# Large-Scale Truss-Sizing Optimization with Enhanced Hybrid HS Algorithm
## 5 Conclusions  
The paper presented a new hybrid metaheuristic optimization algorithm, LSSO-HHSJA, combining the harmony search optimization (HS) and JAYA methods. LSSO-HHSJA forms trial designs enhancing the HS architecture with multiple line searches based on explicitly available gradient information. These line searches are then augmented by JAYA's based operators, which finally allow to minimize the number of structural analyses required in the optimization process. All stages of LSSO-HHSJA attempt to generate trial designs lying on descent directions with respect to the best individual(s) stored in the population of the current iteration. The new algorithm developed in this study was successfully tested in three large-scale sizing optimization problems of truss structures (i.e., planar 200-bar truss, spatial 1938-bar tower, spatial 3586-bar tower) including up to 280 sizing variables and 37,374 nonlinear constraints. LSSO-HHSJA was very competitive with other HS and JAYA variants, other state-of-the art metaheuristic methods (i.e., simulated annealing, big bang-big crunch and sinusoidal differential evolution), and commercially available gradient-based optimizers (i.e., sequential quadratic programming and sequential linear programming). Remarkably, the proposed algorithm always converged to the lowest structural weight, obtained feasible designs, and required less structural analyses than other HS variants that implemented line search and/or parameter adaptation strategies.  
An interesting question that may arise looking at the formulation of LSSO-HHSJA is the following. Would it be possible to \"capture\" the effect of each strategy implemented in LSSO-HHSJA (i.e., the role played by each \"decision\" made by LSSO-HHSJA to activate one or another available option in its formulation) on final results? A careful analysis of the proposed algorithm reveals that all \"decisions\" actually are of two types: (i) to use gradient information, mirroring strategies and line searches to generate new trial designs on descent directions with respect to the current best record or currently selected individuals of population; (ii) to push the search towards the best designs currently stored in the population and at the same time escape from the worst designs. The proposed algorithm has a highly dynamic character that efficiently integrates types (i) and (ii) throughout optimization process. It can be concluded that the separating effects of each search strategy implemented in LSSO-HHSJA on the final results is definitely less important than how these strategies may concur to determine the optimal solution.  
The results of this study confirmed the utility of using trial descent directions to form new candidate solutions. This approach is more effective than simply updating the internal parameters of HS with more or less sophisticated strategies. The JAYA's rationale appears very suited for the purpose as it enhances the search of descent directions by avoiding the worst regions of design space. The generation of new trial designs hence relies only on the best quality directions without performing unnecessary analyses. Future investigations will regard discrete structural optimization problems also with non-explicitly available gradients, and other structural elements such as beams and shells.  
All authors contributed equally to all phases involved the preparation of the article. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data on numerical optimization available upon request.  
The authors declare no conflict of interest.