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.