Automatic design of concrete vaults using iterated local search and extreme value estimation

This paper describes an iterated local search algorithm based on a Gray code global best-descent (ILS-GB) for the automatic design and cost minimization of reinforced concrete vaults for road construction. The study involves a vault which measures 12.40 m in horizontal free span, 3.00 m in vertical height of the lateral walls and 1.00 m in earth cover. This problem includes 49 discrete design variables as well as penalty functions for unfeasible solutions. An objective methodology based on the extreme value theory is used to determine the number of experimental tests required to provide a solution with user-defined accuracy as compared to a global optimum solution. Results indicate that the local optima found by ILS-GB fits a three-parameter Weibull distribution so the estimated location parameter gamma can be used as an estimation of the global minimum cost solution. The minimum value obtained by ILS-GB differed just 0.81% compared to the theoretical minimum value so that, from the structural engineering perspective, the divergence was small enough to be accepted. Finally, the optimization method indicates savings of about 7% compared to a traditional design.