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COOPERATION AND COMPETITION IN MULTIDISCIPLINARY OPTIMIZATION Application to the aerostructural aircraft wing shape optimization
, 2011
"... Abstract This article aims to contribute to numerical strategies for PDEconstrained multiobjective optimization, with a particular emphasis on CPUdemanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that sha ..."
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Abstract This article aims to contribute to numerical strategies for PDEconstrained multiobjective optimization, with a particular emphasis on CPUdemanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that share the same set of design variables. Merits and shortcuts of the mostcommonly used algorithms to identify, or approximate, the Pareto set are reviewed, prior to focusing on the approach by Nash games. A strategy is proposed for the treatment of twodiscipline optimization problems in which one discipline, the primary discipline, is preponderant, or fragile. Then, it is recommended to identify, in a first step, the optimum of this discipline alone using the whole set of design variables. Then, an orthogonal basis is constructed based on the evaluation at convergence of the Hessian matrix of the primary criterion and constraint gradients. This basis is used to split the working design space into two supplementary subspaces to be assigned, in a second step, to two virtual players in competition in an adapted Nash game, devised to reduce a secondary criterion while causing the least degradation to the first. The formulation is proved to potentially provide a set of Nash equilibrium solutions originating from the original singlediscipline optimum point by smooth
Comparison between two multi objective optimization algorithms: PAES and MGDA. Testing MGDA on Kriging metamodels
"... Désidéri and Régis Duvigneau Abstract In multiobjective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES [4], NSGAII [3], etc), have been proposed in the literature and proved to be succe ..."
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Désidéri and Régis Duvigneau Abstract In multiobjective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES [4], NSGAII [3], etc), have been proposed in the literature and proved to be successful to identify the Pareto set. However, these derivativefree algorithms are very demanding in computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced presently. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm (MGDA) is defined as a generalization of the steepestdescent method and compared with PAES by numerical experiments. Using MGDA on a multi objective optimization problem requires the evaluation of a large number of points with regard to criteria, and their gradients. In the particular case of CFD problems, each point evaluation is very costly. Thus here we also propose to construct metamodels and to calculate approximate gradients by local finite differences. 1
Tempo: Robust and SelfTuning Resource Management in Multitenant Parallel Databases *
"... ABSTRACT Multitenant database systems have a component called the Resource Manager, or RM that is responsible for allocating resources to tenants. RMs today do not provide direct support for performance objectives such as: "Average job response time of tenant A must be less than two minutes&q ..."
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ABSTRACT Multitenant database systems have a component called the Resource Manager, or RM that is responsible for allocating resources to tenants. RMs today do not provide direct support for performance objectives such as: "Average job response time of tenant A must be less than two minutes", or "No more than 5% of tenant B's jobs can miss the deadline of 1 hour." Thus, DBAs have to tinker with the RM's lowlevel configuration settings to meet such objectives. We propose a framework called Tempo that brings simplicity, selftuning, and robustness to existing RMs. Tempo provides a simple interface for DBAs to specify performance objectives declaratively, and optimizes the RM configuration settings to meet these objectives. Tempo has a solid theoretical foundation which gives key robustness guarantees. We report experiments done on Tempo using production traces of dataprocessing workloads from companies such as Facebook and Cloudera. These experiments demonstrate significant improvements in meeting desired performance objectives over RM configuration settings specified by human experts.
Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
, 2012
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DOI: 10.1007/9789400752887 Comparison between two multi objective optimization algorithms: PAES and MGDA. Testing MGDA on Kriging metamodels
, 2012
"... Abstract In multiobjective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES [4], NSGAII [3], etc), have been proposed in the literature and proved to be successful to identify the Pareto set. ..."
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Abstract In multiobjective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES [4], NSGAII [3], etc), have been proposed in the literature and proved to be successful to identify the Pareto set. However, these derivativefree algorithms are very demanding in computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced presently. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm (MGDA) is defined as a generalization of the steepestdescent method and compared with PAES by numerical experiments. Using MGDA on a multi objective optimization problem requires the evaluation of a large number of points with regard to criteria, and their gradients. In the particular case of CFD problems, each point evaluation is very costly. Thus here we also propose to construct metamodels and to calculate approximate gradients by local finite differences. 1
REDUCED SAMPLING AND INCOMPLETE SENSITIVITY FOR LOWCOMPLEXITY ROBUST PARAMETRIC OPTIMIZATION
, 2013
"... Abstract. The paper considers robust parametric optimization problems using multipoint formulations and makes the link with momentum based formulations. Optimal sampling issues are discussed and a procedure is proposed to quantify the confidence level on the robustness of the design. We also discus ..."
