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perform better than RPSO in high dimensional dynamic environments by restricting
the information sharing and preventing the convergence of particles to the global best
position, thereby enhancing population diversity. Janson and Middendorf [7]
proposed hierarchical PSO (HPSO), a tree-like structure hierarchical PSO, and
reported improvements over standard PSO for dynamic environments. They also
suggested Partitioned Hierarchical PSO in which a hierarchy of particles is partitioned
into several sub-swarms for a limited number of generations after a change in the
environment is detected [8]. Lung and Dumitresc [19] used two collaborating
populations with same size which one swarm is responsible for preserving the
diversity of the particles by using a crowding differential evolutionary algorithm [20]
while the other keeps track of global optimum with a PSO algorithm.
Li and Yang proposed a FMSO method which maintains the diversity through the
run [16]. To meet this goal two types of swarm are used: a parent swarm which
maintains the diversity and detects the promising search area in the whole search
space using a fast evolutionary programming algorithm, and a group of child swarms
which explore the local area for the local optima found by the parent using a fast PSO
algorithm. This mechanism makes the child swarms spread out over the highest
multiple peaks, as many as possible, and guarantees to converge to a local optimum in
a short time. Moreover, in [15], the authors introduced a clustering particle swarm
optimizer in which a clustering algorithm partitions the swarm into several sub-
swarms each searching for a local optimum.
Liu et al. [17] introduced compound particle swarm optimization (CPSO) utilizing
a new type of particles which helps explore the search space more comprehensively
after a change occurred in the environment. In another work, they used composite
particles which help quickly find the promising optima in the search space while
maintaining the diversity by a scattering operator [18].
Hashemi and Meybodi introduced cellular PSO, a hybrid model of cellular
automata and PSO [6]. In cellular PSO, a cellular automaton partitions the search
space into cells. At any time, in some cells of the cellular automaton a group of
particles search for a local optimum using their best personal experiences and the best
solution found in their neighborhood cells. To prevent losing the diversity, a limit on
the number of particles in each cell is imposed. Furthermore, to track the changes in
the environment, in [6] particles in cellular PSO change their role to quantum
particles and perform a random search around the previously found optima for a few
iterations after a change is detected in the environment.
Kamosi et al. propose some variations of PSO that can perform well for dynamic
environments [9]. In their work, they proposed a multi-swarm algorithm for dynamic
environments which address the diversity loss problem by introducing two types of
swarm: a parent swarm, which explores the search space to find promising area
containing local optima and several non-overlapping child swarms, each of which is
responsible for exploiting a promising area found by the parent swarm.
2 Related Work
A learning automaton (LA) is an adaptive decision-making unit that is situated in a
random environment and learns the optimal state-action set through many repeated
interactions with its environment. The actions are chosen according to a specific
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