Artículos de revistas: "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 (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 (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 (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 (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 (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 (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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Liang, Lei, Yachao Jiang, Jialing Liu, Hailin Li, and Jianjiang Zhou. "Pattern Synthesis of Time-Modulated Sparse Array by an OPM-CVX Algorithm." Mathematical Problems in Engineering 2020 (April 14, 2020): 1–15. http://dx.doi.org/10.1155/2020/5491921.

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This paper addresses the constrained multiobjective optimization problem of time-modulated sparse arrays. The synthesis objective is to find an optimal element arrangement and associated excitation strategy of sparse arrays, which realize the balance of radiation power and sideband suppression performance with minimum number of elements, and suppress side lobe level simultaneously. A novel hybrid algorithm based on orthogonal perturbation method and convex optimization (OPM-CVX) for the synthesis of time-modulated sparse antenna array is presented in this paper. In order to satisfy the main lobe beamforming and side lobe suppression of sparse arrays, the proposed method optimizes element positions with minimum array numbers by orthogonal perturbation method and optimizes excitations of array element with dynamic range ratio constraint by convex optimization. Furthermore, a trapezoidal pulse time-modulated switching function is proposed to find the balance of radiation power and sideband suppression performance. The numerical results indicate that the proposed algorithm can be an effective approach for synthesis problems of time-modulated sparse arrays.

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Xu, Xinlin, Zhongbo Hu, Qinghua Su, and Zenggang Xiong. "Multiobjective Collective Decision Optimization Algorithm for Economic Emission Dispatch Problem." Complexity 2018 (November 13, 2018): 1–20. http://dx.doi.org/10.1155/2018/1027193.

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The collective decision optimization algorithm (CDOA) is a new stochastic population-based evolutionary algorithm which simulates the decision behavior of human. In this paper, a multiobjective collective decision optimization algorithm (MOCDOA) is first proposed to solve the environmental/economic dispatch (EED) problem. MOCDOA uses three novel learning strategies, that is, a leader-updating strategy based on the maximum distance of each solution in an external archive, a wise random perturbation strategy based on the sparse mark around a leader, and a geometric center-updating strategy based on an extreme point. The proposed three learning strategies benefit the improvement of the uniformity and the diversity of Pareto optimal solutions. Several experiments have been carried out on the IEEE 30-bus 6-unit test system and 10-unit test system to investigate the performance of MOCDOA. In terms of extreme solutions, compromise solution, and three metrics (SP, HV, and CM), MOCDOA is compared with other existing multiobjective optimization algorithms. It is demonstrated that MOCDOA can generate the well-distributed and the high-quality Pareto optimal solutions for the EED problem and has the potential to solve the multiobjective optimization problems of other power systems.

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Hu, Peng, Xiaobo Liu, Yaoming Cai, and Zhihua Cai. "Band Selection of Hyperspectral Images Using Multiobjective Optimization-Based Sparse Self-Representation." IEEE Geoscience and Remote Sensing Letters 16, no. 3 (2019): 452–56. http://dx.doi.org/10.1109/lgrs.2018.2872540.

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Feng, Dan, Mingyang Zhang, and Shanfeng Wang. "Multipopulation Particle Swarm Optimization for Evolutionary Multitasking Sparse Unmixing." Electronics 10, no. 23 (2021): 3034. http://dx.doi.org/10.3390/electronics10233034.

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Recently, the multiobjective evolutionary algorithms (MOEAs) have been designed to cope with the sparse unmixing problem. Due to the excellent performance of MOEAs in solving the NP hard optimization problems, they have also achieved good results for the sparse unmixing problems. However, most of these MOEA-based methods only deal with a single pixel for unmixing and are subjected to low efficiency and are time-consuming. In fact, sparse unmixing can naturally be seen as a multitasking problem when the hyperspectral imagery is clustered into several homogeneous regions, so that evolutionary multitasking can be employed to take advantage of the implicit parallelism from different regions. In this paper, a novel evolutionary multitasking multipopulation particle swarm optimization framework is proposed to solve the hyperspectral sparse unmixing problem. First, we resort to evolutionary multitasking optimization to cluster the hyperspectral image into multiple homogeneous regions, and directly process the entire spectral matrix in multiple regions to avoid dimensional disasters. In addition, we design a novel multipopulation particle swarm optimization method for major evolutionary exploration. Furthermore, an intra-task and inter-task transfer and a local exploration strategy are designed for balancing the exchange of useful information in the multitasking evolutionary process. Experimental results on two benchmark hyperspectral datasets demonstrate the effectiveness of the proposed method compared with the state-of-the-art sparse unmixing algorithms.

