Small-scale Subproblems Research Articles

Multi-view clustering via dynamic unified bipartite graph learning

Multi-view clustering algorithms based on graph learning have the ability to extract the potential association between data samples, which has been a concern of many researchers in recent years. However, existing algorithms have two limitations: (1) they directly learn from the raw graph, which includes noise and outliers, and they construct the graph filter statically, biasing the clustering results; (2) during graph construction, they mainly use the information of a single structure and fail to fully extract the multi-granular structural information among the data. To address these issues, this paper proposes a novel multi-view clustering method via dynamic unified bipartite graph learning. Specifically, a learnable graph filter is first refined to dynamically filter the original data feature space, gradually filtering out the undesirable high-frequency noise and achieving a clustering-friendly smooth representation. Second, a unified bipartite graph is constructed by combining the multi-granular structural information of different views to better explore the distinct and common information of each view. In one framework, the dynamic filter and multi-granular structure information are combined to iteratively learn the unified bipartite graph. An efficient iterative algorithm is designed to decompose the objective function into small-scale subproblems for solving. Extensive experiments on benchmark datasets show the superiority of the proposed algorithm over several existing state-of-the-art multi-view clustering algorithms.

Decomposition and approximate dynamic programming approach to optimization of train timetable and skip-stop plan for metro networks

Carefully coordinating train timetables of different operating lines can help reduce transfer delays, which in turn reduces station crowding and improves overall service quality. This paper explores the optimization to train timetable and skip-stop plans that aims to minimize the total passenger waiting time and station crowding. The problem is formulated as a mixed-integer non-linear programming model. To effectively address the complexity of the model, a decomposition and approximate dynamic programming approach is designed to convert the original network-level problem into a series of small-scale subproblems, one for each operating line, to be solved quickly in a distributed manner. The effectiveness and practicability of the model and algorithm are demonstrated on two case networks: a small-scale synthetic network of three metro lines and a real-world network based on Beijing metro. The computational results illustrate that the proposed strategy to generate train timetables and skip-stop plans can effectively reduce passenger waiting time and station crowing. The proposed decomposition and approximate dynamic programming approach is also shown to perform more efficiently than traditional heuristic algorithms, such as genetic algorithm and simulated annealing algorithm for large-scale networks.

Decision variable contribution based adaptive mechanism for evolutionary multi-objective cloud workflow scheduling

Workflow scheduling is vital to simultaneously minimize execution cost and makespan for cloud platforms since data dependencies among large-scale workflow tasks and cloud workflow scheduling problem involve large-scale interactive decision variables. So far, the cooperative coevolution approach poses competitive superiority in resolving large-scale problems by transforming the original problems into a series of small-scale subproblems. However, the static transformation mechanisms cannot separate interactive decision variables, whereas the random transformation mechanisms encounter low efficiency. To tackle these issues, this paper suggests a decision-variable-contribution-based adaptive evolutionary cloud workflow scheduling approach (VCAES for short). To be specific, the VCAES includes a new estimation method to quantify the contribution of each decision variable to the population advancement in terms of both convergence and diversity, and dynamically classifies the decision variables according to their contributions during the previous iterations. Moreover, the VCAES includes a mechanism to adaptively allocate evolution opportunities to each constructed group of decision variables. Thus, the decision variables with a strong impact on population advancement are assigned more evolution opportunities to accelerate population to approximate the Pareto-optimal fronts. To verify the effectiveness of the proposed VCAES, we carry out extensive numerical experiments on real-world workflows and cloud platforms to compare it with four representative algorithms. The numerical results demonstrate the superiority of the VCAES in resolving cloud workflow scheduling problems.

An Improved Dynamic Programming-Based Decentralized Algorithm for AC-OPF of Radially Connected Multi-Level Networks

In this paper, an improved dynamic programming (IDP)-based decentralized algorithm is proposed for the AC-optimal power flow (AC-OPF) of radially connected transmission-distribution-microgrid networks (RCTDMNs). Most of the existing decentralized algorithms need to iterate among networks, which may lead to additional computational and information exchange burden. Different from these algorithms, we decompose the original AC-OPF problem into small-scale subproblems based on dynamic programming (DP) theory, and then solve them in a decentralized manner without iteration among networks. In order to improve the computational performance of DP, its value functions are directly obtained by solving Galerkin projection equations (GPEs) instead of traversing the whole state space. Moreover, a parallel technique is proposed to further accelerate the proposed IDP algorithm when dealing with the AC-OPF problem of RCTDMNs. Case studies on various test systems demonstrate the effectiveness of the proposed method.

