## 4 MAKHA Hybrid Algorithm  
MAKHA is a new hybrid algorithm, which combines some of the mechanisms and processes of MA and KHA to get a reliable algorithm with appreciated performance. The steps of both algorithms include exploration/diversification and exploitation/intensification features as follows. The exploration/diversification features of MA are the somersault process and the watch-jump process, while for KHA, they are the physical random diffusion and the genetic operators. On the other hand, the exploitation/intensification features of MA are the climb and the watch-jump process, while for KHA, they are the induced motion and the foraging activity. Both algorithms attempt to balance between exploration/diversification and exploitation/ intensification features. MA has two exploration operators and two exploitation operators. The watch-jump process acts as both an exploration and an exploitation operator. The somersault operator is a high-performing diversification operator that makes a good use of the pivot function. Since MA is an exploration-dominant algorithm, the exploitation balance is brought to the algorithm by running the climb process twice per iteration. In each process, the MA algorithm uses a large number of cycles that reaches up to 2000 cycles in some problems. Increasing the number of cycles reduces the computational efficiency because it increases the number of function evaluations (NFE). Even though KHA also has two exploration operators and two exploitation operators, its exploration component is not dominating because the physical random diffusion is a less efficient exploration operator than the somersault operator. Thus, the entrapment in local minima is more probable in KHA than in MA. The trapping problem can be addressed in the KHA by the use of two genetic operators (crossover and mutation), which appear in KHA IV algorithm. Since the foraging movement is a high-performing exploitation operator, KHA could be considered an exploitation-dominant algorithm. An equal number of exploration and exploitation operators does not necessitate a balance between exploration and exploitation. The performance of operator is a critical factor. Assessing the performance of an operator can be done by replacing the exploration or exploitation operator in one algorithm with the same type of operator in the other algorithm. Testing the modified algorithms with benchmark problems can reveal whether or not the replaced operator was performing its function efficiently relative to the other operator. To improve the performance of the algorithm such that the modified algorithm outperforms the two original algorithms, we aimed at using the best performing exploration and exploitation operators from the two algorithms. The hybrid algorithm, MAKHA, was constructed from the following processes:  
1. The watch-jump process. 2. The foraging activity process. 3. The physical random diffusion process. 4. The genetic mutation and crossover process. 5. The somersault process. The climb process, which consumes a high NFE, was not included in the hybrid algorithm. The random diffusion step was included in only one of MAKHA's variant as explained below. MAKHA was implemented in two different ways: MAKHA I, which does not use random diffusion; and MAKHA II, which uses the random diffusion step. It was found, as shown in the ResultsSection, that MAKHA I was more suitable for low-dimensional problems, while MAKHA II was better for the high-dimensional problems (NV = 50). Figure 3: The pseudo-code of hybrid MAKHA. The general pseudo-code for this algorithm is shown in Figure 3, while the equations used are as follows:  
* _Initialization procedure:_
* Random generation of population in which the positions of the hybrid agent (monkey/krrill) are created randomly, \(X_{i}=\left(X_{i1},\,X_{i2},\,...,\,X_{i(N)j}\right)\) where \(i=1\) to \(NP\), which represents the number of hybrids, while \(NV\) represents the dimension of the decision variable vector.