Abstract: Genetic stochastic search algorithms (GAs) have soon demonstrated their helpful contribution in finding solutions to the complex real-life optimization problems. In 2005, Mastorakis' method successfully combines the GAs with the Nelder-Mead (NM) simplex optimization technique: the GAs are used first to reach the neighborhood of some global extremum, and the NM algorithm then finds it exactly. Playing games with genetic algorithms has been already proposed: it is a means of seeking better strategies in playing repeated games. These algorithms have been applied extensively for solving Nash equilibria of fuzzy bimatrix games with single objective. The experience shows the ability of the GAs to find solutions to equivalent quadratic programming problems without an exhaustive search. In 2002, Chen extends the applications to multiple objective programming problems, without weighting the desired objectives contrary to the Nishizaki-Sakawa models. This lecture is an attempt to consider the complexity of the real situations, when the decision makers are facing to multiple simultaneous objectives in a fuzzy environment. The software MATHEMATICA 7.0.1 is used to implement these techniques in a high-performance computing environment.

Brief Biography of the Speaker:
Professor Andre A. Keller is an associate researcher in mathematical economics at CLERSE - Centre Lillois d'Etudes et de Recherches Sociologiques et Economiques - a research unit UMR/CNRS 8019 of the French 'Centre National de la Recherche Scientifique (CNRS)' from the University Lille 1, Sciences et Technologies. Prof. Keller is graduated in econometrics and operations research, and received his PhD in Economics in 1977 from the Universite de Paris I. Prof. Keller taught applied mathematics (optimization techniques), econometrics, microeconomics, theory of games and macrodynamics. His experience centers are on discrete mathematics (graph theory), building and simulating large scale macro-econometric models. Since 1985, his research interest has concentrated on modeling high frequency time-series: spectral properties of usual filters, automatic selection of ARIMA models, efficiency tests. Since 1990, Prof. Keller's research is centered on discrete mathematics (graph theory), stochastic differential games and tournaments, circuit theory of environmental systems, dynamics and optimal control under uncertainties, as in a fuzzy environment. Prof. Keller's publications in journals and proceedings are on model building and game theory, with application to macroeconomics and international finance. Books chapters are on semi-reduced forms of econometric models (Martinus Nijhoff, 1984), econometrics of technical change (Springer and IIASA, 1989), advanced time-series analysis (Woodhead-Faulkner), circuits enumeration in digraphs (Springer, 2008), stochastic differential games (Nova Science, 2009), optimal fuzzy control (InTech, 2009), circuit analysis (Nova Science, forthcoming 2010).