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http://dx.doi.org/10.12989/gae.2021.27.1.063

Pareto optimality and game theory for pile design having conflicting objectives  

Hati, Shantanu (Department of Civil Engineering, Indian Institute of Technology (ISM) Dhanbad)
Panda, Sarat K. (Department of Civil Engineering, Indian Institute of Technology (ISM) Dhanbad)
Publication Information
Geomechanics and Engineering / v.27, no.1, 2021 , pp. 63-74 More about this Journal
Abstract
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.
Keywords
game theory; Nash cooperative game; Nash non-cooperative solution; pareto-optimal; pile structure; supercriterion;
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