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Haan, Sebastian, Fabio Ramos, and R. Dietmar Müller. "Multiobjective Bayesian optimization and joint inversion for active sensor fusion." GEOPHYSICS 86, no. 1 (2021): ID1—ID17. http://dx.doi.org/10.1190/geo2019-0460.1.

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A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and how to minimize the total cost. We have developed a probabilistic framework for multiobjective optimization and inverse problems given an expensive cost function for allocating new measurements. This new method is devised to jointly solve multilinear forward models of 2D sensor data and 3D geophysical properties using sparse Gaussian process kernels while taking into account the cross-variances of different parameters. Multiple optimization strategies are tested and evaluated on a set of synthetic and real geophysical data. We determine the advantages on a specific example of a joint inverse problem, recommending where to place new drill-core measurements given 2D gravity and magnetic sensor data; the same approach can be applied to a variety of remote sensing problems with linear forward models — ranging from constraints limiting surface access for data acquisition to adaptive multisensor positioning.

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Jiao, Shengxi, Lu Wen, and Haitao Guo. "Incomplete angle reconstruction algorithm with the sparse optimization and the image optimal criterions." International Journal of Advanced Robotic Systems 17, no. 3 (2020): 172988142091697. http://dx.doi.org/10.1177/1729881420916974.

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To solve the problem of artifact and image degradation caused by incomplete angle projection, this article presents an incomplete angle reconstruction algorithm based on sparse optimization and image optimization criterion (SO-IOC). Firstly, the joint objective function model is established based on the projection sparsity and the natural features of images. Secondly, by means of the idea of alternating direction method of multipliers, the augmented Lagrange method is used to decompose the reconstruction model into simple subproblems and the modified genetic algorithm is used for solving those subproblems. Finally, a multiobjective optimization operation is carried out to coordinate and select the candidate solutions to improve the quality of the reconstructed images. The algebraic reconstruction technique algorithm and the Split Bregman algorithm are compared with the SO-IOC algorithm. In the compared process, the mean relative error and the peak signal-to-noise ratio are used. The experimental results show the SO-IOC algorithm is best among the above three algorithms.

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WEI, JINGXUAN, and YUPING WANG. "AN INFEASIBLE ELITIST BASED PARTICLE SWARM OPTIMIZATION FOR CONSTRAINED MULTIOBJECTIVE OPTIMIZATION AND ITS CONVERGENCE." International Journal of Pattern Recognition and Artificial Intelligence 24, no. 03 (2010): 381–400. http://dx.doi.org/10.1142/s021800141000797x.

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In this paper, an infeasible elitist based particle swarm optimization is proposed for solving constrained optimization problems. Firstly, an infeasible elitist preservation strategy is proposed, which keeps some infeasible solutions with smaller rank values at the early stage of evolution regardless of how large the constraint violations are, and keep some infeasible solutions with smaller constraint violations and rank values at the later stage of evolution. In this manner, the true Pareto front will be found easier. Secondly, in order to find a set of diversity and uniformly distributed Pareto optimal solutions, a new crowding distance function is designed. It can assign large function values not only for the particles located in the sparse regions of the objective space but also for the crowded particles located near to the boundary of the Pareto front as well. Thirdly, a new mutation operator with two phases is proposed. In the first phase, the particles whose constraint violations are less than the threshold value will be used to compute the total force, then the force will be used as a mutation direction, being helpful to find the better solutions along this direction. In order to guarantee the convergence of the algorithm, the second phase of mutation is proposed. Finally, the convergence of the algorithm is proved. The comparative study shows that the proposed algorithm can generate widespread and uniformly distributed Pareto fronts and outperforms those compared algorithms.

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Chen, Yu, Dong Chen, and Xiufen Zou. "Inference of Biochemical S-Systems via Mixed-Variable Multiobjective Evolutionary Optimization." Computational and Mathematical Methods in Medicine 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/3020326.

