The Experts below are selected from a list of 84675 Experts worldwide ranked by ideXlab platform
Martin Stoll - One of the best experts on this subject based on the ideXlab platform.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider a PDE-Constrained Optimization problem where an H1 regularization control term is introduced. We address both time-independent and time-dependent versions with both distributed and boundary control. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider PDE-Constrained Optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
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a low rank in time approach to pde Constrained Optimization
SIAM Journal on Scientific Computing, 2015Co-Authors: Martin Stoll, Tobias BreitenAbstract:The solution of time-dependent PDE-Constrained Optimization problems is a chal- lenging task in numerical analysis and applied mathematics. All-at-once discretizations and corre- sponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder. Here we introduce a low-rank in time technique that exploits the low-rank nature of the solution. The theoretical foundations for this approach originate in the numerical treatment of matrix equations and can be carried over to PDE-Constrained Optimization. We illustrate how three different problems can be rewritten and used within a low-rank Krylov subspace solver with appropriate preconditioning.
Andrew T Barker - One of the best experts on this subject based on the ideXlab platform.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider a PDE-Constrained Optimization problem where an H1 regularization control term is introduced. We address both time-independent and time-dependent versions with both distributed and boundary control. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider PDE-Constrained Optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
Yong Wang - One of the best experts on this subject based on the ideXlab platform.
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combining multiobjective Optimization with differential evolution to solve Constrained Optimization problems
IEEE Transactions on Evolutionary Computation, 2012Co-Authors: Yong Wang, Zixing CaiAbstract:During the past decade, solving Constrained Optimization problems with evolutionary algorithms has received considerable attention among researchers and practitioners. Cai and Wang's method (abbreviated as CW method) is a recent Constrained Optimization evolutionary algorithm proposed by the authors. However, its main shortcoming is that a trial-and-error process has to be used to choose suitable parameters. To overcome the above shortcoming, this paper proposes an improved version of the CW method, called CMODE, which combines multiobjective Optimization with differential evolution to deal with Constrained Optimization problems. Like its predecessor CW, the comparison of individuals in CMODE is also based on multiobjective Optimization. In CMODE, however, differential evolution serves as the search engine. In addition, a novel infeasible solution replacement mechanism based on multiobjective Optimization is proposed, with the purpose of guiding the population toward promising solutions and the feasible region simultaneously. The performance of CMODE is evaluated on 24 benchmark test functions. It is shown empirically that CMODE is capable of producing highly competitive results compared with some other state-of-the-art approaches in the community of Constrained evolutionary Optimization.
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multiobjective Optimization and hybrid evolutionary algorithm to solve Constrained Optimization problems
Systems Man and Cybernetics, 2007Co-Authors: Yong Wang, Zixing Cai, Guanqi Guo, Yuren ZhouAbstract:This paper presents a novel evolutionary algorithm (EA) for Constrained Optimization problems, i.e., the hybrid Constrained Optimization EA (HCOEA). This algorithm effectively combines multiobjective Optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations
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A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization
IEEE Transactions on Evolutionary Computation, 2006Co-Authors: Yong WangAbstract:A considerable number of Constrained Optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving Constrained Optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for Constrained Optimization is presented. In the process of population evolution, our algorithm is based on multiobjective Optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints
Tyrone Rees - One of the best experts on this subject based on the ideXlab platform.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider a PDE-Constrained Optimization problem where an H1 regularization control term is introduced. We address both time-independent and time-dependent versions with both distributed and boundary control. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
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a fast solver for an h1 regularized pde Constrained Optimization problem
Communications in Computational Physics, 2016Co-Authors: Andrew T Barker, Tyrone Rees, Martin StollAbstract:In this paper we consider PDE-Constrained Optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
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optimal solvers for pde Constrained Optimization
SIAM Journal on Scientific Computing, 2010Co-Authors: Tyrone Rees, Sue H Dollar, Andrew J WathenAbstract:Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, particularly in problems of design. The solution of such PDE-Constrained Optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2- and 3-dimensional Poisson problem is the PDE. The large-dimensional linear systems which result from discretization and which need to be solved are of saddle-point type. We introduce two optimal preconditioners for these systems, which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases. The theoretical proof indicates that these approaches may have much broader applicability for other PDEs.
Xinbo Geng - One of the best experts on this subject based on the ideXlab platform.
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data driven decision making in power systems with probabilistic guarantees theory and applications of chance Constrained Optimization
Annual Reviews in Control, 2019Co-Authors: Xinbo GengAbstract:Abstract Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-Constrained Optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-Constrained Optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. We first review three categories of existing methods to chance-Constrained Optimization: (1) scenario approach; (2) sample average approximation; and (3) robust Optimization based methods. Data-driven methods, which are not Constrained by any particular distributions of the underlying uncertainties, are of particular interest. Key results of the analytical reformulation approach for specific distributions are briefly discussed. We then provide a comprehensive review on the applications of chance-Constrained Optimization in power systems. Finally, this paper provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.