Convergence analysis of an ALF-based nonconvex splitting algorithm with SQP structure

<p style='text-indent:20px;'>In this paper, by combining the splitting method of augmented Lagrange function (ALF) with the sequential quadratic programming (SQP) approximation, a novel ALF-based splitting algorithm with SQP structure is proposed for multi-block linear constrained nonconvex separable optimization. The new algorithm uses ALF-based splitting idea to decompose the original problem into several small-scale subproblems. Meanwhile, the SQP approximation and Armijo-type line search are used to solve some subproblems with smoothness concurrently. Under the conventional weak hypothesis, the decreasing property of ALF as merit function is obtained. Furthermore, the global convergence, strong convergence and convergence rate results of the new algorithm in general sense are given.</p>

A semi-supervised label-driven auto-weighted strategy for multi-view data classification

Distinguishing the importance of views plays a key role in multi-view learning as each view often contributes differently to a specific task. However, existing strategies generally attach importance to each view blindly from a data representation perspective, which often fails to identify low-quality views then leading to poor performance. In this paper, by establishing a link between labeled data and the importance of different views, we propose a semi-supervised label-driven auto-weighted strategy that evaluates the importance of views from a labeling perspective to avoid the negative impact of unimportant or low-quality views. Based on this strategy, we propose a transductive semi-supervised auto-weighted multi-view classification model that learns the labels of multi-view data under the more reasonable weights of the views. The model is decoupled into three small-scale sub-problems that can efficiently be optimized. The experimental results on classification tasks show that our proposed method achieves very promising classification accuracy at a lower computational cost compared to other related methods, and the weight change experiments show that our proposed strategy can distinguish view importance more accurately than other related strategies especially when low-quality views are involved in multi-view learning.

A fast sketching-based algorithm for rank-[formula omitted] block term decomposition

The rank-(L,L,1) block term decomposition (BTD) of the tensor has recently received increasing attention in diverse high-order data processing, e.g., hyperspectral image restoration and blind source separation. However, the standard alternating least squares algorithm for the rank-(L,L,1) BTD (BTD-ALS) is computationally expensive, which hinders its application on real large-scale data. In this paper, we propose a fast sketching-based algorithm for the rank-(L,L,1) BTD (FastBTD) to address the computational burden of BTD-ALS. Since the dominant cost of BTD-ALS at each iteration is the sequence of large-scale least squares subproblems, we first project these original subproblems into the low-dimensional subspace by the tensor sketching operator. Then, we can fastly obtain the approximate solutions of the original subproblems by solving these sketched small-scale subproblems at each iteration of FastBTD. The computational complexity of FastBTD (O(2JILR+JIR)) is significantly lower than that of BTD-ALS (O(2I3LR+I3R)) for solving the least squares subproblems at each iteration, when J≪I2. Moreover, we provide the theoretical error bound for FastBTD. Extensive experiments on both synthetic and real data demonstrate that FastBTD achieves substantial speedup while maintaining accuracy compared with BTD-ALS.

Multirobot Adaptive Task Allocation of Intelligent Warehouse Based on Evolutionary Strategy

To solve the dynamic and real-time problem of multirobot task allocation in intelligent warehouse system under parts-to-picker mode, this paper presents a combined solution based on adaptive task pool strategy and Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) algorithm. In the first stage of the solution, a variable task pool is used to store dynamically added tasks, which can dynamically divide continuous and large-scale task allocation problems into small-scale subproblems to solve them to meet dynamic requirements. And an adaptive control strategy is used to automatically adjust the total number of tasks in the task pool to achieve a trade-off among throughput, energy consumption, and waiting time, which has better adaptability than manually adjusting the size of the task pool. In the second stage of the solution, when the task pool is full, tasks in the task pool will be assigned to robots. For the task allocation problem, this paper regards it as an optimization problem and uses the CMA-ES algorithm to find the optimal task assignment solution for all the robots. By comparing with fixed threshold method under 56 different task pool sizes, the experimental results show that the throughput can be close to reaching the optimal level, and the average distance traveled by robots to handle each unit is lower using adaptive threshold method; so, adaptive task pool solution has better adaptability and can find the optimal task pool size by itself. This method can satisfy the dynamic and real-time requirements and can be effectively applied to the intelligent warehouse system.

Machine learning and CBR integrated mechanical product design approach

Many works based on case-based reasoning (CBR) and rule-based reasoning (RBR) have been done to obtain a product concept intelligently, but researches on automatic and intelligent methods for the detailed design process are still lacking. To achieve the intelligent design of the whole process for mechanical product development, an approach based on cases and knowledge is proposed. First, considering that the actual product cases sample is small, correlations among product features and relationships between product features and requirements are evaluated based on design knowledge. According to these correlations and relationships, a design problem is decomposed into multiple parallel small-scale sub-problems not only to increase data samples but reduce data dimensions. Moreover, a hybrid method that combined Hamming distance with Euclidean distance is generated to retrieve similar cases, which can address both numerical and encoding factors. In addition, K-Nearest-Neighbor (KNN) algorithm and Linear regression are adopted to adapt the classification and numeric parameters, respectively, so that the detailed design process can be achieved without fixed knowledge template. Finally, a tool design software is developed based on Visual studio 2015 to verify the practicability of the proposed method.