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Inference of the biochemical systems (BSs) via experimental data is important for understanding how biochemical components in vivo interact with each other. However, it is not a trivial task because BSs usually function with complex and nonlinear dynamics. As a popular ordinary equation (ODE) model, the S-System describes the dynamical properties of BSs by incorporating the power rule of biochemical reactions but behaves as a challenge because it has a lot of parameters to be confirmed. This work is dedicated to proposing a general method for inference of S-Systems by experimental data, using a biobjective optimization (BOO) model and a specially mixed-variable multiobjective evolutionary algorithm (mv-MOEA). Regarding that BSs are sparse in common sense, we introduce binary variables indicating network connections to eliminate the difficulty of threshold presetting and take data fitting error and the L0-norm as two objectives to be minimized in the BOO model. Then, a selection procedure that automatically runs tradeoff between two objectives is employed to choose final inference results from the obtained nondominated solutions of the mv-MOEA. Inference results of the investigated networks demonstrate that our method can identify their dynamical properties well, although the automatic selection procedure sometimes ignores some weak connections in BSs.

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Kabganian, Masoud, Seyed M. Hashemi, and Jafar Roshanian. "Multidisciplinary Design Optimization of a Re-Entry Spacecraft via Radau Pseudospectral Method." Applied Mechanics 3, no. 4 (2022): 1176–89. http://dx.doi.org/10.3390/applmech3040067.

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The design and optimization of re-entry spacecraft or its subsystems is a multidisciplinary or multiobjective optimization problem by nature. Multidisciplinary design optimization (MDO) focuses on using numerical optimization in designing systems with several subsystems or disciplines that have interactions and independent actions. In the present paper, the system-level optimizer, trajectory, geometry and shape, aerodynamics, and aerothermodynamics differential equations, are converted to algebraic equations using the Radau pseudospectral method (RPM) since a spacecraft is a nonlinear, extensive, and sparse system. The solution to the problem with the help of MDO is reached by iterating all the disciplines together; one can simultaneously enhance the design, decrease the time and cost of the entire design cycle, and minimize the structural mass of a re-entry spacecraft. Considering various methods presented in earlier research works, a combined and innovative all-at-once (AAO), RPM-based MDO method, including the key subsystems in the design process of a re-entry capsule-shape spacecraft with a low lift-to-drag ratio (L/D), is presented. Considering the applicable state and control variables, various constraints, and parameters applied to several geometric shapes of a blunt capsule and using Apollo’s aerodynamic and aerothermodynamic coefficients, the optimized dimensions for a re-entry spacecraft are presented. The introduced optimization scheme led to a 17% mass reduction compared to the original mass of the Apollo vehicle. Fast computing and simplified models are used together in this method to analyze a wide range of vehicle shapes and entry types during conceptual design.

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Wang, Li, and Wei Wang. "Hyperspectral Image Reconstruction Based on Reference Point Nondominated Sorting Genetic Algorithm." Mobile Information Systems 2022 (April 5, 2022): 1–24. http://dx.doi.org/10.1155/2022/8455150.

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Spatial and spectral features of hyperspectral imagery reconstruction have gained increasing attention in the latest years. Based on the study of orthogonal matching pursuit (OMP) idea, a hyperspectral image reconstruction algorithm based on reference point nondominated sorting genetic algorithm (NSGA) is proposed. Instead of directly reconstructing the entire hyperspectral data as a traditional OMP reconstruction algorithm, the proposed algorithm explores the idea of the evolution process in the reconstruction. The Gabor redundancy dictionary is established as the sparse basis of hyperspectral images, and the reconstruction model of multiobjective optimization is constructed. In the reconstruction process, the NSGA-III algorithm is used to find the optimal atoms to represent the original signal, and Hermitian inversion lemma is also used to realize the recursive update of the residuals. The initial solution generation, the definition of reference points, the association and niche-preservation operation, and the crossover and mutation operation in NSGA-III are presented in detail. Experimental results on hyperspectral data demonstrate that the proposed algorithm could maintain the reconstruction accuracy, as well as the computational efficiency, and are superior to the state-of-the-art reconstruction algorithms. The proposed algorithm could be applied in the classification and unmixing in hyperspectral images.

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Zhu, Jianjian, and Yanlong Xue. "Construction of a Mental Health Education Model for College Students Based on Fine-Grained Parallel Computing Programming." Mathematical Problems in Engineering 2022 (April 22, 2022): 1–13. http://dx.doi.org/10.1155/2022/4206714.

