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Over the last
decades, there has been a growing interest in algorithms inspired by the
observation of natural phenomena. It has been shown by many researches that
these algorithms are good replacements as tools to solve complex computational
problems. Various heuristic approaches have been adopted by researches
including genetic algorithm (Holland 1975), simulated annealing (Kirkpatrick et
al. 1983), immune system (Farmer et al. 1986), ant system (Dorigo et al. 1996)
and particle swarm optimization (Kennedy and Eberhart 1995; Kennedy and
Eberhart 1997). Unfortunately, there is no algorithm to achieve the best
solution for all optimization problems, and some algorithms give a better
solution for some problems than the others (Wolpert and Macready 1997;
Engelbrecht et al. 2005; Cheng et al. 2007; Elbetagi at al. 2005; Youssef et
al. 2001). Gravitational Search Algorithm (GSA) is one of the latest heuristic
optimization algorithms, which was first introduced by Rashedi et al. (2009) based
on the metaphor of gravitational interaction between masses. GSA is inspired by
the Newton theory that says: “Every particle in the universe attracts
every other particle with a force that is directly proportional to the product
of their masses and inversely proportional to the square of the distance
between them”. Gravity is a force, pulling together all matter. The
original version of GSA was designed for search spaces of real valued vectors.
However, many optimization problems are set in binary discrete space. In this
article, a version of the algorithm for binary encoding is introduced. In the
previous version of GSA, the algorithmic “gravitational forces” lead
directly to changes in the position of search points in a many-dimensional continuous
space (the search space). In the binary version of GSA (BGSA), the outcome of
these forces is converted into a probability value for each element of the
binary vector, which guides whether that elements will take on the value 0 or
1.

This paper is
organized as follows. Section 2 provides a brief Eplanation of GSA. In section
3, we introduce  aspects of binary version
of GSA. An experimental research  is
given in section 4, where the high performance of the algorithm will be
evaluated on nonlinear benchmark functions. Finally in section 5, a conclusion
is given.

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