Multi-Objective Optimization for Shape Design of Arch Dams

Abstract

A multi-objective optimization model is established for the shape design of arch dams. In this model, the geometric parameters describing dam shape is taken as design variables; four objectives are considered of dam volume, maximal tensile stress, maximal pressure stress and relative depth of the zone with tensile stress that is larger than 1.0MPa; and the constraints include geometric constraints, dam volume constraint and mechanical property constrains, i.e., stress constraints, stability constraints, etc. Traditionally, multi-objective optimization schemes transform multiple objective functions into a single objective function in some manner, weighted sum method and Utopia point method for examples, and the resulting problem is solved as a single objective optimization problem. In this paper the cooperative game model analogy to the multi-objective optimization is proposed with each player correspond to one of the objective functions. After defining the utility of each player, the Nash arbitrary scheme is used to solve the cooperative game. The optimization of Baihetan arch dam, which is located in Sichuan province of China, is calculated as an engineering example. The results are compared to those obtained by weighted sum method and Utopia point method and indicate that the cooperative game method is superior to traditional methods. The optimal design saves 9.77×104m3 of dam volume, compared to initial design, along with the decrease of maximal tensile stress with 38.22%, the decrease of maximal pressure stress with 28.83%, and the decrease of relative depth of large tensile stress zone with 10.15%.