# An Improved Novel Global Harmony Search Algorithm Based on Selective Acceptance
## 1 Introduction  
In the past two decades, the interest in the research related to metaheuristic algorithms has increased significantly due to the fact that existing numerical methods do not allow for solving a number of complex optimization problems, such as discrete structural optimization [1], design of water distribution networks [2], and vehicle routing [3]. A metaheuristic algorithm is applied to simulate the randomness and rules in natural phenomena. For example, the genetic algorithm (GA) [4] imitates the process of the biological evolutionary and natural selection. The particle swarm optimization (PSO) [5] was inspired by the animal behavior, namely, the foraging behavior of bird flocking. In addition, there are many algorithms extending PSO and GA, such as the harmony search (HS) algorithm [6] and the honey bee mating optimization (HBMO) [7]. These algorithms have proved their ability to search for better solutions than numerical methods in extensive optimization problems [8; 9; 10]. However, compared with theses algorithms, the HS algorithm which imitates an improvisation process of a harmony has two features. Firstly, it has fewer mathematical requirements and is easy to implement. Secondly, each decision variable in a new solution vector could be generated independently by considering all of the existing solution vectors [11]. Due to these two features, the HS algorithm has stronger adaptability for many engineering problems and could generate competition results compared with the GA [11]. In addition, based on the above advantages, many modified versions of the HS algorithm are proposed to further improve the searching ability of the HS algorithm, such as the improved harmony search (IHS) algorithm [11], the self-adaptive global best harmony search (SGHS) algorithm [12], and the novel global harmony search (NGHS) algorithm [13]. These modified versions of the HS algorithm have better search ability than the original HS algorithm. It is worth noting that, among these HS algorithms, the mechanism that is used to decide whether a new generated harmony (solution vector) is accepted and replaces the worst harmony in the harmony memory (HM) or not is different. The HM is a storage of the harmony. Specifically, the HS, IHS, and SGHS algorithms accept a new generated harmony only when it is better than the worst harmony in the current HM. This mechanism, we call it accept-the-better-only mechanism, reminded us of the tabu search (TS) algorithm [14] which also only accepts the better solution vector in the searching process. Conversely, in the NGHS algorithm, a new generated harmony is accepted and replaced the worst harmony in the HM without preconditions in each iteration. This mechanism, we call it accept-everything mechanism, is the same one used in the PSO and GA. In the PSO algorithm, in each iteration, after calculating the velocity of the particle, the particle will fly to the new position according to its velocity whether the fitness of the new position is better than the current position or not. However, while we were discussing these two acceptance mechanisms, we suddenly came up with an old algorithm, the simulated annealing (SA) algorithm [15]. In the SA algorithm, in each iteration, the new solution vector is accepted or not according to the acceptable probability (AP), which is calculated by the Boltzmann distribution. Thus, the SA algorithm inspired us to investigate whether the AP affects the search ability or not in the NGHS algorithm. Therefore, in this paper, we proposed the selective acceptance novel global harmony search (SAGHS) algorithm, which combined the selective acceptance mechanism with the NGHS algorithm. Moreover, we proposed a proportion formula to calculate the AP according to the convergence degree. To verify the searching performance of the SANGHS algorithm, we used the SANGHS algorithms in ten well-known optimization problems and two engineering problems and compared the experimental results with other 15 algorithms.