Keywords: hybrid metaheuristics, metaheuristics, truss optimization, design variables, response variables, fair comparison.

Several procedures have been developed for simple sizing, combined sizingshaping, or topology design of trusses. Discrete and continuous variables are applied to determine the optimal cross-sectional areas of the members and the optimal geometry of the nodal points. Depending on the structural model, linear or nonlinear constraints must be evaluated inside the optimization process. The optimal truss design problems are hard nonlinear or NP hard discrete mathematical programming problems with implicit response variables which may be challenging problems, even more so in the case of small or medium size structures. Metaheuristic methods attempt to solve hard combinatorial optimization problems through controlled randomization. For obtaining near optimum solutions of such problems, a better minimum of an objective function should be searched for among a huge number of local minima, since it is almost impossible to find an exact optimum. Over the last years, interest in hybrid metaheuristics has risen considerably in the field of truss design. The best results found for many benchmark problems are obtained by hybrid algorithms. Combinations of algorithms such as metaheuristics and mathematical programming have provided very powerful search algorithms. The recently developed hybrid metaheuristic methods combine different searching approaches which are able to detect the global-local solution, using the idea of the probabilistic diversification and intensification in the local search. The "intensification" means decreasing of the objective function value to find a better solution closer to the local minimum. The "diversification" means a jump from a searching region to other regions in order to avoid getting trapped in a single local minimum. The aim of this study is to review these hybrid metaheuristic techniques and their application in the field of truss optimization. According to the methodological progress in this field, two different types of combinations are considered in this paper: (1) combining metaheuristics with metaheuristics; (2) combining metaheuristic combinations with mathematical programming. On the surface, we see a colourful picture of a large amount of competitive approaches, but rigorous reporting of experimental results is still in its infancy and much progress is needed to achieve the level of quality commonly observed in more established experimental sciences. Without a fair comparison standard based on appropriate bias-free nonparametric statistics, it is very hard to select the really competitive elements from the different approaches or label an approach as the best.

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