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Papers by André A. Keller

Research paper thumbnail of Mixed-Integer Nonlinear Programming

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Nested Optimization of Hierarchical Systems

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Design of Multi-Objective Optimization Problems

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Pareto Optimality

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Many-Objective Optimization and Parallel Computation

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Genetic Search Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Evolutionary Strategy Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Fuzzy Logic Programming

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Founding Multi-Optimization Techniques

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Graph Theory and Economic Models: from Small to Large Size Applications

Electronic Notes in Discrete Mathematics, Mar 1, 2007

This empirical study explores the structure of macroeconomic models using major concepts and algo... more This empirical study explores the structure of macroeconomic models using major concepts and algorithms of the graph theory. Different sizes of applications with dynamic effects are considered. We will firstly examine the matching problem when assigning the equations to the variables. We'll also propose a simple method for improving the regular circular embedding of graphs on the basis of one of the longest circuit and adequate permutations. The determination of the maximal list of edgedisjoint circuits also produces an useful insight into the structure. A typology of the interdependent variables is proposed using the all-pairs shortest paths matrix. This classification is based on both the emissions of nodes towards the rest of the directed graph and the perturbations that the rest of the graph exerts on these nodes. The computations have been done using the softwares M AT HEM AT ICA 5.1, LIN DO 6.1 and our own programs in Fortran 77L and C++.

Research paper thumbnail of Decomposition-Based and Hybrid Evolutionary Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Noncooperative Games in a Fuzzy Environment

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Plenary lecture 7: genetic search algorithms to fuzzy multiobjective games: a mathematica implementation

Genetic stochastic search algorithms (GAs) have soon demonstrated their helpful contribution in f... more 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.

Research paper thumbnail of Swarm Intelligence and Co-Evolutionary Algorithms

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Extended Multi-Objective Optimization Problems

Research paper thumbnail of Pareto-Optimal Front Determination

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Evolution Strategy Algorithms

Research paper thumbnail of Fifty Collected Test Functions

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Plenary lecture 8: generalized differential-difference equations to economic dynamics and control

Proceedings of the 2010 American Conference on Applied Mathematics, Jan 27, 2010

Dynamic economic models generally consists in difference or differential behavioral equations. Se... more Dynamic economic models generally consists in difference or differential behavioral equations. Several arguments are in favor of continuous time systems: the multiplicity of decisions overlapping in time, a more adequate formulation of market adjustments and distributed lag processes, the properties of estimators, etc. The type of dynamic equations also refer to historical and practical reasons. In some cases of the economic dynamics, delay differential equations (DDEs) may be more suitable to a wide range of economic models. The dynamics of the early Kalecki's business cycle model is represented by a linear first-order DDE with constant coefficients, in the capital stock. Such a DDE, with constant or flexible lags, also occurs in the continuous time Solow's vintage capital growth model. This is due to the heterogeneity of goods and assets. In some qualitative study, the time delay is replaced by the Taylor series for a sufficiently small delay and a not too large higher-order derivative. DDEs with constant lags may be preferably solved by using Laplace transforms. Numerous techniques are also proposed for the solutions of DDEs, like the inverse scattering method, the Jacobian elliptic function method, numerical techniques, the differential transform method, etc. This study uses a block diagram approach with help of the software MATHEMATICA 6.0., and its specialized packages for signal processing, such as the "Control System Professional".

Research paper thumbnail of Plenary lecture 7: circuit analysis to natural resources and environmental economic dynamics and control

Proceedings of the 2010 International Conference on Mathematical Models For Engineering Science, Nov 30, 2010

This study extends to the natural resource and environmental economics the use of the conventiona... more This study extends to the natural resource and environmental economics the use of the conventionalcircuit analysis and control in engineering. Resources and environmental management problemsare investigated with help of continuous-time and discrete-time systems: optimal use of natural resources, growth models with polluting events and fishery models with open-access to the industry. This study introduces the fundamental block-diagram approach, with small-size applications to natural resources, pollution and fisheries management problems. The software MATHEMATICA (version 7.0.1.0) and its application packages are used for analyzing and solving the systems, symbolically and numerically.

