A Study of Nash-Evolutionary Algorithms for Reconstruction Inverse Problems in Structural Engineering

In this paper we deal with solving inverse problems in structural engineering (both the reconstruction inverse problem and the fully stressed design problem are considered). We apply a game-theory based Nash-evolutionary algorithm and compare it with the standard panmictic evolutionary algorithm. The procedure performance is analyzed on a ten bar sized test case of discrete real cross-section types structural frame, where a significant increase of performance is achieved using the Nash approach, even achieving super-linear speed-up.

[1]  Keith Michael Mueller.  Sizing of Members in the Fully Stressed Design of Frame Structures , 2000 .

[2]  M. Sefrioui,et al.  Nash genetic algorithms: examples and applications , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[3]  David Greiner,et al.  Gray Coding in Evolutionary Multicriteria Optimization: Application in Frame Structural Optimum Design , 2005, EMO.

[4]  Jacques Periaux,et al.  Distributed evolutionary optimization using Nash games and GPUs – Applications to CFD design problems , 2013 .

[5]  Luis F. Gonzalez,et al.  Active flow control bump design using hybrid nash-game coupled to evolutionary algorithms , 2010 .

[6]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[7]  G. Winter,et al.  Single and multiobjective frame optimization by evolutionary algorithms and the auto-adaptive rebirth operator , 2004 .

[8]  Min Liu,et al.  Fully Stressed Design of Frame Structures and Multiple Load Paths , 2002 .

[9]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Jacques Periaux,et al.  Evolutionary Optimization and Game Strategies for Advanced Multi-Disciplinary Design , 2015 .

[11]  David Greiner,et al.  A comparative study of the influence of codification on discrete optimum design of frame structures , 2013 .

[12]  G. Winter,et al.  Optimising frame structures by different strategies of genetic algorithms , 2001 .

[13]  J. Périaux,et al.  Increasing parallelism of evolutionary algorithms by Nash games in design inverse flow problems , 2013 .