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Jie Zhang - One of the best experts on this subject based on the ideXlab platform.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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An adaptive hybrid surrogate model
Structural and Multidisciplinary Optimization, 2012Co-Authors: Jie Zhang, Souma Chowdhury, Achille MessacAbstract:The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test Problems and to a complex Engineering Design Problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.
Achille Messac - One of the best experts on this subject based on the ideXlab platform.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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An adaptive hybrid surrogate model
Structural and Multidisciplinary Optimization, 2012Co-Authors: Jie Zhang, Souma Chowdhury, Achille MessacAbstract:The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test Problems and to a complex Engineering Design Problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.
Souma Chowdhury - One of the best experts on this subject based on the ideXlab platform.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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An adaptive hybrid surrogate model
Structural and Multidisciplinary Optimization, 2012Co-Authors: Jie Zhang, Souma Chowdhury, Achille MessacAbstract:The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test Problems and to a complex Engineering Design Problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.
Andy J. Keane - One of the best experts on this subject based on the ideXlab platform.
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Evolving Intervening Variables for Response Surface Approximations
2014Co-Authors: Prasanth B. Nair, Andy J. KeaneAbstract:Genetic Programming (GP) is a powerful string processing technique based on the Darwinian paradigm of natural selection. Although initially conceived with the more general aim of automatically producing computer code for com-plex tasks, it can also be used to evolve symbolic expressions, provided that we have a fitness criterion that measures the quality of an expression. In this paper we present a GP approach for generating functions in closed analytic form that map the input space of a complex function approximation Problem into one where the output is more amenable to linear regression. In other words, intervening variables are evolved in each dimension, such that the fi-nal approximation model has good generalization properties and at the same time, due to its linearity, can easily be incorporated into further calculations. We employ least squares and cross-validation error measures to derive the fit-ness function that drives the evolutionary process. Results are presented for a one-dimensional test Problem to illustrate some of the proposed ideas – this is followed by a more thorough empirical study, including multi-dimensional approximations and an Engineering Design Problem. Nomenclature x = vector of Design variables k = number of Design variables (Problem dimensionality) n = number of training points y = response y ̂ = approximated response xi = ith element of x ξ = vector of intervening variables z = vector of Design variables in the transformed space φ(.) = basis function c = basis function centre (k-vector) αi = the weights of the basis function predictor I
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Non-Stationary Kriging For Design Optimization
Engineering Optimization, 2011Co-Authors: David John James Toal, Andy J. KeaneAbstract:Traditional surrogate modelling techniques, such as kriging, have been employed quite effectively within Design optimizations. However, such models can fail to accurately reproduce non-stationary responses. The following paper explores the application of non-stationary kriging to Design optimization and attempts to determine its applicability with regard to the optimization of both stationary and non-stationary objective functions. A series of analytical test Problems and an Engineering Design Problem are used to compare the performance of non-stationary and adaptive partial non-stationary kriging to traditional stationary kriging.
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International Conference on Computational Science (1) - The Development of a Grid Based Engineering Design Problem Solving Environment
2002Co-Authors: A D Scurr, Andy J. KeaneAbstract:This paper gives an overview of the grid based Engineering Design Problem Solving Environment (PSE) being developed at Southampton University. Our current PSE is based on our Options optimiser and the Cardiff VCCE and XML component model. Essentially, VCCE provides a GUI to enable a user to setup and execute a computation by creating a task graph from available components via drag and drop operations on a sketchpad display.In order to provide an environment that more naturally meets the data-centric view of users, two major enhancements to the PSE are planned. The first concerns scheduling and task farming. The ultimate goal is to achieve within the PSE, an asynchronous computational workflow pattern where analysis tasks can seek to exploit whatever computational resources are available in various workstation clusters. The second enhancement concerns computational resource control and job control and the setting up of an Engineering Design Grid Portal.
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metamodeling techniques for evolutionary optimization of computationally expensive Problems promises and limitations
Genetic and Evolutionary Computation Conference, 1999Co-Authors: Mohammed Elbeltagy, Prasanth Nai, Andy J. KeaneAbstract:It is often the case in many Problems in science and Engineering that the analysis codes used are computationally very expensive. This can pose a serious impediment to the successful application of evolutionary optimization techniques. Metamodeling techniques present an enabling methodology for reducing the computational cost of such optimization Problems. We present here a general framework for coupling metamodeling techniques with evolutionary algorithms to reduce the computational burden of solving this class of optimization Problems. This framework aims to balance the concerns of optimization with that of Design of experiments. Experiments on test Problems and a practical Engineering Design Problem serve to illustrate our arguments. The practical limitations of this approach are also outlined.
Weiyang Tong - One of the best experts on this subject based on the ideXlab platform.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.
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A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation
Structural and Multidisciplinary Optimization, 2013Co-Authors: Souma Chowdhury, Weiyang Tong, Achille Messac, Jie ZhangAbstract:Engineering Design Problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous Design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive Design Problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional Design Problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test Problems: (i) a set of 9 unconstrained Problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) Problems. We also explore the applicability of this algorithm to a large scale Engineering Design Problem—-wind farm layout optimization.