## 1 Introduction  
The use of stochastic global optimization methods has gained popularity in a wide variety of scientific and engineering applications as those methods have some advantages over deterministic optimization methods [1]. Those advantages include the lack of the need for a good initial guess and the ability to handle multi-modal and non-convex objective functions without the assumptions of continuity and differentiability. Several stochastic methods have been proposed and investigated in challenging optimization problems using continuous variables. Such methods include simulated annealing, genetic algorithms, differential evolution, particle swarm optimization, harmony search, and ant colony optimization. In general, these methods may show different numerical performances and, consequently, the search for more effective and reliable stochastic global optimization methods is currently an active area of research. In particular, the Monkey Algorithm (MA) [2] and the Krill-Herd Algorithm (KHA) [3] are two new, nature-inspired stochastic optimization method that are gaining popularity in finding the global minimum of diverse science and engineering application problems. For example, MA and its variants were recently used for the power system optimization [4], the coordinated control of low frequency oscillation [5], and for finding optimal sensor placement in structural health monitoring [6; 7; 8]. KHA is a new method and has been used in network route optimization [9] and economic load dispatch [10]. Since the development of those two algorithms, some modifications have been proposed to improve their performance. The modifications often involved variations of the search rules or hybridization with other algorithms. For example, chaotic search methods were added to MA [11] and KHA [12; 13; 14] to improve their performance. MA modifications also included the use of new parameters that change their value during the optimization [11], changing the watch-jump process of MA to make use of information obtained by other monkeys [5], redesigning the MA steps to facilitate discrete optimization problems [15], and incorporating an asynchronous climb process [7]. Other KHA modifications included the addition of local Levy-flight move [16], adapting KHA to discrete optimization [9], better exchange of information between top krill during motion calculation [17], and hybridization of KHA with Harmony Search [18] and Simulated Annealing [19]. Hybridization is an enhancement in optimization algorithms in which operators from a certain algorithm are combined with other operators from another algorithm to produce more reliable and effective synergistic entity and get better results than that of the main parent algorithms. For example, SA (simulated annealing) is trajectory-based technique that is better at intensification or exploitation; it can detect the best solution with high probability in a confined search space. On the other hand, GA (Genetic algorithm) is regarded as population-based algorithm, which carrys out a diversification process and identifies promising regions of the search space [20; 21]. An integration of both algorithms generated the SA-GA hybrid, which outperformed simple GA and a Monte Carlo search in terms of reliability and efficiency of the results. The improved genetic algorithm was implemented to optimize the weight of a pressure vessel under the burst pressure constraint [22]. It was contrived to cope with the phenomena of stagnation in earlier and later stages so that the ability of GA to escape entrapment in local minimum was used and wisely associated with SA's intensification behavior. Other examples of hybrids display the enhancement in results better than their parent algorithms. Hybrid Evolutionary Firefly Algorithm (HEFA) is a combination of FA and DE (Differential evolution) in which population was initiated, fitness values were evaluated, population was sorted and then split to two halves, the fitter half follows the FA, while the worse half evolves with the DE.