# Revised Gravitational Search Algorithms Based on Evolutionary-Fuzzy Systems
###### Abstract  
The choice of the best optimization algorithm is a hard issue, and it sometime depends on specific problem. The Gravitational Search Algorithm (GSA) is a search algorithm based on the law of gravity, which states that each particle attracts every other particle with a force called gravitational force. Some revised versions of GSA have been proposed by using intelligent techniques. This work proposes some GSA versions based on fuzzy techniques powered by evolutionary methods, such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE), to improve GSA. The designed algorithms tune a suitable parameter of GSA through a fuzzy controller whose membership functions are optimized by GA, PSO and DE. The results show that Fuzzy Gravitational Search Algorithm (FGSA) optimized by DE is optimal for unimodal functions, whereas FGSA optimized through GA is good for multimodal functions.  
gravitational search algorithm; fuzzy systems; evolutionary algorithm 1  
[PERSON], [PERSON], [PERSON], [PERSON], L.  
Improvements of the original version of GSA have been achieved by using the binary discrete space. In fact, there are many optimization problems [13; 29; 30; 31; 32; 33; 34], where the solutions are encoded as binary vectors. [PERSON] et al. [35] proposed a binary version of GSA, called BGSA. This work shows the efficiency of BGSA in solving various nonlinear benchmark functions.  
This paper aims to improve GSA for certain benchmark functions. The task is to design a fuzzy system able to tune suitable parameters of GSA, taking into account the exploration, the exploitation capabilities and escaping being trapped in local optima. The novelty of the proposed approach is the choice of adjusting, in a fuzzy way, a specific GSA parameter, which may be used both as fuzzy input and output. The fuzzy input is the parameter value in the previous state, whereas the fuzzy output is the GSA parameter value in the current state. In this way, the GSA parameter is tuned depending on the parameter value in the previous state and the remaining fuzzy inputs. Moreover, to assure an intelligent strategy for exploration and exploitation, the fuzzy rules are designed to prevent problems of getting trapped into local optima and premature convergence. The main idea is to design a Fuzzy Gravitational Search Algorithm (FGSA) where the membership functions of the fuzzy controller are optimized by applying evolutionary algorithms such as GA, PSO and DE. The complexity problem is avoided because the fuzzy controller is optimized just one time and than used in GSA. Therefore, FGSA contains the contribution of the optimized fuzzy controller, which does not add considerable complexity with respect to GSA. Finally, the challenge of this work is to improve the average best so far solution of [22; 26; 27; 28; 35] for certain benchmark functions.  
The paper is organized as follows. Section 2 describes GSA with the same notation of [22]. The revised GSA optimized through intelligent techniques is described in Section 3. Section 4 contains the discussion of the simulation results of the proposed algorithms. Section 5 concludes the paper.