# Large-Scale Truss-Sizing Optimization with Enhanced Hybrid HS Algorithm
## 1 Introduction
[54; 55; 56] developed an efficient JAYA variant for weight minimization of truss structures, trying to avoid unnecessary structural analyses that would not yield design improvements. While this enhancement made JAYA suitable also for structural optimization problems, since only one test case in [54; 55; 56] included more than 200 sizing variables, similar to HS, also JAYA's performance in large-scale structural optimization should further be investigated. The above arguments indicate that very few studies focused on the use of metaheuristic algorithms in large-scale structural optimization problems. The same conclusion can be drawn for all methods besides HS and JAYA. In order to overcome this limitation, a novel hybrid harmony search-JAYA algorithm for large-scale sizing optimization of truss structures is developed in this paper. As mentioned above, both HS and JAYA are highly attractive algorithms for the engineering community: the former has a well-established practice over 20 years while the latter has an inherently powerful search engine. Here, we try to combine these algorithms in order to solve large-scale structural optimization problems where it is essential to limit the total number of structural analyses required by the search process as each analysis is computationally expensive. The HS engine is the backbone of the newly developed algorithm, but trial designs and search directions generated in the HS phase are enhanced by the JAYA strategy. Explicit gradient information available from the formulation of the truss optimization problem are utilized to perturb design. The new algorithm developed in this study, denoted as LSSO-HHSA (i.e., Large-Scale Structural Optimization-Hybrid Harmony Search JAYA), is, in essence, an enhanced hybrid HS algorithm with multiple line searches, which uses the JAYA search strategy to minimize the number of structural analyses required in the optimization process. This makes LSSO-HHSA suitable for computationally expensive large-scale structural optimization problems, including multiple loading conditions, hundreds of variables, and thousands of nonlinear constraints on nodal displacements and element stresses. In large-scale structural optimization, metaheuristic algorithms are competitive with gradient-based algorithms as long as the number of structural analyses per design cycle \(N_{AN\text{-}cycle}\) is significantly smaller than the number of optimization variables \(NDV\). In metaheuristic optimization, \(N_{AN\text{-}cycle}\) is usually equal to or at most twice the population size \(N_{pop}\). In gradient-based optimization,\(N_{AN\text{-}cycle}\) is at least equal to (_NDV+1_) if one assumes that forward finite differences are used for computing gradients of nonlinear constraints with respect to design variables. A vast number of studies demonstrated that population-based metaheuristic optimizers can find global optima or nearly global optimum designs even if \(N_{POP}<<NDV\). Basically, by improving the quality of the trial designs generated in each iteration, it is possible to efficiently search the design space even with up to one order of magnitude smaller populations than the number of design variables. Such a condition is also satisfied by the formulation of the proposed LSSO-HHSJA algorithm. In summary, the proposed LSSO-HHSJA formulation attempts to reduce the number of structural analyses entailed by the optimum design of large-scale structures. For this purpose, trial designs are generated by perturbing optimization variables along descent directions where it is very likely to reduce cost function in a fast way. Such a goal is accomplished both directly, using explicitly available gradient information in the HS phase, and indirectly, correcting trial designs with JA-based operators that push the search towards the best designs included in the current population or in a neighborhood of the currently analyzed trial design.