An Chen

Xiaopeng Jiang, Thinh On, NhatHai Phan et al.

Mobile apps, such as mHealth and wellness applications, can benefit from deep learning (DL) models trained with mobile sensing data collected by smart phones or wearable devices. However, currently there is no mobile sensing DL system that simultaneously achieves good model accuracy while adapting to user mobility behavior, scales well as the number of users increases, and protects user data privacy. We propose Zone-based Federated Learning (ZoneFL) to address these requirements. ZoneFL divides the physical space into geographical zones mapped to a mobile-edge-cloud system architecture for good model accuracy and scalability. Each zone has a federated training model, called a zone model, which adapts well to data and behaviors of users in that zone. Benefiting from the FL design, the user data privacy is protected during the ZoneFL training. We propose two novel zone-based federated training algorithms to optimize zone models to user mobility behavior: Zone Merge and Split (ZMS) and Zone Gradient Diffusion (ZGD). ZMS optimizes zone models by adapting the zone geographical partitions through merging of neighboring zones or splitting of large zones into smaller ones. Different from ZMS, ZGD maintains fixed zones and optimizes a zone model by incorporating the gradients derived from neighboring zones' data. ZGD uses a self-attention mechanism to dynamically control the impact of one zone on its neighbors. Extensive analysis and experimental results demonstrate that ZoneFL significantly outperforms traditional FL in two models for heart rate prediction and human activity recognition. In addition, we developed a ZoneFL system using Android phones and AWS cloud. The system was used in a heart rate prediction field study with 63 users for 4 months, and we demonstrated the feasibility of ZoneFL in real-life.

Xiaodong Ren, Daofu Guo, Zhigang Ren et al.

By remarkably reducing real fitness evaluations, surrogate-assisted evolutionary algorithms (SAEAs), especially hierarchical SAEAs, have been shown to be effective in solving computationally expensive optimization problems. The success of hierarchical SAEAs mainly profits from the potential benefit of their global surrogate models known as "blessing of uncertainty" and the high accuracy of local models. However, their performance leaves room for improvement on highdimensional problems since now it is still challenging to build accurate enough local models due to the huge solution space. Directing against this issue, this study proposes a new hierarchical SAEA by training local surrogate models with the help of the random projection technique. Instead of executing training in the original high-dimensional solution space, the new algorithm first randomly projects training samples onto a set of low-dimensional subspaces, then trains a surrogate model in each subspace, and finally achieves evaluations of candidate solutions by averaging the resulting models. Experimental results on six benchmark functions of 100 and 200 dimensions demonstrate that random projection can significantly improve the accuracy of local surrogate models and the new proposed hierarchical SAEA possesses an obvious edge over state-of-the-art SAEAs

An Chen, Zhigang Ren, Muyi Wang et al.

Problem decomposition plays a vital role when applying cooperative coevolution (CC) to large scale global optimization problems. However, most learning-based decomposition algorithms either only apply to additively separable problems or face the issue of false separability detections. Directing against these limitations, this study proposes a novel decomposition algorithm called surrogate-assisted variable grouping (SVG). SVG first designs a general-separability-oriented detection criterion according to whether the optimum of a variable changes with other variables. This criterion is consistent with the separability definition and thus endows SVG with broad applicability and high accuracy. To reduce the fitness evaluation requirement, SVG seeks the optimum of a variable with the help of a surrogate model rather than the original expensive high-dimensional model. Moreover, it converts the variable grouping process into a dynamic-binary-tree search one, which facilitates reutilizing historical separability detection information and thus reducing detection times. To evaluate the performance of SVG, a suite of benchmark functions with up to 2000 dimensions, including additively and non-additively separable ones, were designed. Experimental results on these functions indicate that, compared with six state-of-the-art decomposition algorithms, SVG possesses broader applicability and competitive efficiency. Furthermore, it can significantly enhance the optimization performance of CC.

Zhigang Ren, Yongsheng Liang, Muyi Wang et al.

Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.

Yongsheng Liang, Zhigang Ren, Bei Pang et al.

As a model-based evolutionary algorithm, estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied to global optimization. However, traditional Gaussian EDA (GEDA) may suffer from premature convergence and has a high risk of falling into local optimum when dealing with multimodal problem. In this paper, we first attempts to improve the performance of GEDA by utilizing historical solutions and develops a novel archive-based EDA variant. The use of historical solutions not only enhances the search efficiency of EDA to a large extent, but also significantly reduces the population size so that a faster convergence could be achieved. Then, the archive-based EDA is further integrated with a novel adaptive clustering strategy for solving multimodal optimization problems. Taking the advantage of the clustering strategy in locating different promising areas and the powerful exploitation ability of the archive-based EDA, the resultant algorithm is endowed with strong capability in finding multiple optima. To verify the efficiency of the proposed algorithm, we tested it on a set of well-known niching benchmark problems and compared it with several state-of-the-art niching algorithms. The experimental results indicate that the proposed algorithm is competitive.

