Keywords: structural design, economic optimization, ant colony optimization, concrete structures.

This paper deals with the economic optimization of reinforced concrete bridge piers of rectangular hollow section typically used in road construction. It shows the efficiency of a heuristic optimization by the ant colony algorithm (ACO) [1]. The evaluation of solutions follows the Spanish Code for structural concrete. Design loads are in accordance to the national IAP Code for road bridges. The example studied relates to hollow rectangular section reinforced concrete (RC) piers used in the construction of prestressed concrete viaducts. The method is applied to the main pier of a 60-90-60 m span viaduct over the river Palancia on the motorway Valencia to Zaragoza (Castellon, Spain). The total height of the pier is 23.97 m. The total number of variables is 95: 79 for the column and 16 for the footing. Variables for the column include 10 geometrical values for the thicknesses of the walls at different heights; 6 variables for the concrete grades; and 63 variables for the reinforcement of the column following a standard setup. All variables are discrete in this analysis. The most important parameters are the vertical height, the width and the depth of the pier of 4.84 m and 2.60 m respectively, the vertical and horizontal loads on the top bearings and the partial coefficients of safety. Structural restrictions considered followed standard provisions for these piers, except for the ULS of buckling which has been dealt with by the stiffness method as reported by Manterola [2].

The proposed ACO algorithm follows an original formulation of the path followed by ants that includes both the trace followed by former ants and the random selection of new paths. The ACO algorithm was programmed in Fortran. Typical runs for 500 ants and 100 stages amount 49 minutes in a processor Core 2 Duo of 1.86 GHz. The calibration of the proposed ACO algorithm recommended 500 ant population, 100 stages and 0.8 and 0.2 for the parameters that deal in the formulation with former paths and random new paths. The main results of the ACO analysis are reported as regards concrete grades, thicknesses of the walls and reinforcement. The sequence of concrete grades in the 6 stages of the column is 40-40-35-30-25-25. The cost of the best solution is 67666 euros. The deviation with respect to the best of the random results is of 0.88%. The depth of the bottom walls is 0.275 and 0.325 m. The overall ratio of reinforcement in the hollow column is 86.32 kg/m³. Hence it is concluded that results of the optimization search tend to slender and highly reinforced structural piers. Finally, results indicate that ant colony optimization is a forthcoming option for improving the design costs of real RC structures.

1

M. Dorigo, V. Maniezzo and A. Colorni, "The ant system: optimization by a colony of cooperating agents", IEEE Transactions on Systems, Man and Cybernetics, Part B, 26(1), 29-41, 1996. doi:10.1109/3477.484436

2

J. Manterola, "Bridges: Volume IV (in Spanish)", ETS Ingenieros Caminos, Madrid, 2000.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £62 +P&P)