Keywords: optimal truss design, robust truss optimization, uncertain load direction, unified uncertainty management..

In this paper, we present a new challenging benchmark problem and its exact solution for a recently developed robust truss optimization model when the only source of uncertainty is the variability of the applied load directions. The essence of the novel concept is independent from the theoretical description of the uncertainty which may be either probabilistic (stochastic) or possibilistic (fuzzy). In the presented unified (non-probabilistic and non-possibilistic) approach, the varying load directions are handled by quadratically constrained parameter sets. Naturally the presented load direction handling method can be replaced by any other uncertainty representation which can be described by an appropriate combination of box constraints and linear or quadratic relations. The result of the optimization is a robust minimal-weight truss design which is invariant to the investigated load uncertainty type. The well-known ten-bar plane truss problem with problem specific robust additional parameters was used to illustrate the validity and efficiency of the presented approach. The presented correctly described benchmark problem and its exact solution may be used for testing the quality of exact and heuristic solution procedures to be developed in the future.

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