# A Novel Optimization Algorithm Combing
## 1 Introduction  
As computer technology gains momentum, more and more researchers develop and apply optimization algorithms to solve optimization problems. These algorithms can be broadly divided into gradient-based and gradient-free (or stochastic) optimization algorithms. Gradient-based optimization algorithms search along the gradient direction. They are of high convergence rate and are particularly suitable for solving problems with large design space [1]. However, their optimization results are close to the extreme point near the point of the initial parameter, rather than the maximum point of the entire design space [2]. On the contrary, gradient-free optimization algorithms are robust and quite effective for solving multi-modal optimization problems [3]. Such algorithms can be easily integrated into different optimization designs, but they are computationally expensive, especially in cases of numerous design parameters [4]. Due to the feature of their random search, these stochastic algorithms tend to converge slowly [5], especially near the area of global optimum. Therefore, it is significant to improve the convergence of stochastic algorithms through some modifications. First proposed by [PERSON] [6], the artificial bee colony (ABC) algorithm is a gradient-free optimization algorithm that is widely used in multi-variable and multi-objective optimizations [7]. [PERSON]'s further research [8; 9] shows that the ABC algorithm outperforms other stochastic algorithms, such as the genetic algorithm (GA), particle swarm algorithm (PSO), and particle swarm inspired evolutionary algorithm (PS-EA). However, the ABC algorithm is good at exploration but poor atexploitation [10]. Integrating gradient-based searching method into evolution algorithms may improve exploitation [11; 12; 13; 14]. In recent years, some novel algorithms based on gradient information have been brought forward to modify the ABC algorithm. For example, a hybrid algorithm called ABC-SQP was developed by [PERSON] [15]. It combines the artificial bee colony algorithm with sequential quadratic programming. Another algorithm, the gradient-based artificial bee colony algorithm (GdABC), was brought forward by [PERSON] et al. [16] to improve the local search ability. Both ABC-SQP and GdABC use the global exploration capability of the ABC algorithm and the exploitation capability of gradient-based local search algorithm. However, in these hybrid algorithms, the search equation of the original program is not modified, and the procedures of the random searching algorithm and the gradient-based local search algorithm are independent of each other. Thus, the program parts of a gradient optimization still tend to fall into the local optimum. Other researchers have improved the search strategy of ABC algorithm by modifying the search equation according to the information of best solutions [17; 18; 19; 20]. For example, [PERSON] and [PERSON] [21] found that the global best solution could help improve exploitation. They proposed the Gbest-guided artificial bee colony search (GABC) algorithm. Due to the great advantage of the convergence property of GABC, many GABC-based algorithms have been developed [22; 23; 24; 25; 26; 27]. For example, [PERSON] et al. [22] incorporated the information of current iteration best solution into solution search equation and introduced global artificial bee colony search algorithm (GABCS). In the original GABC algorithm, the convergence performance is improved by adding a coefficient factor to the solution search equation. However, the selection of the coefficient factor is just based on testing. In the study of [PERSON] and [PERSON], the best value of the coefficient factor they chose is not suitable for all problems. Therefore, the theoretical analysis and the conclusion of the GABC algorithm are inadequate. It is necessary to make up for this weakness. We present an idea of establishing a new solution search equation leaving out the coefficient factor and introducing variable gradients.