An Chen, Yipeng Zhang, Zhigang Ren et al.

By taking the idea of divide-and-conquer, cooperative coevolution (CC) provides a powerful architecture for large scale global optimization (LSGO) problems, but its efficiency relies highly on the decomposition strategy. It has been shown that differential grouping (DG) performs well on decomposing LSGO problems by effectively detecting the interaction among decision variables. However, its decomposition accuracy depends highly on the threshold. To improve the decomposition accuracy of DG, a global information based adaptive threshold setting algorithm (GIAT) is proposed in this paper. On the one hand, by reducing the sensitivity of the indicator in DG to the roundoff error and the magnitude of contribution weight of subcomponent, we proposed a new indicator for two variables which is much more sensitive to their interaction. On the other hand, instead of setting the threshold only based on one pair of variables, the threshold is generated from the interaction information for all pair of variables. By conducting the experiments on two sets of LSGO benchmark functions, the correctness and robustness of this new indicator and GIAT were verified.

Bei Pang, Zhigang Ren, Yongsheng Liang et al.

It has been shown that cooperative coevolution (CC) can effectively deal with large scale optimization problems (LSOPs) through a divide-and-conquer strategy. However, its performance is severely restricted by the current context-vector-based sub-solution evaluation method since this method needs to access the original high dimensional simulation model when evaluating each sub-solution and thus requires many computation resources. To alleviate this issue, this study proposes an adaptive surrogate model assisted CC framework. This framework adaptively constructs surrogate models for different sub-problems by fully considering their characteristics. For the single dimensional sub-problems obtained through decomposition, accurate enough surrogate models can be obtained and used to find out the optimal solutions of the corresponding sub-problems directly. As for the nonseparable sub-problems, the surrogate models are employed to evaluate the corresponding sub-solutions, and the original simulation model is only adopted to reevaluate some good sub-solutions selected by surrogate models. By these means, the computation cost could be greatly reduced without significantly sacrificing evaluation quality. Empirical studies on IEEE CEC 2010 benchmark functions show that the concrete algorithm based on this framework is able to find much better solutions than the conventional CC algorithms and a non-CC algorithm even with much fewer computation resources.

Zhigang Ren, Bei Pang, Yongsheng Liang et al.

It has been shown that cooperative coevolution (CC) can effectively deal with large scale optimization problems (LSOPs) through a divide-and-conquer strategy. However, its performance is severely restricted by the current context-vector-based sub-solution evaluation method since this method needs to access the original high dimensional simulation model when evaluating each sub-solution and thus requires many computation resources. To alleviate this issue, this study proposes a novel surrogate model assisted cooperative coevolution (SACC) framework. SACC constructs a surrogate model for each sub-problem obtained via decomposition and employs it to evaluate corresponding sub-solutions. The original simulation model is only adopted to reevaluate some good sub-solutions selected by surrogate models, and these real evaluated sub-solutions will be in turn employed to update surrogate models. By this means, the computation cost could be greatly reduced without significantly sacrificing evaluation quality. To show the efficiency of SACC, this study uses radial basis function (RBF) and success-history based adaptive differential evolution (SHADE) as surrogate model and optimizer, respectively. RBF and SHADE have been proved to be effective on small and medium scale problems. This study first scales them up to LSOPs of 1000 dimensions under the SACC framework, where they are tailored to a certain extent for adapting to the characteristics of LSOP and SACC. Empirical studies on IEEE CEC 2010 benchmark functions demonstrate that SACC significantly enhances the evaluation efficiency on sub-solutions, and even with much fewer computation resource, the resultant RBF-SHADE-SACC algorithm is able to find much better solutions than traditional CC algorithms.

Yongsheng Liang, Zhigang Ren, Xianghua Yao et al.

As a typical model-based evolutionary algorithm (EA), estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied to global optimization. However, the common-used Gaussian EDA (GEDA) usually suffers from premature convergence which severely limits its search efficiency. This study first systematically analyses the reasons for the deficiency of the traditional GEDA, then tries to enhance its performance by exploiting its evolution direction, and finally develops a new GEDA variant named EDA2. Instead of only utilizing some good solutions produced in the current generation when estimating the Gaussian model, EDA2 preserves a certain number of high-quality solutions generated in previous generations into an archive and takes advantage of these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model which in turn can guide EDA2 towards more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA2 since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA2, we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs, including IPOP-CMAES, AMaLGaM, three high-powered DE algorithms, and a new PSO algorithm. The experimental results demonstrate that EDA2 is efficient and competitive.