Relevant bibliographies by topics / Multiobjective sparse optimization

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Multiobjective sparse optimization'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Multiobjective sparse optimization"

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Huang, Junhao, Weize Sun, and Lei Huang. "Joint Structure and Parameter Optimization of Multiobjective Sparse Neural Network." Neural Computation 33, no. 4 (2021): 1113–43. http://dx.doi.org/10.1162/neco_a_01368.

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This work addresses the problem of network pruning and proposes a novel joint training method based on a multiobjective optimization model. Most of the state-of-the-art pruning methods rely on user experience for selecting the sparsity ratio of the weight matrices or tensors, and thus suffer from severe performance reduction with inappropriate user-defined parameters. Moreover, networks might be inferior due to the inefficient connecting architecture search, especially when it is highly sparse. It is revealed in this work that the network model might maintain sparse characteristic in the early stage of the backpropagation (BP) training process, and evolutionary computation-based algorithms can accurately discover the connecting architecture with satisfying network performance. In particular, we establish a multiobjective sparse model for network pruning and propose an efficient approach that combines BP training and two modified multiobjective evolutionary algorithms (MOEAs). The BP algorithm converges quickly, and the two MOEAs can search for the optimal sparse structure and refine the weights, respectively. Experiments are also included to prove the benefits of the proposed algorithm. We show that the proposed method can obtain a desired Pareto front (PF), leading to a better pruning result comparing to the state-of-the-art methods, especially when the network structure is highly sparse.
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Cocchi, Guido, Tommaso Levato, Giampaolo Liuzzi, and Marco Sciandrone. "A concave optimization-based approach for sparse multiobjective programming." Optimization Letters 14, no. 3 (November 16, 2019): 535–56. http://dx.doi.org/10.1007/s11590-019-01506-w.

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Yue, Caitong, Jing Liang, Boyang Qu, Yuhong Han, Yongsheng Zhu, and Oscar D. Crisalle. "A novel multiobjective optimization algorithm for sparse signal reconstruction." Signal Processing 167 (February 2020): 107292. http://dx.doi.org/10.1016/j.sigpro.2019.107292.

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Wu, Yu, Yongshan Zhang, Xiaobo Liu, Zhihua Cai, and Yaoming Cai. "A multiobjective optimization-based sparse extreme learning machine algorithm." Neurocomputing 317 (November 2018): 88–100. http://dx.doi.org/10.1016/j.neucom.2018.07.060.

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Li, Hui, Qingfu Zhang, Jingda Deng, and Zong-Ben Xu. "A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization." IEEE Transactions on Neural Networks and Learning Systems 29, no. 5 (May 2018): 1716–31. http://dx.doi.org/10.1109/tnnls.2017.2677973.

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Chen, Zhi-Kun, Feng-Gang Yan, Xiao-Lin Qiao, and Yi-Nan Zhao. "Sparse Antenna Array Design for MIMO Radar Using Multiobjective Differential Evolution." International Journal of Antennas and Propagation 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/1747843.

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A two-stage design approach is proposed to address the sparse antenna array design for multiple-input multiple-output radar. In the first stage, the cyclic algorithm (CA) is used to establish a covariance matrix that satisfies the beam pattern approximation for a full array. In the second stage, a sparse antenna array with a beam pattern is designed to approximate the desired beam pattern. This paper focuses on the second stage. The optimization problem for the sparse antenna array design aimed at beam pattern synthesis is formulated, where the peak side lobe (PSL) is weakly constrained by the mean squared error. To solve this optimization problem, the differential evolution (DE) algorithm with multistrategy is introduced and PSL suppression is treated as an inequality constraint. However, in doing so, a new multiobjective optimization problem is created. To address this new problem, a multiobjective differential evolution algorithm based on Pareto technique is proposed. Numerical examples are provided to demonstrate the advantages of the proposed approach over state-of-the-art methods, including DE and genetic algorithm.
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Gebken, Bennet, and Sebastian Peitz. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems." Journal of Optimization Theory and Applications 188, no. 3 (January 13, 2021): 696–723. http://dx.doi.org/10.1007/s10957-020-01803-w.

