Pareto optimality and game theory for pile design having conflicting objectives

Based on concept of Pareto-optimal solution and game theory associated with Nash non-cooperative and cooperative solution, a mathematical procedure is presented for optimum design of axially loaded pile structure. The decision making situation is formulated as a constrained optimization problem with two objectives of contradictory in nature. The factor of safety is taken as the design variable. Geometric constraints are considered by imposing a lower and upper bound on the design variable. Two objectives considered are: maximization of ultimate load carrying capacity of pile and minimization of associated cost. The generation of Pareto-optimal solution and methodology based on game theory concept is described. The design problem is mathematically formulated as two-person game. To obtain the starting point of game, Nash non-cooperative solution or Nash equilibrium solution is evaluated for an irrational play. For cooperative game, a negotiation model is developed for overall benefit of all players. Game is terminated when the optimal trade-off between two objectives is reached with maximization of supercriterion. Two numerical examples of practical interest are solved to demonstrate the methodology.