MARTÍNEZ MARTÍN, FRANCISCO J. (2008). Heuristic optimization of reinforced concrete bridge piers of rectangular hollow section. Doctoral Thesis. School of Civil Engineering. 327 pages. framarm1@hotmail.com
There are two main objectives of this Thesis. The first objective is the search and comparison of algorithms that allow to automate the optimal design of reinforced concrete structures of bridge piers with rectangular hollow sections without a previous knowledge. The second objective is to extract general conclusions about the solutions with less cost, which were studied for different heights of piers and different lengths of spans for railway and road bridges. The robustness of the solutions for a variable number of executions performed for the piers and optimizations methods was studied with a t of Student distribution, which gives a confidence interval for the solutions.
Different heuristics methods had been applied to the same pier for their comparison. The methods used were the random walk (RW), three methods of local search and six of evolutionary algorithm. The methods of local search that have been used are the descent local search (DLS), the threshold accepting (TA) and the simulated annealing (SA). Regarding the evolutionary algorithms, four types of ant colony optimization (AS, ACS, ASO1 and ASO2) and two types of genetic algorithms (GEN1 and GEN2) were used. The solution with the lowest cost was the AS with 68819.41 € , but the differences of the rest of solutions with the least cost was, except for the RW, less than 1%. On the other hand, the time necessary for running the problem with evolutionary algorithm was, in general, bigger than the time necessary for running the local search methods. In addition, it is presented a comparison of the results got with the heuristic methods and the pier actually built, which had been designed by traditional methods by consulting of engineers.
The parametric study was carried out by a type of ant colony optimization (ASO2) which had good solutions with small dispersion, good enough running times and was appropriated for the application to problems with different number of variables and dissimilar solution space without being necessary a previous study of the feasible solutions. In this study, the solutions with the least cost for different height of piers and different length of spans showed amount of reinforcement, concrete and cost.  As a result, it was showed that the total amount of material reduced until a definite height and grew up in taller piers. Besides the footing results were similar than for the smaller piers and increased for taller piers even their cost and their proportion cost of the support with relation at cost of the footing.
The possibility that the walls of the column were not vertical was considered for piers of 90 metres of height. The differences of the costs for two walls not parallel to the direction pf PK or in the transverse direction were not significant. Regarding  the possibility that the four walls weren’t verticals, it would cause an increment of the cost in the internal formwork that mark the difference with the possibility with having only two verticals walls. 
As regards the structure, optimum structures reduce their reinforcement, thickness of the walls and resistance of the concrete as the sections were near from the head of the support since they hold less stress. It was not habitual that the sections of the support had cracking because they were heavily compressed, but this compression, that would be stronger in the stretches near to the base, imply the necessity of concrete of greater resistance for checking SLS of fissuration and ULS of fatigue in the concrete. In relation with the footings point out that smaller piers fit their size in the way that the bigger stress in the ground was less than the admissible strain and for the bigger piers were more restrictiver the no take off condition that the admissible strain condition. The concrete in the footings were HA-25 in the most of the situations that is because was the cheaper concrete and have resistance enough for the stress that they have to support.