## 5 Results and Discussions
### Compared Algorithms and Parametric Setup  
The performance of the suggested modification of the COBRA algorithm (which will be called COBRA-SHA hereinafter) was compared with other state-of-the-art algorithms like PSO [7], WPS [26], FFA [23], CSA [22], BA [24] and FSS [25]. These algorithms have several parameters that should be initialized before running. The optimal control parameters usually depend on problems and they are unknown without prior knowledge. Therefore, the initial values of the necessary parameters for all algorithms were taken from original papers dedicated to them and proposed by authors. Furthermore, the proposed approach was compared with modifications of the FFA, CSA and BA algorithms, which also use the external archives, as it was established previously that their usage improves the workability of the listed heuristics [48]. Let us denote them as FFA-a, CSA-a and BA-a, respectively. To show the advantage of the proposed modification more clearly, it was also compared with the fuzzy-controlled COBRA-f [29] and also with a similar modification of the COBRA meta-heuristic, in which unlike COBRA-SHA, each component algorithm can use only its own external archive (this modification was named COBRA-fas) [53]. Parameters of the fuzzy controllers for the COBRA-fas and COBRA-SHA approaches were found by PSO in the same way as for the COBRA-f algorithm [10], namely the following parameters were obtained: \([-3;-2;0;10]\), \([-3;-2;5;10]\) and \([-12;-2;0;19]\) respectively. Thus, the fuzzy sets for the outputs of the obtained controllers can be represented by Figure 1.  
For all mentioned biology-inspired component algorithms, the initial population size was equal to 100 on each of 23 benchmark functions from SET-1 for comparison, while the maximum number of iterations was equal to 1000. Thus, to check the efficiency of the proposed algorithm COBRA-SHA, the maximum number of function evaluations was set to \(100,000\). The same number of function evaluations was used for the fuzzy-controlled COBRA-f and modification COBRA-fas. There were also 30 program runs of all algorithms, included in the comparison, for benchmark problems from SET-1. While solving optimization problems from SET-2, the maximum generation number was 5000 and the population size for each component algorithm as well as for the FFA-a, CSA-a and BA-a modifications was equal to 100. Therefore, the maximum number of function evaluations for the COBRA-f, COBRA-fas and COBRA-SHA algorithms was set to \(500,000\). It should be noted that the number of programs runs of all algorithms for benchmark problems from SET-2 was the same as for the problems from SET-1. Finally, 16 test functions taken from the CEC 2014 Special Session on Real-Parameter Optimization [51] were solved 51 times by all mentioned heuristics. All these functions are minimization problems; they are all also shifted and scaled. The same search ranges were defined for all of them: \([-100,100]^{D}\), where \(D=30\) is the number of dimensions. For all algorithms included in the comparison, the maximum number of function evaluations was equal to \(300,000\). The population size for component algorithms and their modifications was set to 100. During the experiments, the maximum archive size \(A_{s}\) for each component of the COBRA-fas and COBRA-SHA meta-heuristics as well as for the FFA-a, CSA-a and BA-a algorithms was equal to 50. In addition, previously conducted experiments showed that the probability of using the external archive should have the following values for FFA-a, CSA-a and BA-a: 0.75, 0.6 and 0.15 respectively [49]. The same probabilities were used for the respective components of the COBRA-fas and COBRA-SHA approaches. For the rest of their component algorithms, the probability of using the external archive was set to 0 (the archive was not used specifically during the execution of a given component algorithm but was updated if conditions applied).