## 3 The Optimization Algorithm Used in the Identification Process
### Summary of HS-JAYA Algorithm and Discussion on Local Search Schemes in Metaheuristic Optimization  
The main features of HS-JAYA may be summarized as follows. All stages of the proposed algorithm aim to reduce the FE analyses of the identification process. For that purpose, material/structural parameters to be identified are always perturbed by moving along descent directions that can minimize the error functional \(\Omega\) stated in the inverse problem. Candidate solutions are directly generated in the HS phase by using gradient information or approximate line search (also including mirroring), and then corrected/refined by JA-based operators that push optimization search towards the best solution of the population or the best design within a local neighborhood of the currently analyzed trial solution. Gradient information is obtained at low computational cost by properly combining the directions of (i) the largest variation of \(\Omega\), (ii) the second largest variation of \(\Omega\), and (iii) the fastest reduction of \(\Omega\). The elitist mechanisms implemented in HS-JAYA allow the number of analyses per optimization cycle to be significantly reduced with respect to the typically required N\({}_{\text{POP}}\) analyses by the most common implementations of HS and JAYA. Exploration and exploitation mechanisms are continuously alternated in HS-JAYA's metaheuristic search process and integrated by the optimizer even at the single variable level when a new trial design has to be generated. Furthermore, HS-JAYA is a parameter-free algorithm as it requires only population size to be specified by the user. Typical parameters defined in HS, such as pitch adjusting rate, harmony memory considering rate and bandwidth, become unnecessary or they are adaptively changed in HS-JAYA based on the trend of optimization history. Finally, HS-JAYA has a robust convergence criterion that avoids premature termination of the optimization process and convergence to false optima. The HS-JAYA formulation significantly enhances the LSSO-HHSJA algorithm [54] previously applied to sizing optimization of truss structures. However, while for LSSO-HHSJA, the cost function gradients were explicitly available and constant over the whole design space, HS-JAYA has to deal with an implicit cost function, the error functional \(\Omega\) of the identification problem. Renewal of suboptimal designs of population (this task entails the use of JAYA operators) cannot be performed by simply evaluating a cost function defined explicitly as it occurred for LSSO-HHSJA because evaluating the error functional for a new trial design always entails finite element analysis. An interesting issue is how the formulation of HS-JAYA relates to the local search schemes usually adopted in metaheuristic optimization. The concept of \"global\" and \"local\" search depends on the algorithm's nature. Metaheuristic optimizers very often work with a population of candidate solutions, and global search means to explore the whole design space by considering a large number of candidate solutions or assigning large perturbations to optimization variables. However, for single-point algorithms such as simulated annealing, global search means simultaneous perturbation of all optimization variables while local search perturbs variables one by one. A common approach in metaheuristic optimization is to use hybrid algorithms where a metaheuristic search engine globally explores the design space and identifies a set of  
Figure 6: Flow chart of the HS-JAYA algorithm developed in this study. designs later refined by local search. The local search process may employ gradient-based optimizers or specific operators taken from other metaheuristic algorithms. The former approach was utilized by [PERSON] et al. [55], who selected HS as main search engine and sequential quadratic programming (SQP) to perform local search in the neighborhood of the best designs included in the harmony memory.