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AbstractWe present an efficient descent method for unconstrained, locally Lipschitz multiobjective optimization problems. The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth multiobjective optimization problems with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy a necessary condition for Pareto optimality. Using a set of test problems, we compare our method with the multiobjective proximal bundle method by Mäkelä. The results indicate that our method is competitive while being easier to implement. Although the number of objective function evaluations is larger, the overall number of subgradient evaluations is smaller. Our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth problems. Finally, we demonstrate how our method can be used for solving sparse optimization problems, which are present in many real-life applications.
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Tian, Ye, Xingyi Zhang, Chao Wang, and Yaochu Jin. "An Evolutionary Algorithm for Large-Scale Sparse Multiobjective Optimization Problems." IEEE Transactions on Evolutionary Computation 24, no. 2 (April 2020): 380–93. http://dx.doi.org/10.1109/tevc.2019.2918140.

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Wang, Zhao, Jinxin Wei, Jianzhao Li, Peng Li, and Fei Xie. "Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing." Electronics 10, no. 17 (August 27, 2021): 2079. http://dx.doi.org/10.3390/electronics10172079.

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Mixed pixels inevitably appear in the hyperspectral image due to the low resolution of the sensor and the mixing of ground objects. Sparse unmixing, as an emerging method to solve the problem of mixed pixels, has received extensive attention in recent years due to its robustness and high efficiency. In theory, sparse unmixing is essentially a multiobjective optimization problem. The sparse endmember term and the reconstruction error term can be regarded as two objectives to optimize simultaneously, and a series of nondominated solutions can be obtained as the final solution. However, the large-scale spectral library poses a challenge due to the high-dimensional number of spectra, it is difficult to accurately extract a few active endmembers and estimate their corresponding abundance from hundreds of spectral features. In order to solve this problem, we propose an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) to solve the large-scale sparse unmixing problem. The single endmember in the spectral library is used to reconstruct the hyperspectral image, respectively, and the corresponding score of each endmember can be obtained. Then the endmember scores are used as a prior knowledge to guide the generation of the initial population and the new offspring. Finally, a series of nondominated solutions are obtained by the nondominated sorting and the crowding distances calculation. Experiments on two benchmark large-scale simulated data to demonstrate the effectiveness of the proposed algorithm.
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Fang, Xiaoping, Yaoming Cai, Zhihua Cai, Xinwei Jiang, and Zhikun Chen. "Sparse Feature Learning of Hyperspectral Imagery via Multiobjective-Based Extreme Learning Machine." Sensors 20, no. 5 (February 26, 2020): 1262. http://dx.doi.org/10.3390/s20051262.

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Hyperspectral image (HSI) consists of hundreds of narrow spectral band components with rich spectral and spatial information. Extreme Learning Machine (ELM) has been widely used for HSI analysis. However, the classical ELM is difficult to use for sparse feature leaning due to its randomly generated hidden layer. In this paper, we propose a novel unsupervised sparse feature learning approach, called Evolutionary Multiobjective-based ELM (EMO-ELM), and apply it to HSI feature extraction. Specifically, we represent the task of constructing the ELM Autoencoder (ELM-AE) as a multiobjective optimization problem that takes the sparsity of hidden layer outputs and the reconstruction error as two conflicting objectives. Then, we adopt an Evolutionary Multiobjective Optimization (EMO) method to solve the two objectives, simultaneously. To find the best solution from the Pareto solution set and construct the best trade-off feature extractor, a curvature-based method is proposed to focus on the knee area of the Pareto solutions. Benefited from the EMO, the proposed EMO-ELM is less prone to fall into a local minimum and has fewer trainable parameters than gradient-based AEs. Experiments on two real HSIs demonstrate that the features learned by EMO-ELM not only preserve better sparsity but also achieve superior separability than many existing feature learning methods.
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Dissertations / Theses on the topic "Multiobjective sparse optimization"

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Levato, Tommaso. "Algorithms for ell_0-norm Optimization Problems." Doctoral thesis, 2020. http://hdl.handle.net/2158/1188438.

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Spalke, Tobias [Verfasser]. "Application of multiobjective optimization concepts in inverse radiotherapy planning / put forward by Tobias Spalke." 2009. http://d-nb.info/995810087/34.

