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One of the most crucial problems in geo-engineering is the instability of unsaturated slopes, causing severe loss of life and property worldwide. In this study, five novel meta-heuristic methods are employed to optimize locating the Critical Failure Surface (CFS) and corresponding Factor of Safety (FOS). A Finite Element Method (FEM) code is incorporated to convert the strong form of the Richard’s differential equation to the weak form. More importantly, the derived code can consider both the seismic and seepage conditions additional to the static loading. Eventually, the proposed optimization procedure is validated against benchmark examples and some insights are provided.

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The multi-material size optimization of transmission tower trusses is carried out in the present study. Three real-size examples are designed, and statically analyzed, and the Black Hole Mechanics Optimization (BHMO) algorithm, a recently developed metaheuristic optimizer methodology, is employed. The BHMO algorithm's innovative search strategy, which draws inspiration from black hole quantum physics, along with a robust mathematical kernel based on the covariance matrix between variables and their associated costs, efficiently converges to global optimum solutions. Besides, three alloys of steel are taken into account in these examples for discrete size variables, each of which is defined in the problem by a weighted coefficient in terms of the elemental weight. The results also indicate that using multiple materials or alloys in addition to diverse cross-sectional sizes leads to the lowest possible cost and the most efficient solution.