The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Oliver Schutze - One of the best experts on this subject based on the ideXlab platform.
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a Scalar Optimization approach for averaged hausdorff approximations of the pareto front
Engineering Optimization, 2016Co-Authors: Oliver Schutze, Christian Dominguezmedina, Nareli Cruzcortes, Luis Gerardo De La Fraga, Gregorio Toscano, Ricardo LandaAbstract:This article presents a novel method to compute averaged Hausdorff () approximations of the Pareto fronts of multi-objective Optimization problems. The underlying idea is to utilize directly the Scalar Optimization problem that is induced by the performance indicator. This method can be viewed as a certain set based Scalarization approach and can be addressed both by mathematical programming techniques and evolutionary algorithms (EAs). In this work, the focus is on the latter where a first single objective EA for such approximations is proposed. Finally, the strength of the novel approach is demonstrated on some bi-objective benchmark problems with different shapes of the Pareto front.
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multilevel subdivision techniques for Scalar Optimization problems
2012Co-Authors: Michael Dellnitz, Oliver SchutzeAbstract:In this chapter, we give an overview of algorithms for the numerical treatment of global Optimization problems which are based on a multilevel subdivision technique. These set-oriented methods create a sequence of box collections which converges to the relative global attractor of one (or several) dynamical system(s). This set is of particular interest for general dynamical systems and in particular for dynamical systems derived from mathematical programming techniques such as Newton’s method or a line searcher since it contains all the relevant dynamics. In the context of Optimization this can be the set of roots or the set of global minimizers, according to the given problem. We present several algorithms for different Optimization problems and illustrate them on several low-dimensional academic examples.
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Computing approximate solutions of Scalar Optimization problems and applications in space mission design
IEEE Congress on Evolutionary Computation, 2010Co-Authors: Oliver Schutze, Adriana Lara, Carlos Coello A. Coello, Massimiliano VasileAbstract:In many applications it can be advantageous for the decision maker to have multiple options available for a possible realization of the project. One way to increase the number of interesting choices is in certain cases to consider in addition to the optimal solution x* also nearly optimal or approximate solutions which differ in the design space from x* by a certain value. In this paper we address the efficient computation and discretization of the set E of ϵ-approximate solutions for Scalar Optimization problems. For this we will suggest two strategies to archive and update the data coming from the generation process of the search procedure, and will use Differential Evolution coupled with the new archivers for the computation of E. Finally, we will demonstrate the behavior of the archiver empirically on some academic functions as well as on two models related to space mission design.
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IEEE Congress on Evolutionary Computation - Computing approximate solutions of Scalar Optimization problems and applications in space mission design
IEEE Congress on Evolutionary Computation, 2010Co-Authors: Oliver Schutze, Carlos Coello Coello, Adriana Lara, Massimiliano VasileAbstract:In many applications it can be advantageous for the decision maker to have multiple options available for a possible realization of the project. One way to increase the number of interesting choices is in certain cases to consider in addition to the optimal solution x∗ also nearly optimal or approximate solutions which differ in the design space from x∗ by a certain value. In this paper we address the efficient computation and discretization of the set E of ∊-approximate solutions for Scalar Optimization problems. For this we will suggest two strategies to archive and update the data coming from the generation process of the search procedure, and will use Differential Evolution coupled with the new archivers for the computation of E. Finally, we will demonstrate the behavior of the archiver empirically on some academic functions as well as on two models related to space mission design.
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Direct Calibration by Fitting of Cuboids to a Single Image Using Differential Evolution
International Journal of Computer Vision, 2009Co-Authors: Luis Gerardo De La Fraga, Oliver SchutzeAbstract:In this article we propose a new method to calibrate directly the camera by which it was taken an image of a cuboid, and to find at the same time the orientation and side lengths of the cuboid. This is a highly non-linear Optimization problem that is solved directly using a heuristic called differential evolution. We show in this paper that this problem is very difficult if one tries to solve it with a conventional Scalar Optimization procedure. Although differential evolution is a heuristic, we find valid results in 100% of the executions. We test our method with synthetic and real images.
Massimiliano Vasile - One of the best experts on this subject based on the ideXlab platform.
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Computing approximate solutions of Scalar Optimization problems and applications in space mission design
IEEE Congress on Evolutionary Computation, 2010Co-Authors: Oliver Schutze, Adriana Lara, Carlos Coello A. Coello, Massimiliano VasileAbstract:In many applications it can be advantageous for the decision maker to have multiple options available for a possible realization of the project. One way to increase the number of interesting choices is in certain cases to consider in addition to the optimal solution x* also nearly optimal or approximate solutions which differ in the design space from x* by a certain value. In this paper we address the efficient computation and discretization of the set E of ϵ-approximate solutions for Scalar Optimization problems. For this we will suggest two strategies to archive and update the data coming from the generation process of the search procedure, and will use Differential Evolution coupled with the new archivers for the computation of E. Finally, we will demonstrate the behavior of the archiver empirically on some academic functions as well as on two models related to space mission design.
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IEEE Congress on Evolutionary Computation - Computing approximate solutions of Scalar Optimization problems and applications in space mission design
IEEE Congress on Evolutionary Computation, 2010Co-Authors: Oliver Schutze, Carlos Coello Coello, Adriana Lara, Massimiliano VasileAbstract:In many applications it can be advantageous for the decision maker to have multiple options available for a possible realization of the project. One way to increase the number of interesting choices is in certain cases to consider in addition to the optimal solution x∗ also nearly optimal or approximate solutions which differ in the design space from x∗ by a certain value. In this paper we address the efficient computation and discretization of the set E of ∊-approximate solutions for Scalar Optimization problems. For this we will suggest two strategies to archive and update the data coming from the generation process of the search procedure, and will use Differential Evolution coupled with the new archivers for the computation of E. Finally, we will demonstrate the behavior of the archiver empirically on some academic functions as well as on two models related to space mission design.