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Books on the topic "Multiobjective sparse optimization"

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United States. National Aeronautics and Space Administration., ed. Multiobjective optimization of hybrid regenerative life support technologies, (topic D, technology assessment): NASA interim progress report. [Washington, DC: National Aeronautics and Space Administration, 1995.

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Multiobjective optimization of hybrid regenerative life support technologies, (topic D, technology assessment): NASA interim progress report. [Washington, DC: National Aeronautics and Space Administration, 1995.

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Book chapters on the topic "Multiobjective sparse optimization"

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Li, Yangyang, Xiaoyu Bai, Xiaoxu Liang, and Licheng Jiao. "Sparse Restricted Boltzmann Machine Based on Multiobjective Optimization." In Lecture Notes in Computer Science, 899–910. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68759-9_73.

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Tenente, Marcos, Carla Henriques, Álvaro Gomes, Patrícia Pereira da Silva, and António Trigo. "Multiple Impacts of Energy Efficiency Technologies in Portugal." In Springer Proceedings in Political Science and International Relations, 131–46. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-18161-0_9.

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AbstractPortuguese programs aimed at fostering Energy Efficiency (EE) measures often rely on cost–benefit approaches only considering the use phase and neglecting other potential impacts generated. Therefore, this work suggests a novel methodological framework by combining Hybrid Input–Output Lifecycle Analysis (HIO-LCA) with the Portuguese seasonal method for computing the households’ energy needs. A holistic assessment of the energy, economic, environmental, and social impacts connected with the adoption of EE solutions is conducted aimed at supporting decision-makers (DMs) in the design of suitable funding policies. For this purpose, 109,553 EE packages have been created by combining distinct thermal insulation options for roofs and façades, with the replacement of windows, also considering the use of space heating and cooling and domestic heating water systems. The findings indicate that it is possible to confirm that various energy efficiency packages can be used to achieve the best performance for most of the impacts considered. Specifically, savings-to-investment ratio (SIR), Greenhouse gases (GHG), and energy payback times (GPBT and EPBT) present the best performances for packages that exclusively employ extruded polystyrene (XPS) for roof insulation (packages 151 and 265). However, considering the remaining impacts created by the investment in energy efficiency measures, their best performances are obtained when roof and façades insulation is combined with the use of space heating and cooling and DHW systems to replace the existing equipment. If biomass is assumed to be carbon–neutral, solution 18,254 yields the greatest reduction in GHG emissions. Given these trade-offs, it is evident that multiobjective optimization methods employing the impacts and benefits assessed are crucial for helping DMs design future EE programs following their preferences.
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Ganesan, T., I. Elamvazuthi, and P. Vasant. "Swarm Intelligence for Multiobjective Optimization of Extraction Process." In Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics, 516–44. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9644-0.ch020.

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Multi objective (MO) optimization is an emerging field which is increasingly being implemented in many industries globally. In this work, the MO optimization of the extraction process of bioactive compounds from the Gardenia Jasminoides Ellis fruit was solved. Three swarm-based algorithms have been applied in conjunction with normal-boundary intersection (NBI) method to solve this MO problem. The gravitational search algorithm (GSA) and the particle swarm optimization (PSO) technique were implemented in this work. In addition, a novel Hopfield-enhanced particle swarm optimization was developed and applied to the extraction problem. By measuring the levels of dominance, the optimality of the approximate Pareto frontiers produced by all the algorithms were gauged and compared. Besides, by measuring the levels of convergence of the frontier, some understanding regarding the structure of the objective space in terms of its relation to the level of frontier dominance is uncovered. Detail comparative studies were conducted on all the algorithms employed and developed in this work.
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Ohsaki, M., T. Ogawa, and R. Tateishi. "Multiobjective Shape Optimization of Shells Considering Roundness and Elastic Stiffness." In Space Structures 5, 1: 377–385. Thomas Telford Publishing, 2002. http://dx.doi.org/10.1680/ss5v1.31739.0041.

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Manne, Janga Reddy. "Multiobjective Optimization in Water and Environmental Systems Management- MODE Approach." In Advances in Computer and Electrical Engineering, 120–36. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9479-8.ch004.