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Mental health and mental health problems of college students are becoming more and more obvious, and there is more and more negative news caused by psychological problems, and society from all walks of life has given high attention to this problem. Given the new situations and new problems, how to keep up with the times and reform and innovate in the content, method, and path of psychological education in colleges and universities is an important work of ideological and political education in colleges and universities. Because fine-grained category information can provide rich semantic clues, fine-grained parallel computing techniques are widely used in tasks such as sensitive feature filtering, medical image classification, and dangerous goods detection. In this study, we adopt a fine-grained parallel computing programming approach and propose a multiobjective matrix regular optimization algorithm that can simultaneously perform the joint square root, low-rank, and sparse regular optimization for bilinear visual features, which is used to stabilize the higher-order semantic information in bilinear features, improve the generalization ability of features, and apply it to the construction of mental health education models for college students to promote the construction of mental health education bases, improve mental health education network platform, and strengthen the construction of mental health education data platform. A new practical aspect has been added to the abstract. The saliency-guided data augmentation method in this study is an improvement on random data augmentation but reduces the randomness in the data augmentation process and significantly improves the results. The best result belongs to SCutMix data augmentation, which improves by 1.9% compared to the baseline network.

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Xu, Meiling. "The Combination of Internet of Things Technology Based on Probability Model Network and Mass Education." Wireless Communications and Mobile Computing 2022 (May 12, 2022): 1–8. http://dx.doi.org/10.1155/2022/2782473.

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With the continuous development of the Internet of things, educational informatization has become a hot spot in the application of education. Internet of things technology, combined with various subject fields of education, can better achieve subject teaching objectives and teaching assistance. In the multimode teaching optimization model, weight distribution is a complex multiobjective decision-making problem. In this paper, a Bayesian network based on probability model is proposed, which is combined with the large entropy criterion to determine the comprehensive weight. The combination of Bayesian network and Bayesian statistics can make full use of the information of domain knowledge and sample data. Bayesian network uses arc to represent the dependence between variables and probability distribution table to represent the strength of dependence. It organically combines prior information with sample knowledge to promote the integration of prior knowledge and data, which is particularly effective when sample data is sparse or difficult to obtain. Bayesian network is used to associate objective attributes and influencing factors to self-study the target weight. By grasping the characteristics of information technology and the nature of university citizenship curriculum, this paper further analyzes the internal relationship between them, promotes the deep integration of the two, and improves the effectiveness of university citizenship curriculum teaching. By grasping the characteristics of information technology and the nature of the school civics curriculum, we promote a deeper integration of the two. It is my education that is more advanced.

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Chen, Shuo, Peng Cui, and Hongyuan Mei. "A Sustainable Design Strategy Based on Building Morphology to Improve the Microclimate of University Campuses in Cold Regions of China Using an Optimization Algorithm." Mathematical Problems in Engineering 2021 (June 8, 2021): 1–16. http://dx.doi.org/10.1155/2021/2304796.

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The microclimate affects the quality and efficiency of outdoor spaces of campuses, especially in the cold regions of China. In this paper, we propose a multiobjective optimization method to improve the thermal comfort of the outdoor environment of university campuses in severe cold regions. We used morphology data from 41 universities in the cold region of China to create a layout prototype of a campus cluster. Multiobjective optimization was used, and the effects of sunlight, solar radiation, and wind on the outdoor thermal comfort in winter were considered. A parameterized platform was established for the multiobjective optimization of the microclimate of the simplified model of the campus. A multiobjective optimization based on an evolutionary algorithm was used to obtain 108 groups of nondominated solutions. The optimum outdoor microclimate of the campus was obtained at a building density of 0.21–0.23, a plot ratio of 1.51–1.88, and a road width of 11–14 m. We recommend that buildings are designed based on the wind direction in winter and that the space between buildings is increased.

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Pleumpirom, Yuttapong, and Sataporn Amornsawadwatana. "Multiobjective Optimization of Aircraft Maintenance in Thailand Using Goal Programming: A Decision-Support Model." Advances in Decision Sciences 2012 (August 30, 2012): 1–17. http://dx.doi.org/10.1155/2012/128346.

