supply chain modeling (Yang et al.
2014
; Castillo-Villar et al.
2014
) and
control (Mahmoodabadi et al.
2014a
; Wang and Liu
2012
; Wibowo and Jeong
2013
). Due to the necessity of addressing a variety of constrained and uncon-
strained optimization problems, many changes and novelties in optimization
approaches and techniques have been proposed during the recent decade. In gen-
eral, optimization algorithms are divided into two main classi
cations: deterministic
and stochastic algorithms (Blake
1989
). Due to employing the methods of suc-
cessive search based upon the derivative of objective functions, deterministic
optimization algorithms are appropriate for convex, continuous and differentiable
objective functions. On the other hand, stochastic optimization techniques are
applicable to address most of real optimization problems, which are heavily non-
linear, complex and non-differentiable. In this regard, a great number of studies
have recently been devoted to stochastic optimization algorithms, especially,
genetic algorithm optimization and particle swarm optimization.
The genetic algorithm, which is a subclass of evolutionary algorithms, is an
optimization technique inspired by natural evolution, that is, mutation, inheritance,
selection and crossover to gain optimal solutions. Lately, it was enhanced by using
a novel multi-parent crossover and a diversity operator instead of mutation in order
to gain quick convergence (Elsayed et al.
2014
), utilizing it in conjunction with
several features selection techniques,
involving principle components analysis,
sequential
floating, and correlation-based feature selection (Aziz et al.
2013
), using
the controlled elitism and dynamic crowding distance to present a general algorithm
for the multi-objective optimization of wind turbines (Wang et al.
2011
), and
utilizing a real encoded crossover and mutation operator to gain the near global
optimal solution of multimodal nonlinear optimization problems (Thakur
2014
).
Particle swarm optimization is a population-based optimization algorithm mim-
icking the behavior of social species such as
fl
fl
flocking birds, swimming wasps,
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