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Many real world problems are characterized by multiple goals, often conflicting in nature and compete with one another. Multi-objective optimization problems (MOOPs) require the simultaneous optimization of several non-commensurable and conflicting objectives. In the past, several studies have used conventional approaches to solve the MOOPs by adopting weighted approach or constrained approach, which may face difficulties while generating Pareto optimal solutions, if optimal solution lies on non-convex or disconnected regions of the objective function space. An effective algorithm should have an ability to learn from earlier performance to direct proper selection of weights for further evolutions. To achieve these goals, multi-objective evolutionary algorithms (MOEAs) have become effective means in recent past, which can generate a population of solutions in each iteration and offer a set of alternatives in a single run. This chapter presents an effective MOEA, namely multi-objective differential evolution (MODE) for problems of solving water, environmental systems.
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Kuyucu, Tüze, Ivan Tanev, and Katsunori Shimohara. "Efficient Evolution of Modular Robot Control via Genetic Programming." In Engineering Creative Design in Robotics and Mechatronics, 59–85. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-4225-6.ch005.

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In Genetic Programming (GP), most often the search space grows in a greater than linear fashion as the number of tasks required to be accomplished increases. This is a cause for one of the greatest problems in Evolutionary Computation (EC): scalability. The aim of the work presented here is to facilitate the evolution of control systems for complex robotic systems. The authors use a combination of mechanisms specifically designed to facilitate the fast evolution of systems with multiple objectives. These mechanisms are: a genetic transposition inspired seeding, a strongly-typed crossover, and a multiobjective optimization. The authors demonstrate that, when used together, these mechanisms not only improve the performance of GP but also the reliability of the final designs. They investigate the effect of the aforementioned mechanisms on the efficiency of GP employed for the coevolution of locomotion gaits and sensing of a simulated snake-like robot (Snakebot). Experimental results show that the mechanisms set forth contribute to significant increase in the efficiency of the evolution of fast moving and sensing Snakebots as well as the robustness of the final designs.
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Conference papers on the topic "Multiobjective sparse optimization"

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Lee, Yong Hoon, R. E. Corman, Randy H. Ewoldt, and James T. Allison. "A Multiobjective Adaptive Surrogate Modeling-Based Optimization (MO-ASMO) Framework Using Efficient Sampling Strategies." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67541.

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A novel multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework is proposed to utilize a minimal number of training samples efficiently for sequential model updates. All the sample points are enforced to be feasible, and to provide coverage of sparsely explored sparse design regions using a new optimization subproblem. The MO-ASMO method only evaluates high-fidelity functions at feasible sample points. During an exploitation sample phase, samples are selected to enhance solution accuracy rather than the global exploration. Sampling tasks are especially challenging for multiobjective optimization; for an n-dimensional design space, a strategy is required for generating model update sample points near an (n − 1)-dimensional hypersurface corresponding to the Pareto set in the design space. This is addressed here using a force-directed layout algorithm, adapted from graph visualization strategies, to distribute feasible sample points evenly near the estimated Pareto set. Model validation samples are chosen uniformly on the Pareto set hypersurface, and surrogate model estimates at these points are compared to high-fidelity model responses. All high-fidelity model evaluations are stored for later use to train an updated surrogate model. The MO-ASMO algorithm, along with the set of new sampling strategies, are tested using two mathematical and one realistic engineering problems. The second mathematical test problems is specifically designed to test the limits of this algorithm to cope with very narrow, non-convex feasible domains. It involves oscillatory objective functions, giving rise to a discontinuous set of Pareto-optimal solutions. Also, the third test problem demonstrates that the MO-ASMO algorithm can handle a practical engineering problem with more than 10 design variables and black-box simulations. The efficiency of the MO-ASMO algorithm is demonstrated by comparing the result of two mathematical problems to the results of the NSGA-II algorithm in terms of the number of high fidelity function evaluations, and is shown to reduce total function evaluations by several orders of magnitude when converging to the same Pareto sets.
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Rangavajhala, Sirisha, Anoop A. Mullur, and Achille Messac. "Equality Constraints in Multiobjective Robust Design Optimization: Implications and Tradeoffs." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79961.