Research paper thumbnail of Mixed-Integer Nonlinear Programming

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Nested Optimization of Hierarchical Systems

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Design of Multi-Objective Optimization Problems

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Pareto Optimality

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Many-Objective Optimization and Parallel Computation

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Genetic Search Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Evolutionary Strategy Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Fuzzy Logic Programming

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Founding Multi-Optimization Techniques

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Graph Theory and Economic Models: from Small to Large Size Applications

Electronic Notes in Discrete Mathematics, Mar 1, 2007

This empirical study explores the structure of macroeconomic models using major concepts and algo... more This empirical study explores the structure of macroeconomic models using major concepts and algorithms of the graph theory. Different sizes of applications with dynamic effects are considered. We will firstly examine the matching problem when assigning the equations to the variables. We'll also propose a simple method for improving the regular circular embedding of graphs on the basis of one of the longest circuit and adequate permutations. The determination of the maximal list of edgedisjoint circuits also produces an useful insight into the structure. A typology of the interdependent variables is proposed using the all-pairs shortest paths matrix. This classification is based on both the emissions of nodes towards the rest of the directed graph and the perturbations that the rest of the graph exerts on these nodes. The computations have been done using the softwares M AT HEM AT ICA 5.1, LIN DO 6.1 and our own programs in Fortran 77L and C++.

Research paper thumbnail of Decomposition-Based and Hybrid Evolutionary Algorithms

BENTHAM SCIENCE PUBLISHERS eBooks, Mar 26, 2019

Research paper thumbnail of Noncooperative Games in a Fuzzy Environment

BENTHAM SCIENCE PUBLISHERS eBooks, Dec 13, 2017

Research paper thumbnail of Plenary lecture 7: genetic search algorithms to fuzzy multiobjective games: a mathematica implementation

Genetic stochastic search algorithms (GAs) have soon demonstrated their helpful contribution in f... more 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.

Research paper thumbnail of Swarm Intelligence and Co-Evolutionary Algorithms

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Extended Multi-Objective Optimization Problems

Research paper thumbnail of Pareto-Optimal Front Determination

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Evolution Strategy Algorithms

Research paper thumbnail of Fifty Collected Test Functions

Multi-Objective Optimization In Theory and Practice II: Metaheuristic Algorithms, 2019

Research paper thumbnail of Plenary lecture 8: generalized differential-difference equations to economic dynamics and control

Proceedings of the 2010 American Conference on Applied Mathematics, Jan 27, 2010

Dynamic economic models generally consists in difference or differential behavioral equations. Se... more Dynamic economic models generally consists in difference or differential behavioral equations. Several arguments are in favor of continuous time systems: the multiplicity of decisions overlapping in time, a more adequate formulation of market adjustments and distributed lag processes, the properties of estimators, etc. The type of dynamic equations also refer to historical and practical reasons. In some cases of the economic dynamics, delay differential equations (DDEs) may be more suitable to a wide range of economic models. The dynamics of the early Kalecki's business cycle model is represented by a linear first-order DDE with constant coefficients, in the capital stock. Such a DDE, with constant or flexible lags, also occurs in the continuous time Solow's vintage capital growth model. This is due to the heterogeneity of goods and assets. In some qualitative study, the time delay is replaced by the Taylor series for a sufficiently small delay and a not too large higher-order derivative. DDEs with constant lags may be preferably solved by using Laplace transforms. Numerous techniques are also proposed for the solutions of DDEs, like the inverse scattering method, the Jacobian elliptic function method, numerical techniques, the differential transform method, etc. This study uses a block diagram approach with help of the software MATHEMATICA 6.0., and its specialized packages for signal processing, such as the "Control System Professional".

Research paper thumbnail of Plenary lecture 7: circuit analysis to natural resources and environmental economic dynamics and control

Proceedings of the 2010 International Conference on Mathematical Models For Engineering Science, Nov 30, 2010

This study extends to the natural resource and environmental economics the use of the conventiona... more This study extends to the natural resource and environmental economics the use of the conventionalcircuit analysis and control in engineering. Resources and environmental management problemsare investigated with help of continuous-time and discrete-time systems: optimal use of natural resources, growth models with polluting events and fishery models with open-access to the industry. This study introduces the fundamental block-diagram approach, with small-size applications to natural resources, pollution and fisheries management problems. The software MATHEMATICA (version 7.0.1.0) and its application packages are used for analyzing and solving the systems, symbolically and numerically.