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This paper provides a test method to make a fair comparison between different heuristics in structure optimization. When statistical methods are applied to the structural optimization (namely heuristics or meta-heuristics with several tunable parameters and starting seeds), the "one problem - one result" is extremely far from the fair comparison. From statistical point of view, the minimal requirement is a so-called "small-sample" according to the fundamental elements of the theory of the experimental design and evaluation and the protocol used in the drug development processes. The viability and efficiency of the proposed statistically correct methodology is demonstrated using the well-known ten-bar truss on a set of the heuristics from the brutal-force-search up to the most sophisticated hybrid approaches.

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This article presents a comprehensive review of chaos embedded meta-heuristic optimization algorithms and describes the evolution of this algorithms along with some improvements, their combination with various methods as well as their applications. The reported results indicate that chaos embedded algorithms may handle engineering design problems efficiently in terms of precision and convergence and, in most cases they outperform the results presented in the previous works. The main goal of this paper is to providing useful references to fundamental concepts accessible to the broad community of optimization practitioners.

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This study presents shape optimization of a gravity dam imposing stability and principal stress constraints. A gravity dam is a large scale hydraulic structure consisting of huge amount of concrete material. Hence, an optimum design gives a cost-benefit structure due to the fact that small changes in shape of dam cross-section leads to large saving of concrete volume. Three recently developed meta-heuristics are utilized for optimizing the structure. These algorithms are charged system search (CSS), colliding bodies optimization (CBO) and its enhanced edition (ECBO). This article also provides useful formulations for stability analysis of gravity dams which can be extended to further researches.

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Spillway design poses a significant challenge in effectively managing the energy within water flow to prevent erosion and destabilization of dam structures. Traditional approaches typically advocate for standard hydraulic jump stilling basins or other energy dissipators at spillway bases yet constructing such basins can be prohibitively large and costly, particularly when extensive excavation is necessary. Consequently, growing interest in cascade hydraulic structures has emerged over recent decades as an alternative for energy dissipation. These structures utilize a series of arranged steps to facilitate water flow, effectively dissipating energy as it traverses the cascade. Commonly deployed in scenarios involving high dams or steep gradients, the stepped configuration ensures efficient aeration and substantial energy dissipation along the structure, thereby reducing the size and cost of required stilling basins. Despite extensive research on hydraulic characteristics using physical and numerical models and established design procedures, construction cost optimization of step cascades remains limited but promising. This paper aims to address this gap by employing two novel gradient-based meta-heuristic optimization techniques to enhance the efficiency and cost-effectiveness of cascade stilling basin designs. Through comparative analyses and evaluations, this study demonstrates the efficacy of these techniques and offers insights for future research and applications in hydraulic structures design optimization.