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In the present paper, we explore issues in handling equality constraints in multiobjective robust design optimization (RDO) problems. Satisfying an equality constraint exactly under uncertainty can be a challenging task. The challenge of handling equality constraints is compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the performance and the variation of the performance for each design objective in a multiobjective RDO problem is a complex task by itself. Equality constraints add to this complexity because of the additional tradeoffs that are introduced between constraint satisfaction under uncertainty and multiobjective performance. Satisfying equality constraints at their mean values, an approach typically followed, could lead to undesirable results. In this paper, we study the implications of equality constraint satisfaction in a multiobjective RDO problem, and provide a new problem formulation approach to resolve the above discussed tradeoffs. We illustrate that the proposed formulation can be used as an effective multiobjective design space exploration tool, with emphasis on equality constraint satisfaction under uncertainty. We present numerical examples to illustrate our theoretical developments.
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Simov, Peter, and Scott Ferguson. "Investigating the Significance of “One-to-Many” Mappings in Multiobjective Optimization." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28689.

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Significant research has focused on multiobjective design optimization and negotiating trade-offs between conflicting objectives. Many times, this research has referred to the possibility of attaining similar performance from multiple, unique design combinations. While such occurrences may allow for greater design freedom, their significance has yet to be quantified for trade-off decisions made in the design space (DS). In this paper, we computationally explore which regions of the performance space (PS) exhibit “one-to-many” mappings back to the DS, and examine the behavior and validity of the corresponding region associated with this mapping. Regions of interest in the PS and DS are identified and generated using indifference thresholds to effectively “discretize” both spaces. The properties analyzed in this work are a mapped region’s location in the PS and DS and the total hypervolume of the mappings. Our proposed approach is demonstrated on two different multiobjective engineering problems. The results indicate that one-to-many mappings occur in engineering design problems, and that while these mappings can result in significant design space freedom, they often result in notable performance sacrifice.
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Mattson, Christopher A., Vicky Lofthouse, and Tracy Bhamra. "Exploring Decision Tradeoffs in Sustainable Design." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47295.

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Sustainable design involves three essential areas: economic sustainability, environmental sustainability, and social sustainability. For even the simplest of products, the complexities of these three areas and their tradeoffs cause decision-making transparency to be lost in most practical situations. The existing field of multiobjective optimization offers a natural framework to explore the tradeoffs in the sustainability space (defined by economic, environmental, and social sustainability issues), thus offering both the designer and the decision makers a means of understanding the sustainability tradeoffs. To facilitate this, a decision making approach that capitalizes on the principles and power of multiobjective optimization is presented. This paper concludes that sustainable development can indeed benefit from tradeoff characterization using multiobjective optimization techniques — even when using only basic models of sustainability. Interestingly, the unique characteristics of the three essential sustainable development areas lead to an alternative view of some traditional multiobjective optimization concepts, such as weak Pareto optimality. The sustainable engineering design of a hypodermic needle is presented as a simple hypothetical example for method demonstration and discussion.
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Curtis, Shane K., Braden J. Hancock, and Christopher A. Mattson. "Use Scenarios for Design Space Exploration With a Dynamic Multiobjective Optimization Formulation." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71039.

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In a recent publication, we presented a new strategy for engineering design and optimization, which we termed formulation space exploration. The formulation space for an optimization problem is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into this new space, the solution to any optimization problem is no longer predefined by the optimization problem formulation. This method allows a designer to both diverge the design space during conceptual design and converge onto a solution as more information about the design objectives and constraints becomes available. Additionally, we introduced a new way to formulate multiobjective optimization problems, allowing the designer to change and update design objectives, constraints, and variables in a simple, fluid manner that promotes exploration. In this paper, we investigate three use scenarios where formulation space exploration can be utilized in the early stages of design when it is possible to make the greatest contributions to development projects. Specifically, we look at s-Pareto frontier generation in the formulation space, formulation space boundary exploration, and a new way to perform inverse optimization. The benefits of these methods are illustrated with the conceptual design of an impact driver.
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Rangavajhala, Sirisha, and Achille Messac. "Decision Making and Constraint Tradeoff Visualization for Design Under Uncertainty." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35385.