Amir G. Aghdam - One of the best experts on this subject based on the ideXlab platform.
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Interconnection-BasedPerformanceAnalysisforaClassof DecentralizedControllers
2020Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. A LQ cost function is deflned in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled e‐ciently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than flnding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and Scalar Optimization problems will both be equal to zero.
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Interconnection-based performance analysis for a class of decentralized controllers
Automatica, 2010Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and Scalar Optimization problems will both be equal to zero.
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Performance analysis for a class of decentralized control systems
2008 American Control Conference, 2008Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo- hierarchical structure. Given such a system, one can use the existing techniques to design a decentralized controller for the reference hierarchical model, which is obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is often fascinating as far as the computational complexity is concerned, it may not provide a satisfactory performance for the original pseudo-hierarchical system. A LQ cost function is defined in order to evaluate the discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation should then be solved to compute this performance index. However, due to the large- scale nature of the system, this equation can by no means be handled for many real-world systems. Thus, attaining an upper bound on this cost function can be much more desirable than finding its exact value. For this purpose, a novel technique is proposed, which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also proved that as the pseudo-hierarchical system approaches its reference hierarchical model, the bounds obtained from the LMI and Scalar Optimization problems will both go to zero. In the particular case, when the two models are identical (i.e., the original system is exactly hierarchical), both upper bounds will be zero.
Xiaoqi Yang - One of the best experts on this subject based on the ideXlab platform.
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Duality for Multiobjective Optimization via Nonlinear Lagrangian Functions
Journal of Optimization Theory and Applications, 2020Co-Authors: X X Huang, Xiaoqi YangAbstract:In this paper, a strong nonlinear Lagrangian duality result is established for an inequality constrained multiobjective Optimization problem. This duality result improves and unifies existing strong nonlinear Lagrangian duality results in the literature. As a direct consequence, a strong nonlinear Lagrangian duality result for an inequality constrained Scalar Optimization problem is obtained. Also, a variant set of conditions is used to derive another version of the strong duality result via nonlinear Lagrangian for an inequality constrained multiobjective Optimization problem.
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A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems
Journal of Global Optimization, 2005Co-Authors: Guang-ya Chen, Xiaoqi Yang, H. YuAbstract:Scalarization method is an important tool in the study of vector Optimization as corresponding solutions of vector Optimization problems can be found by solving Scalar Optimization problems. In this paper we introduce a nonlinear Scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear Scalarization function are established. This nonlinear Scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems.
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On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization
Journal of Global Optimization, 2002Co-Authors: X X Huang, Xiaoqi YangAbstract:In this paper, nonconvex multiobjective Optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one Scalar Optimization problem and the existence of an exact penalty function of a Scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.
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Efficiency and Approachability of Nonconvex Bicriteria Programs
Journal of Mathematical Analysis and Applications, 2001Co-Authors: X. X. Huang, Xiaoqi YangAbstract:Abstract In this paper we investigate equivalences between an efficient solution of a bicriteria program and a lower envelope point of a certain image set of the bicriteria program. We also employ various kinds of approachabilities to characterize efficiency and proper efficiency for nonconvex bicriteria programs. In particular, nonlinear Lagranian functions are applied to construct dual problems and to study stability for the corresponding constrained Scalar Optimization problems. Under certain conditions we show that the finite approachability, proper efficiency, stability, and exact penalization of the relevant constrained Scalar Optimization problems are equivalent.
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The gap function of a convex multicriteria Optimization problem
European Journal of Operational Research, 1998Co-Authors: Guang-ya Chen, Xiaoqi YangAbstract:We generalize the concept of a gap function previously defined for a convex (Scalar) Optimization problem to a convex multicriteria Optimization problem and study its various properties.
Somayeh Sojoudi - One of the best experts on this subject based on the ideXlab platform.
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Interconnection-BasedPerformanceAnalysisforaClassof DecentralizedControllers
2020Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. A LQ cost function is deflned in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled e‐ciently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than flnding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and Scalar Optimization problems will both be equal to zero.
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Interconnection-based performance analysis for a class of decentralized controllers
Automatica, 2010Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and Scalar Optimization problems will both be equal to zero.
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Performance analysis for a class of decentralized control systems
2008 American Control Conference, 2008Co-Authors: Somayeh Sojoudi, Amir G. AghdamAbstract:This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo- hierarchical structure. Given such a system, one can use the existing techniques to design a decentralized controller for the reference hierarchical model, which is obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is often fascinating as far as the computational complexity is concerned, it may not provide a satisfactory performance for the original pseudo-hierarchical system. A LQ cost function is defined in order to evaluate the discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation should then be solved to compute this performance index. However, due to the large- scale nature of the system, this equation can by no means be handled for many real-world systems. Thus, attaining an upper bound on this cost function can be much more desirable than finding its exact value. For this purpose, a novel technique is proposed, which only requires solving a simple LMI Optimization problem with three variables. The problem is then reduced to a Scalar Optimization problem, for which an explicit solution is provided. It is also proved that as the pseudo-hierarchical system approaches its reference hierarchical model, the bounds obtained from the LMI and Scalar Optimization problems will both go to zero. In the particular case, when the two models are identical (i.e., the original system is exactly hierarchical), both upper bounds will be zero.