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The purpose of this paper is to develop the multiobjective optimization model in order to evaluate suppliers for aircraft maintenance tasks, using goal programming. The authors have developed a two-step process. The model will firstly be used as a decision-support tool for managing demand, by using aircraft and flight schedules to evaluate and generate aircraft-maintenance requirements, including spare-part lists. Secondly, they develop a multiobjective optimization model by minimizing cost, minimizing lead time, and maximizing the quality under various constraints in the model. Finally, the model is implemented in the actual airline's case.

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Yang, Yuzhen, and Xingsheng Gu. "Cultural-Based Genetic Tabu Algorithm for Multiobjective Job Shop Scheduling." Mathematical Problems in Engineering 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/230719.

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The job shop scheduling problem, which has been dealt with by various traditional optimization methods over the decades, has proved to be an NP-hard problem and difficult in solving, especially in the multiobjective field. In this paper, we have proposed a novel quadspace cultural genetic tabu algorithm (QSCGTA) to solve such problem. This algorithm provides a different structure from the original cultural algorithm in containing double brief spaces and population spaces. These spaces deal with different levels of populations globally and locally by applying genetic and tabu searches separately and exchange information regularly to make the process more effective towards promising areas, along with modified multiobjective domination and transform functions. Moreover, we have presented a bidirectional shifting for the decoding process of job shop scheduling. The computational results we presented significantly prove the effectiveness and efficiency of the cultural-based genetic tabu algorithm for the multiobjective job shop scheduling problem.

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Shi, Feng, and Jingna Lin. "Virtual Machine Resource Allocation Optimization in Cloud Computing Based on Multiobjective Genetic Algorithm." Computational Intelligence and Neuroscience 2022 (March 10, 2022): 1–10. http://dx.doi.org/10.1155/2022/7873131.

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Cloud computing is an important milestone in the development of distributed computing as a commercial implementation, and it has good prospects. Infrastructure as a service (IaaS) is an important service mode in cloud computing. It combines massive resources scattered in different spaces into a unified resource pool by means of virtualization technology, facilitating the unified management and use of resources. In IaaS mode, all resources are provided in the form of virtual machines (VM). To achieve efficient resource utilization, reduce users’ costs, and save users’ computing time, VM allocation must be optimized. This paper proposes a new multiobjective optimization method of dynamic resource allocation for multivirtual machine distribution stability. Combining the current state and future predicted data of each application load, the cost of virtual machine relocation and the stability of new virtual machine placement state are considered comprehensively. A multiobjective optimization genetic algorithm (MOGANS) was designed to solve the problem. The simulation results show that compared with the genetic algorithm (GA-NN) for energy saving and multivirtual machine redistribution overhead, the virtual machine distribution method obtained by MOGANS has a longer stability time. Aiming at this shortage, this paper proposes a multiobjective optimization dynamic resource allocation method (MOGA-C) based on MOEA/D for virtual machine distribution. It is illustrated by experimental simulation that moGA-D can converge faster and obtain similar multiobjective optimization results at the same calculation scale.

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Zheng, X. Y., X. M. Yang, and K. L. Teo. "Sharp Minima for Multiobjective Optimization in Banach Spaces." Set-Valued Analysis 14, no. 4 (2006): 327–45. http://dx.doi.org/10.1007/s11228-006-0023-7.

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Cobos-Sánchez, Clemente, José Antonio Vilchez-Membrilla, Almudena Campos-Jiménez, and Francisco Javier García-Pacheco. "Pareto Optimality for Multioptimization of Continuous Linear Operators." Symmetry 13, no. 4 (2021): 661. http://dx.doi.org/10.3390/sym13040661.

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This manuscript determines the set of Pareto optimal solutions of certain multiobjective-optimization problems involving continuous linear operators defined on Banach spaces and Hilbert spaces. These multioptimization problems typically arise in engineering. In order to accomplish our goals, we first characterize, in an abstract setting, the set of Pareto optimal solutions of any multiobjective optimization problem. We then provide sufficient topological conditions to ensure the existence of Pareto optimal solutions. Next, we determine the Pareto optimal solutions of convex max–min problems involving continuous linear operators defined on Banach spaces. We prove that the set of Pareto optimal solutions of a convex max–min of form max∥T(x)∥, min∥x∥ coincides with the set of multiples of supporting vectors of T. Lastly, we apply this result to convex max–min problems in the Hilbert space setting, which also applies to convex max–min problems that arise in the design of truly optimal coils in engineering.

