Keywords: ANGEL hybrid heuristic method, discrete sizing-shaping truss optimization.

In this paper, a hybrid metaheuristic method is presented for discrete sizing and continuous shaping truss optimisation problems. The geometrically nonlinear space structure is formulated as a large displacement structural model. The minimal weight design is subjected to stress, local buckling, and displacement constraints. The combined sizing-shaping truss optimization problems are formulated as nonlinear discrete optimization problems, where the response variables are implicit functions of the design variables.

The proposed hybrid method ANGEL combines ant colony optimisation (ACO), a genetic algorithm (GA), and a local search strategy (LS). The ACO and the GA search alternately and cooperatively in the solution space. The powerful LS algorithm, which is based on the local linearization of the constraint set and the objective function, is applied to yield a better feasible or less unfeasible solution when the ACO or the GA obtains a solution. According to the discrete nature of the sizing variables, in the LS process a local improvement step is formulated as a mixed integer linear programming problem (MILP). This process can be replaced by an effective rounding heuristic, which is combined with continuous shape improvement steps. In the heuristic LS process a local improvement step can be formulated as a linear programming (LP) problem.

In this study, a hybrid meta-heuristic method is discussed for discrete sizing and continuous shaping truss optimization problems. The proposed hybrid method is an extended version of the previously published ANGEL method [1,2,3,4] applied for different discrete and continuous optimization problems. The naming ANGEL of the proposed method is an acronym, that combines ant colony optimization (ACO), a genetic algorithm (GA), and a local search strategy (LS). Through Pedersen's benchmark example [5], the efficiency of the proposed method is demonstrated. With the help of the statistical evaluation of the best feasible solutions of thirty independent runs the stability and dependability of the process has been proven . Finally, the results of the mixed continuous-discrete optimization obtained by the proposed hybrid ANGEL method is compared with the results of the continuous results.

1

A. Csébfalvi, "A Hybrid Method for Mixed Shaping-Sizing Optimization Problem", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 5, 2009. doi:10.4203/ccp.92.5

2

A. Csébfalvi, "An ANGEL Method for Discrete Optimization Problems", Periodica Polytechnica Ser. Civ. Eng., 51(2), 37-46, 2007. doi:10.3311/pp.ci.2007-2.06

3

A. Csébfalvi, "An ANGEL Heuristic Method for Combined Shaping and Sizing Optimization of Bridges", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 83, 2008. doi:10.4203/ccp.89.83

4

A. Csébfalvi, "A hybrid meta-heuristic method for continuous engineering optimization", Periodica Polytechnica Ser. Civ. Eng., 53(2), 93-100, 2009. doi:10.3311/pp.ci.2009-2.05

5

P. Pedersen, "On the optimal layout of multi-purpose trusses", Comput Struct, 2, 695-712, 1972. doi:10.1016/0045-7949(72)90032-6

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