A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization

© 1997-2012 IEEE. Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-The-Art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points.

A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization

© 1997-2012 IEEE. Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-The-Art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points.

Spectral Processing for Denoising and Compression of 3D Meshes Using Dynamic Orthogonal Iterations

Recently, spectral methods have been extensively used in the processing of 3D meshes. They usually take advantage of some unique properties that the eigenvalues and the eigenvectors of the decomposed Laplacian matrix have. However, despite their superior behavior and performance, they suffer from computational complexity, especially while the number of vertices of the model increases. In this work, we suggest the use of a fast and efficient spectral processing approach applied to dense static and dynamic 3D meshes, which can be ideally suited for real-time denoising and compression applications. To increase the computational efficiency of the method, we exploit potential spectral coherence between adjacent parts of a mesh and then we apply an orthogonal iteration approach for the tracking of the graph Laplacian eigenspaces. Additionally, we present a dynamic version that automatically identifies the optimal subspace size that satisfies a given reconstruction quality threshold. In this way, we overcome the problem of the perceptual distortions, due to the fixed number of subspace sizes that is used for all the separated parts individually. Extensive simulations carried out using different 3D models in different use cases (i.e., compression and denoising), showed that the proposed approach is very fast, especially in comparison with the SVD based spectral processing approaches, while at the same time the quality of the reconstructed models is of similar or even better reconstruction quality. The experimental analysis also showed that the proposed approach could also be used by other denoising methods as a preprocessing step, in order to optimize the reconstruction quality of their results and decrease their computational complexity since they need fewer iterations to converge.

Scatter Matrix Based Domain Adaptation for Bi-Temporal Polarimetric SAR Images

Time series analysis (TSA) based on multi-temporal polarimetric synthetic aperture radar (PolSAR) images can deeply mine the scattering characteristics of objects in different stages and improve the interpretation effect, or help to extract the range of surface changes. However, as far as classification is concerned, it is difficult to directly generate the classification map for a new temporal image, by the use of conventional TSA or change detection methods. Once some labeled samples exist in historical temporal images, semi-supervised domain adaptation (DA) is able to use historical label information to infer the categories of pixels in the new image, which is a potential solution to the above problem. In this paper, a novel semi-supervised DA algorithm is proposed, which inherits the merits of maximum margin criterion and principal component analysis in the DA learning scenario. Using a kernel mapping function established on the statistical distribution of PolSAR data, the proposed algorithm aims to find an optimal subspace for eliminating domain influence and keeping the key information of bi-temporal images. Experiments on both UAVSAR and Radarsat-2 multi-temporal datasets show that, superior classification results with the average accuracy of about 80% can be obtained by a simple classifier trained with historical labeled samples in the learned low- dimensional subspaces.

Discriminative Sparsity Graph Embedding for Unconstrained Face Recognition

In this paper, we propose a new dimensionality reduction method named Discriminative Sparsity Graph Embedding (DSGE) which considers the local structure information and the global distribution information simultaneously. Firstly, we adopt the intra-class compactness constraint to automatically construct the intrinsic adjacent graph, which enhances the reconstruction relationship between the given sample and the non-neighbor samples with the same class. Meanwhile, the inter-class compactness constraint is exploited to construct the penalty adjacent graph, which reduces the reconstruction influence between the given sample and the pseudo-neighbor samples with the different classes. Then, the global distribution constraints are introduced to the projection objective function for seeking the optimal subspace which compacts intra-classes samples and alienates inter-classes samples at the same time. Extensive experiments are carried out on AR, Extended Yale B, LFW and PubFig databases which are four representative face datasets, and the corresponding experimental results illustrate the effectiveness of our proposed method.

Proxy-Based Optimal Dynamic Control Allocation for Multi-Input, Multi-Output Over-Actuated Systems

In over-actuated systems, an output can be realized through various control effort combinations. It is desirable to allocate the control efforts dynamically (as opposed to statically) in an optimal manner. In this paper, a proxy-based control allocation approach is proposed for multi-input, multi-output over-actuated systems. Instead of using real-time optimization for control allocation, the proposed method establishes an energy optimal subspace; it then defines a causally implementable proxy to accurately measure the deviation of the controlled system from the energy optimal subspace using matrix fraction description and spectral factorization. The control allocation problem is thus converted to a regulation problem, and is solved using a standard H∞ approach. The proposed method is validated through simulation examples, in comparison with an existing dynamic control allocation method. Significant improvements in energy efficiency without affecting the controlled output are demonstrated.