# A Novel Optimization Algorithm Combing
## 4 Experiments
### Discussion  
It can be observed from the trends of Figure 3 that the convergence rate of the GABCG algorithm is similar to the GABC algorithm in the first few steps but is slightly faster in the subsequent steps. In the early stages of the search, the sample points are not fully distributed throughout the search space, so the exploration of algorithm is more important than the exploitation, and thus the effect of gradient acceleration in the new algorithm is small and the convergence rate of the new algorithm is not better than that of the GABC algorithm. It should be noted that the gradient calculation increases the computation amount of the program. However, in our new algorithm, only gradients of current global best solutions and abandoned solutions are necessary, so it does not have a significant impact on the computational complexity of the whole algorithm. The advantage of gradient acceleration is not obvious in the early stage of random search. In order to further reduce computational costs, we recommend not changing the original algorithm in some steps at the beginning of the process.  
From [PERSON] and [PERSON]'s study [PERSON] and [PERSON] (2018), it can be concluded that driving the new candidate solution toward the global best solution can increase the exploitation of the ABC algorithm. In this research, since the gradient information not only provides a more accurate estimate of the global best solution for the GABC algorithm but also makes the sample screening more efficient, the exploitation is further enhanced. The findings of this paper can also apply to other GABC-based algorithms, such as SABC-GB [PERSON] and [PERSON] (2018), GABCS [PERSON] and [PERSON] (2018), MPGABC (a new GABC variant combing the novel search strategy with probability model) [PERSON] and [PERSON] (2018), WGABC (a linear weighted GABC algorithm) [PERSON] and [PERSON] (2018), and gdbABC (an improved GABC algorithm with gradient-based information) [PERSON] and [PERSON] (2018). It is interesting that gdbABC controls the direction of search movement by a Newton-Raphson formula with the gradient information. To avoid premature convergence, it uses a distribution-based strategy in case of several local suboptimal solutions. From [PERSON]'s research [PERSON] and [PERSON] (2018), it can be found that gdbABC does not perform well for the optimizations of Rosenbrock and Griewank functions. Therefore, in order to enhance the applicability of the gradient-based algorithm, it is necessary to balance exploitation and exploration.  
In addition to gdbABC [PERSON] and [PERSON] (2018), ABC-SQP [PERSON] and [PERSON] (2018) and GdABC [PERSON] and [PERSON] (2018) also apply gradient information to [PERSON]'s method. As a result of searching along the gradient direction, they bring the results of new candidate solutions closer to the optimal value. However, since [PERSON]'s method cannot skip the local optimum [PERSON] and [PERSON] (2018), these gradient-based algorithms may perform poorly on complex multimodal problems. The GABCG algorithm do not change the original search strategy completely but estimate the global best solution more accurately and enhance the abandoned judgement with the gradient information. Therefore, our improvements are a constraint optimization for the original algorithm, while improving its convergence without losing its applicability. Inspired by this thought, our future work ought to focus on optimizing other efficient and adaptable algorithms with gradient information.