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29

Solatikia, Farnaz, Erdem Kiliç, and Gerhard Wilhelm Weber. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces." Organizacija 47, no. 2 (2014): 90–97. http://dx.doi.org/10.2478/orga-2014-0010.

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Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.

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30

Luo, Naili, Wu Lin, Peizhi Huang, and Jianyong Chen. "An Evolutionary Algorithm with Clustering-Based Assisted Selection Strategy for Multimodal Multiobjective Optimization." Complexity 2021 (January 12, 2021): 1–13. http://dx.doi.org/10.1155/2021/4393818.

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In multimodal multiobjective optimization problems (MMOPs), multiple Pareto optimal sets, even some good local Pareto optimal sets, should be reserved, which can provide more choices for decision-makers. To solve MMOPs, this paper proposes an evolutionary algorithm with clustering-based assisted selection strategy for multimodal multiobjective optimization, in which the addition operator and deletion operator are proposed to comprehensively consider the diversity in both decision and objective spaces. Specifically, in decision space, the union population is partitioned into multiple clusters by using a density-based clustering method, aiming to assist the addition operator to strengthen the population diversity. Then, a number of weight vectors are adopted to divide population into N subregions in objective space (N is population size). Moreover, in the deletion operator, the solutions in the most crowded subregion are first collected into previous clusters, and then the worst solution in the most crowded cluster is deleted until there are N solutions left. Our algorithm is compared with other multimodal multiobjective evolutionary algorithms on the well-known benchmark MMOPs. Numerical experiments report the effectiveness and advantages of our proposed algorithm.

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31

Dai, Cai, and Yuping Wang. "A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/906147.

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In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

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32

OBAYASHI, Shigeru, Daisuke SASAKI, and Akira OYAMA. "Finding Tradeoffs by Using Multiobjective Optimization Algorithms." TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 47, no. 155 (2004): 51–58. http://dx.doi.org/10.2322/tjsass.47.51.

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33

Zheng, Xi Yin, and Xiao Qi Yang. "Weak sharp minima for piecewise linear multiobjective optimization in normed spaces." Nonlinear Analysis: Theory, Methods & Applications 68, no. 12 (2008): 3771–79. http://dx.doi.org/10.1016/j.na.2007.04.018.

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34

Huynh, Diem Thi Hong. "Approximations of Variational Problems in Terms of Variational Convergence." Science and Technology Development Journal 20, K2 (2017): 107–16. http://dx.doi.org/10.32508/stdj.v20ik2.456.

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We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

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35

Dai, Cai, and Xiujuan Lei. "A Decomposition-Based Multiobjective Evolutionary Algorithm with Adaptive Weight Adjustment." Complexity 2018 (September 12, 2018): 1–20. http://dx.doi.org/10.1155/2018/1753071.

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Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems (MOPs) and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some MOPs with complex Pareto optimal fronts (PFs) (i.e., PFs with a sharp peak or low tail or discontinuous PFs). To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment (IMOEA/DA) is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution (if have). Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence.

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36

Looye, Gertjan, and Hans-Dieter Joos. "Design of Autoland Controller Functions with Multiobjective Optimization." Journal of Guidance, Control, and Dynamics 29, no. 2 (2006): 475–84. http://dx.doi.org/10.2514/1.8797.

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37

Cheng, Franklin Y., and Dan Li. "Multiobjective optimization of structures with and without control." Journal of Guidance, Control, and Dynamics 19, no. 2 (1996): 392–97. http://dx.doi.org/10.2514/3.21631.

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38

Oyama, Akira, and Meng-Sing Liou. "Multiobjective Optimization of Rocket Engine Pumps Using Evolutionary Algorithm." Journal of Propulsion and Power 18, no. 3 (2002): 528–35. http://dx.doi.org/10.2514/2.5993.

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39

Liu, Zhi-Zhong, and Yong Wang. "Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces." IEEE Transactions on Evolutionary Computation 23, no. 5 (2019): 870–84. http://dx.doi.org/10.1109/tevc.2019.2894743.

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40

Singh, Nagendra, and Yogendra Kumar. "Multiobjective Economic Load Dispatch Problem Solved by New PSO." Advances in Electrical Engineering 2015 (February 19, 2015): 1–6. http://dx.doi.org/10.1155/2015/536040.

