Combining game theory and genetic algorithms with application to DDM-nozzle optimization problems

Périaux, Jacques; Chen, H. Q.; Mantel, B.; Sefrioui, M.; Sui, Haiteng

doi:10.1016/s0168-874x(00)00055-x

Cited by 78 publications

(34 citation statements)

References 5 publications

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“…Although the framework of the algorithm is similar to popular evolutionary programming, its mutation operation is similar to game strategy. With the ever-increasing complexity of design engineering problems, game strategies have been proposed to save CPU usage and increase model quality [33,34], in which game strategies are hybridized and coupled with multi-objective evolutionary algorithms to improve the quality of solutions.…”

Section: Related Workmentioning

confidence: 99%

Game Theory-Inspired Evolutionary Algorithm for Global Optimization

Yang

2017

Algorithms

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Many approaches that model specific intelligent behaviors perform excellently in solving complex optimization problems. Game theory is widely recognized as an important tool in many fields. This paper introduces a game theory-inspired evolutionary algorithm for global optimization (GameEA). A formulation to estimate payoff expectations is provided, which is a mechanism to make a player become a rational decision-maker. GameEA has one population (i.e., set of players) and generates new offspring only through an imitation operator and a belief-learning operator. An imitation operator adopts learning strategies and actions from other players to improve its competitiveness and applies these strategies to future games where one player updates its chromosome by strategically copying segments of gene sequences from a competitor. Belief learning refers to models in which a player adjusts his/her strategies, behavior or chromosomes by analyzing the current history information to improve solution quality. Experimental results on various classes of problems show that GameEA outperforms the other four algorithms on stability, robustness, and accuracy.

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Section: Related Workmentioning

confidence: 99%

Game Theory-Inspired Evolutionary Algorithm for Global Optimization

Yang

2017

Algorithms

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“…In particular the Hessian of L 1 is large and dense and Newton-based methods are therefore expected to be too expensive, unless perhaps (limited memory) quasi-Newton approximations can be used. Périaux et al (2001) and Habbal et al (2004) used a nonlinear Jacobi-type algorithm (Facchinei and Kanzow 2010) where the two players update their strategies simultaneously, i.e. both optimization problems are solved at the same time and independent of each other.…”

Section: Algorithm For Finding a Generalized Nash Equilibriummentioning

confidence: 99%

“…Using the same convex pay-off functional for both players, it was shown that the solution to the game was obtained as an eigenvalue problem. Périaux et al (2001) used genetic algorithms in a shape optimization problem to find a Nash equilibrium for players optimizing the shape and flow in a nozzle. Banichuk (1973) calculated analytical solutions to optimization problems of elastic beams subjected to loads of various forms from a predefined set.…”

Section: Introductionmentioning

confidence: 99%

Game theory approach to robust topology optimization with uncertain loading

Holmberg

Thore

Klarbring

2016

Struct Multidisc Optim

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The paper concerns robustness with respect to uncertain loading in topology optimization problems. Using a game theoretic framework we formulate problems, or games, defining generalized Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.

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“…Addy and White [10] performed the optimization of drag minimums without allowing for a dynamic variation of nozzle geometry. More recent nozzle optimization studies considered supersonic species transport, flow parameters, different nozzle geometries [11], multiple objective design optimization of internal aerodynamic shape operating in transonic flow with genetic algorithms [12], and length optimization of expansion deflection nozzles investigating the effect of various throat parameters on nozzle contour [13]. However, within the knowledge of the authors, the dynamic variation of nozzle geometry and the increase in internal surface roughness have not been investigated simultaneously in a nozzle optimization study previously.…”

Section: Introductionmentioning

confidence: 99%