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Abstract. The paper considers robust parametric optimization problems using multipoint formulations and makes the link with momentum based formulations. Optimal sampling issues are discussed and a procedure is proposed to quantify the confidence level on the robustness of the design. We also discuss incomplete sensitivity evaluations to take into account the computational complexity constraint. This permits to take advantage of what was previously developed for efficient monopoint design where the cost of the optimization is comparable to one state evaluations. The proposed algorithm is fully parallel and the timetosolution is comparable to monopoint situations. Concepts are introduced through simple examples and the paper ends with the design of the shape of an aircraft robust over a range of transverse winds. 1.
ProjectTeam Opale Optimization and Control, Numerical Algorithms and Integration of Multidisciplinary Complex P.D.E. Systems
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A COOPERATIVE ALGORITHM FOR MULTIOBJECTIVE OPTIMIZATION: MULTIPLEGRADIENT DESCENT ALGORITHM (MGDA)
"... The MultipleGradient Descent Algorithm (MGDA) has been proposed and tested for the treatment of multiobjective differentiable optimization. Originally introduced in [1], the method has been tested and reformulated in [4]. Its efficacy to identify the Pareto front has been demonstrated in [5], in c ..."
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The MultipleGradient Descent Algorithm (MGDA) has been proposed and tested for the treatment of multiobjective differentiable optimization. Originally introduced in [1], the method has been tested and reformulated in [4]. Its efficacy to identify the Pareto front has been demonstrated in [5], in comparison with an evolutionary strategy. Recently, a variant, MGDAII, has been proposed in which the descent direction is calculated by a direct procedure [3] based on a GramSchmidt orthogonalization process (GSP) with special normalization. This algorithm was tested in the context of a simulation by domain partitioning, as a technique to match the different interface components concurrently [2]. The experimentation revealed the importance of scaling, and a slightly modified normalization procedure was proposed (MGDAIIb). Two variants have since been proposed. The first, MGDAIII, realizes two enhancements. Firstly, the GSP is conducted incompletely whenever a test reveals that the current estimate of the direction of search is adequate also w.r.t. the gradients not yet taken into account; this improvement simplifies the identification of the search direction when the gradients point roughly in the same direction, and makes the Fréchet derivative common to several objectivefunctions larger. Secondly, the order in which the different gradients are considered in the GSP is defined in a unique way devised to favor an incomplete GSP. In the second variant, MGDAIV, the question of scaling is addressed when the Hessians are known. A variant is also proposed in which the Hessians are estimated by the BroydenFletcher GoldfarbShanno
A COMPETITIVE ALGORITHM FOR TWOOBJECTIVE OPTIMIZATION: NASH GAME WITH TERRITORY SPLITTING
"... This contribution pertains to PDEconstrained multiobjective optimization, with a par ticular emphasis on CPUdemanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that share the same set of design variables. ..."
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This contribution pertains to PDEconstrained multiobjective optimization, with a par ticular emphasis on CPUdemanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that share the same set of design variables. A strategy has been proposed [3] for the treatment of twodiscipline optimization problems in which one discipline, the primary discipline, is preponderant, or fragile. It is recommended to identify, in a first step, the optimum of this discipline alone using the whole set of design variables. Then, an orthogonal basis is constructed based on the evaluation at convergence of the Hessian matrix of the primary criterion and constraint gradients. This basis is used to split the working design space into two supplementary sub spaces to be assigned, in a second step, to two virtual players in competition in an adapted Nash game, devised to reduce a secondary criterion while causing the least degradation to the first. The formulation is proved to potentially provide a set of Nash equilibrium solutions originating from the original singlediscipline optimum point by smooth continuation, thus introducing competition gradually. This approach is first demonstrated over a testcase of aerostructural aircraft wing shape optimization, in which the eigensplitbased optimization reveals clearly superior [2] [4]. A significant reduction of 8 % of the structural criterion was realized while maintaining the flowfield configuration close to optimality (drag increase ¡ 3 %), by an automatic procedure of orthogonal decomposition of the parameter space (see Figure 1). Other examples of