# Large-Scale Truss-Sizing Optimization with Enhanced Hybrid HS Algorithm
## 1 Introduction
The most common goal in structural optimization is to minimize the weight of the structure in the presence of limitations on deformations, stresses, critical loads, natural frequencies, etc. However, other objectives can be considered such as, for example, to minimize stresses or maximize stiffness. Structural optimization problems may be of three types: (i) sizing optimization where design variables correspond to geometric dimensions such as, for example, the cross-sectional areas of the elements forming the structure; (ii) shape optimization where design variables define the profile of the structure (e.g., coordinates of nodes); (iii) topology optimization where design variables define the distribution of the material in the structure. The easiness of implementation of HS soon attracted many structural optimization experts that developed several variants of the algorithm after the pioneering studies by [PERSON] and [PERSON] [31; 32]. In particular, researchers attempted to (i) minimize the sensitivity of convergence behavior to the setting of _HMCR_, _PAR_ and _bw_ parameters; (ii) reduce the number of structural analyses and speed up the search process by removing trial solutions yielding no improvements in design. These abilities turn very useful, especially in the optimization of large-scale structures. For example, [PERSON] [33] used an adaptive error strategy to handle slightly infeasible designs. [PERSON] and [PERSON] [34] considered designs deemed worse than the worst design stored in [HM], yet distant from local optima. [PERSON] and [PERSON] [35] generated random trial solutions within intelligently specified search neighborhoods. [PERSON] et al. [36] dynamically updated the _PAR_ and _bw_ parameters in the search process, while [PERSON] and [PERSON] [37] used another dynamic scheme for updating the _HMCR_ and _PAR_ parameters. [PERSON] et al. [38] probabilistically selected HS parametersto the adapt search to varying features of design space. A self-adaptive HS algorithm also implemented by [PERSON] [39]. [PERSON] and [PERSON] [40] developed a multi-adaptive HS variant updating internal parameters linearly or exponentially. [PERSON] and [PERSON] [41] developed a parameter-setting-free technique selecting specific operators for each variable stored in [HM]. [PERSON] and [PERSON] [42] developed a multi-population approach where each sub-population operates on a different region of search space. Finally, HS was hybridized with other metaheuristic methods [43; 44; 45; 46; 47; 48], gradient-based optimizers [49] and approximate line search strategies exploiting explicitly available gradient information [50; 51; 52]. In a very recent study, [PERSON] et al. [53] synthesized all approaches mentioned above by combining the HS metaheuristic engine with search direction mechanisms, gradient information-based search, and 1-D simulated annealing search. While the different studies published in the literature considered structures of increasing complexity over the years, it has to be noted that only Ref. [51] directly deals with large-scale structural optimization problems, including more than 250 sizing variables. The JAYA algorithm was developed by [PERSON] [12] in 2016. This population-based method relies on the simplest search strategy ever implemented in metaheuristic optimization: trial solutions are generated, always moving towards the best design and away from the worst design of the population. Remarkably, JAYA needs only two standard control parameters, such as population size and limit number of iterations. The very simple formulation and inherently efficient search strategy explain why JAYA is probably the most exploited metaheuristic algorithm in the last few years. However, while JAYA often achieves a high success rate in finding the global optimum regardless of population size and initial solutions, the number of required analyses is not always significantly lower than those reported for the other state-of-the-art metaheuristic methods (see, for example, Ref. [53]). In this regard, [PERSON] et al.