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In design optimization problems under uncertainty, two conflicting issues are generally of interest to the designer: feasibility and optimality. In this research, we adopt the philosophy that design, especially under uncertainty, is a decision making process, where the associated tradeoffs can be conveniently understood using multiobjective optimization. The importance of constraint feasibility and the associated tradeoffs, especially in the presence of equality constraints, is examined in this paper. We propose a three-step decision making framework that facilitates effective decision making under uncertainty: (1) formulating a multiobjective problem that effectively models the tradeoffs under uncertainty, (2) generating design alternatives by solving the proposed multiobjective robust design formulation, and (3) choosing a final design using filtering and constraint uncertainty visualization schemes. The proposed framework can be used to systematically explore the design space from a constraint tradeoff perspective. A tolerance synthesis example is used to illustrate the proposed decision making process.
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Lautenschlager, Uwe, Hans A. Eschenauer, and Farrokh Mistree. "Multiobjective Flywheel Design: A DOE-Based Concept Exploration Task." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3961.

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Abstract In structural design, expensive function evaluations can be replaced by accurate function approximations to facilitate the effective solution of multiobjective problems. In this paper we address the question: How can we solve multiobjective shape optimization problems effectively using a Design-of-Experiments (DOE) -based approach? To answer this question we address issues of creating non-orthogonal experimental designs, when dependencies among the parameters that represent shape functions are present. A screening strategy is used to gain knowledge about the structural behavior within the design space and the trade-off among multiple design objectives is efficiently modeled through employing response surfaces during design optimization. The shape optimization of a flywheel where two conflicting design goals are present is used to illustrate the approach. Our focus is on the method rather than the results per se.
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Grignon, Pierre M., and Georges M. Fadel. "Multiobjective Optimization by Iterative Genetic Algorithm." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8576.

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Abstract This paper presents a method to simultaneously produce multiple solutions to unconstrained multi-objective optimization problems. The proposed methodology uses populations of sets instead of populations of individuals and iterative calls to a Genetic Algorithm (IGA) to obtain a set of solutions spread across the Pareto set in the objective space. The superiority of such an approach to single run, conventional population Pareto GAs is shown. The various difficulties of the algorithm and the methods used to overcome them are detailed. Finally, the paper expands upon how this method can be used with or without user inputs, and shows an analysis of its performance by applying it to a succession of increasingly difficult problems, identifying its range of application.
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Ferguson, Scott, Ashwin Gurnani, Joseph Donndelinger, and Kemper Lewis. "A Study of Convergence and Mapping in Multiobjective Optimization Problems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84852.

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In this paper, we investigate the issue of convergence in multiobjective optimization problems when using a Multi-Objective Genetic Algorithm (MOGA) to determine the set of Pareto optimal solutions. Additionally, given a Pareto set for a multi-objective problem, the mapping between the performance and design space is studied to determine design variable configurations for a given set of performance specifications. The advantage of this study is that the design variable information is obtained without having to repeat system analyses. The tools developed in this paper have been applied to develop a Technical Feasibility Model (TFM) used by General Motors as well as a simple multiobjective optimization problem in this paper. The multi-objective problem is primarily used to illustrate the developed methodology.
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Eddy, John, and Kemper E. Lewis. "Visualization of Multidimensional Design and Optimization Data Using Cloud Visualization." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34130.

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As our ability to generate more and more data for increasingly large engineering models improves, the need for methods for managing that data becomes greater. Information management from a decision-making perspective involves being able to capture and represent significant information to a designer so that they can make effective and efficient decisions. However, most visualization techniques used in engineering, such as graphs and charts, are limited to two-dimensional representations and at most three-dimensional representations. In this paper, we present a new visualization technique to capture and represent engineering information in a multidimensional context. The new technique, Cloud Visualization, is based upon representing sets of points as clouds in both the design and performance spaces. The technique is applicable to both single and multiobjective optimization problems and the relevant issues with each type of problem are discussed. A multiobjective case study is presented to demonstrate the application and usefulness of the Cloud Visualization techniques.
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Reports on the topic "Multiobjective sparse optimization"

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Allen, J. C., and D. Acero. Multiobjective Optimization on Function Spaces: A Kolmogorov Approach. Fort Belvoir, VA: Defense Technical Information Center, July 2005. http://dx.doi.org/10.21236/ada439625.

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