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Proposed in this paper is a new particle swarm optimization technique for the solution of economic load dispatch as well as environmental emission of the thermal power plant with power balance and generation limit constraints. Economic load dispatch is an online problem to minimize the total generating cost of the thermal power plant and satisfy the equality and inequality constraints. Thermal power plants use fossil fuels for the generation of power; fossil fuel emits many toxic gases which pollute the environment. This paper not only considers the economic load dispatch problem to reduce the total generation cost of the thermal power plant but also deals with environmental emission minimization. In this paper, fuel cost and the environmental emission functions are considered and formulated as a multiobjective economic load dispatch problem. For obtaining the solution of multiobjective economic load dispatch problem a new PSO called moderate random search PSO was used. MRPSO enhances the ability of particles to explore in the search spaces more effectively and increases their convergence rates. The proposed algorithm is tested for the IEEE 30 bus test systems. The results obtained by MRPSO algorithm show that it is effective and efficient.

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41

Chai, Runqi, Al Savvaris, Antonios Tsourdos, Senchun Chai, and Yuanqing Xia. "Unified Multiobjective Optimization Scheme for Aeroassisted Vehicle Trajectory Planning." Journal of Guidance, Control, and Dynamics 41, no. 7 (2018): 1521–30. http://dx.doi.org/10.2514/1.g003189.

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42

Suzuki, Shinji, and Takeshi Yoshizawa. "Multiobjective trajectory optimization by goal programming with fuzzy decisions." Journal of Guidance, Control, and Dynamics 17, no. 2 (1994): 297–303. http://dx.doi.org/10.2514/3.21197.

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43

Sai, Aditya, Carolina Vivas-Valencia, Thomas F. Imperiale, and Nan Kong. "Multiobjective Calibration of Disease Simulation Models Using Gaussian Processes." Medical Decision Making 39, no. 5 (2019): 540–52. http://dx.doi.org/10.1177/0272989x19862560.

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Background. Developing efficient procedures of model calibration, which entails matching model predictions to observed outcomes, has gained increasing attention. With faithful but complex simulation models established for cancer diseases, key parameters of cancer natural history can be investigated for possible fits, which can subsequently inform optimal prevention and treatment strategies. When multiple calibration targets exist, one approach to identifying optimal parameters relies on the Pareto frontier. However, computational burdens associated with higher-dimensional parameter spaces require a metamodeling approach. The goal of this work is to explore multiobjective calibration using Gaussian process regression (GPR) with an eye toward how multiple goodness-of-fit (GOF) criteria identify Pareto-optimal parameters. Methods. We applied GPR, a metamodeling technique, to estimate colorectal cancer (CRC)–related prevalence rates simulated from a microsimulation model of CRC natural history, known as the Colon Modeling Open Source Tool (CMOST). We embedded GPR metamodels within a Pareto optimization framework to identify best-fitting parameters for age-, adenoma-, and adenoma staging–dependent transition probabilities and risk factors. The Pareto frontier approach is demonstrated using genetic algorithms with both sum-of-squared errors (SSEs) and Poisson deviance GOF criteria. Results. The GPR metamodel is able to approximate CMOST outputs accurately on 2 separate parameter sets. Both GOF criteria are able to identify different best-fitting parameter sets on the Pareto frontier. The SSE criterion emphasizes the importance of age-specific adenoma progression parameters, while the Poisson criterion prioritizes adenoma-specific progression parameters. Conclusion. Different GOF criteria assert different components of the CRC natural history. The combination of multiobjective optimization and nonparametric regression, along with diverse GOF criteria, can advance the calibration process by identifying optimal regions of the underlying parameter landscape.

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44

Kramer, Oliver. "A Review of Constraint-Handling Techniques for Evolution Strategies." Applied Computational Intelligence and Soft Computing 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/185063.

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Evolution strategies are successful global optimization methods. In many practical numerical problems constraints are not explicitly given. Evolution strategies have to incorporate techniques to optimize in restricted solution spaces. Famous constraint-handling techniques are penalty and multiobjective approaches. Past work has shown that in particular an ill-conditioned alignment between the coordinate system of Gaussian mutation and the constraint boundaries leads to premature convergence. Covariance matrix adaptation evolution strategies offer a solution to this alignment problem. Last, metamodeling of the constraint boundary leads to significant savings of constraint function calls and to a speedup by repairing infeasible solutions. This work gives a brief overview over constraint-handling methods for evolution strategies by demonstrating the approaches experimentally on two exemplary constrained problems.

