## 3 The Optimization Algorithm Used in the Identification Process
### Summary of HS-JAYA Algorithm and Discussion on Local Search Schemes in Metaheuristic Optimization
However, a drawback of this approach may be the computational cost of gradient-based local optimization, which should be less expensive than a metaheuristic search. In this regard, it should be noted that gradient-based algorithms require at least (NDV+1) analyses to evaluate sensitivities plus additional analyses to solve the approximate subproblem and minimize the cost function along the search direction found by solving the approximate subproblem. This cost soon becomes unaffordable if the number of optimization variables is comparable with population size. The use of specific operators from other metaheuristic methods also is well-documented in the optimization literature. For example, [PERSON] et al. [56] used GA for global search and SA for local searches in the neighborhood of best individuals stored in the population. SA inherently has hill-climbing capability, which allows local minima to be bypassed. However, the cooling schedule of SA should be carefully chosen. Memetic algorithms (MA) represent an important category of hybrid algorithms, which combine a metaheuristic technique with one or more problem-specific local searchers. For example, [PERSON] et al. [57] used a particle swarm optimization algorithm (PSO) to explore the design space, and a pattern search (PS) to perform exploitation of the best designs identified by PSO; the algorithm was successfully applied to optimize parameters of support vector machine space. More recently, [PERSON] and [PERSON] [58] developed a very efficient MA architecture for joint minimization of energy costs and scheduling in distributed computing; their MA formulation used GA for exploration, host-based hill-climbing and first-fit decreasing without placement for local search, properly selecting neighbors to limit computational effort. HS-JAYA relies on a completely different rationale with respect to the aforementioned hybrid optimization schemes [55; 56; 57; 58]. In fact, whilst those algorithms employed well-distinct methods for global search (exploitation) and local search (exploitation) and each method was utilized only for exploration or only for exploitation, the present algorithm dynamically mixes HS and JAYA operators regardless of being in the exploration or exploitation phases. Remarkably, exploration and exploitation can be mixed even in the formation of a new trial design. HS-JAYA always attempts to generate better trial designs than the current best record \(\mathbf{X}_{\text{OPT}}\). For that purpose, HS-JAYA adopts only elitist strategies such as, for example, descent directions originating from \(\mathbf{X}_{\text{OPT}}\), mirroring and elaboration of adjacent values to the optimum value of the currently perturbed variable. The basic JAYA equation is modified into several forms to permanently steer HS-JAYA's search towards the global optimum based on the specific scenario encountered in the optimization history. Consequently, HS-JAYA requires just a few analyses for improving population, while hybrid metaheuristic algorithms with local search such as those applied in [55; 56; 57; 58] may even fail to improve selected designs for the exploitation phase. Such an ability inherently allow HS-JAYA to significantly limit the total energy consumption related to computations.