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45

Zheng, XiYin, and XiaoQi Yang. "The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces." Science in China Series A: Mathematics 51, no. 7 (2008): 1243–56. http://dx.doi.org/10.1007/s11425-008-0021-3.

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46

Kim, Jin-Hyuk, Kwang-Jin Choi, Afzal Husain, and Kwang-Yong Kim. "Multiobjective Optimization of Circumferential Casing Grooves for a Transonic Axial Compressor." Journal of Propulsion and Power 27, no. 3 (2011): 730–33. http://dx.doi.org/10.2514/1.50563.

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47

Chi, Doris A., Edwin González M., Renato Valdivia, and Eduardo Gutiérrez J. "Parametric Design and Comfort Optimization of Dynamic Shading Structures." Sustainability 13, no. 14 (2021): 7670. http://dx.doi.org/10.3390/su13147670.

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This work implements parametric tools to optimize the environmental design of urban adaptive shadings through multiobjective evolutionary algorithms that look for solutions of dynamic (time-changing) structures used in open public spaces. The proposal is located in Malecon Cancun Tajamar in the southeast part of Mexico, and the main objective is to enhance the thermal comfort of users as well as to become part of the social dynamics of the place reinforcing identity through appropriation. The proposed workflow includes four steps: (1) geometric modelling by parametric modelling tools; (2) simulation of environmental parameters by using BPS tools; (3) shape optimization by using an evolutionary algorithm; and (4) environmental verification of the results. The Universal Thermal Climate Index (UTCI) was used to assess the outdoor thermal comfort derived from the dynamic shadings. The results showed a significant improvement in the thermal comfort with absolute UTCI differences of 3.9, 7.4, and 3.1 °C at 8, 12, and 16 h, respectively, during the summer; and absolute differences of 1.4, 3.5, and 2 °C at 8, 12, and 16 h, respectively, during the winter. The proposed workflow can help to guide the early design process of dynamic shadings by finding optimal solutions that enhance outdoor thermal comfort.

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48

Ding, Xie Ping. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces." Journal of Global Optimization 53, no. 3 (2011): 381–90. http://dx.doi.org/10.1007/s10898-011-9717-y.

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49

Temple, Dylan Walker, and Matthew Collete. "Understanding the Trade-offs Between Producibility and Resistance for Differing Vessels and Missions." Journal of Ship Production and Design 32, no. 01 (2016): 59–70. http://dx.doi.org/10.5957/jspd.2016.32.1.59.

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Design optimization to increase the efficiency of vessels is common place in engineering. However, most optimization focuses on a single aspect of design such as hydrodynamics, structures, or production. In reality, the lifetime cost of a ship is a combination of these different categories and, for an engineer in the design phase, it is important to understand the trade-offs between them. By understanding these trade-offs, design decisions can be made that ensure reduced costs to the shipowner. However, the development of these trade spaces is difficult and necessitates exploration over a large region of design space. As an example, this work develops these trade spaces between two major competing facets of the lifetime costs: fuel consumption and build cost. Hull forms are transformed using two independent transformation functions to rapidly alter the table of offsets defining the ship's geometry. Using this transformation method with a multiobjective genetic algorithm, Pareto fronts between a lifetime resistance metric and a producibility metric based on curvature are developed. Pareto-optimal fronts are then found for both a nominal DTMB-5145 combatant and a KCS SIMMAN container ship. With these fronts, the trade-offs in early stage hull form design is explored, and vessels that minimize these two costs are examined. The work also explores the differences between the trade spaces for the differing types of vessels and mission profiles. Using this method, these trade spaces can be used to explore the design space of vessels earlier in the design phase and gain an understanding of how decisions will affect the total lifetime costs of the ship.

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50

KAMBAYASHI, Keita, Nozomu KOGISO, Takayuki YAMADA, Kazuhiro IZUI, Shinji NISHIWAKI, and Masato TAMAYAMA. "Multiobjective Topology Optimization for a Multi-layered Morphing Flap Considering Multiple Flight Conditions." TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 63, no. 3 (2020): 90–100. http://dx.doi.org/10.2322/tjsass.63.90.

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