Device Access Optimization for Virtual Power Plants in Heterogeneous Networks

In virtual power plants (VPPs), distributed devices (such as residential appliances, energy storage, and electric vehicles) communicate with control centers via wireless access points (APs). Nevertheless, with a massive number of devices connected to APs, VPPs would be adversely affected by packet loss and consequently suffer from revenue reduction. Therefore, devices’ access connections need to be delicately designated to mitigate these negative impacts. This paper studies the device access optimization problem from the perspective of VPP operations. An optimization model to minimize the revenue reduction induced by packet loss is first formulated to designate APs for devices in heterogeneous communication networks. The significance of various device data is determined by revenue reduction as a result of packet loss. Additionally, the heterogeneous access network model is established to characterize different types of APs. To make the model implementable, this paper further proposes a layered decomposition solution algorithm, which decomposes optimization tasks into small-scale sub-problems and successively assigns them to different layers of APs. Sub-problems are further decomposed for APs to greedily cut revenue reduction by evaluating devices’ marginal contributions to revenue reduction. Numerical case studies are also conducted to verify the benefits of device access optimization.

Solving Capacitated Vehicle Routing Problem by an Improved Genetic Algorithm with Fuzzy C-Means Clustering

Aiming at solving the vehicle routing problem, an improved genetic algorithm based on fuzzy C-means clustering (FCM) is proposed to solve the vehicle routing problem with capacity constraints. On the basis of genetic algorithm, the FCM algorithm is used to decompose the large-scale vehicle routing optimization problem into small-scale subproblems, which can effectively improve the efficiency of the algorithm. At the same time, a generation method of the initial solution to CVRP problem is designed. The improved algorithm has good robustness and can also reduce the possibility of falling into local optimization in the search process. Finally, a simulation example is provided to verify the efficiency and superiority of the proposed algorithm.

Resource Allocation for Joint Communication and Localization Systems With MU-MIMO

Joint communication and localization is an attractive technique to simultaneously provide data transmission and localization services, and efficient resource allocation could bring a high data rate and high localization accuracy in limited resources, which is significant for multi-user conditions. In this paper, we concentrate on the joint multiple resource allocation to achieve a trade-off between the performance of the communication and localization process in the millimeter multi-user Multiple Input Multiple Output(MU-MIMO) system. We first develop a robust beam scheduling and user grouping approach using the mutual angle information and channel correlation coefficient to reduce the multi-user interference. Then, we formulate a multi-domain resource allocation problem, where the joint impact of beamforming, bandwidth reservation, and power control is considered. Furthermore, an efficient algorithm is proposed to iteratively perform the sub-carrier and power allocation until satisfying the data rate and localization error-bound constraints after decomposing the large-scale problem into two small-scale sub-problems by the difference of the convex function algorithm. Numerical results show that the proposed algorithm achieves a good trade-off between data rate and localization error and has better performance than other previously proposed algorithms in the literature.

Fast Multiview Clustering With Spectral Embedding.

Spectral clustering has been a hot topic in unsupervised learning owing to its remarkable clustering effectiveness and well-defined framework. Despite this, due to its high computation complexity, it is unable of handling large-scale or high-dimensional data, particularly multi-view large-scale data. To address this issue, in this paper, we propose a fast multi-view clustering algorithm with spectral embedding (FMCSE), which speeds up both the spectral embedding and spectral analysis stages of multi-view spectral clustering. Furthermore, unlike conventional spectral clustering, FMCSE can acquire all sample categories directly after optimization without extra k-means, which can significantly enhance efficiency. Moreover, we also provide a fast optimization strategy for solving the FMCSE model, which divides the optimization problem into three decoupled small-scale sub-problems that can be solved in a few iteration steps. Finally, extensive experiments on a variety of real-world datasets (including large-scale and high-dimensional datasets) show that, when compared to other state-of-the-art fast multi-view clustering baselines, FMCSE can maintain comparable or even better clustering effectiveness while significantly improving clustering efficiency.

Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem

In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.

Supervised multi-view classification via the sparse learning joint the weighted elastic loss

Multi-view data contains the global shared information of all views and the specific information of each view. Usually, the features of all views are concatenated into vectors to be dealt with in the multi-view classification methods, which inevitably ignores the extraction of important views for a specific task and increases the computational complexity. To address the above limitations, we propose a novel supervised classification method via the sparse learning joint the weighted elastic loss. Specifically, for the samples in each class, an elastic sub-model is established by combining the weighted elastic loss and the sparse regularizers. The weighted elastic loss can explore the complementary information of all views and the specific information of each view. The sparse regularizers can select the views that are important to the classification task. Finally, the elastic sub-models of all classes are fused to form the generalized additive classification model. An effective algorithm is designed to optimize the model through solving several small-scale subproblems, which can reduce the computational complexity. The comprehensive evaluations with several advanced methods prove the superiority of the proposed method. Especially on the large-scale Animal dataset, the training time (3.7×103 s) is one time faster than that of the second place (7.5×103 s).

Distributed Cooperative Driving in Multi-Intersection Road Networks

Cooperative driving at isolated intersections attracted great interest and had been well discussed in recent years. However, cooperative driving in multi-intersection road networks remains to be further investigated, because many algorithms for isolated intersection cannot be directly adopted for road networks. In this paper, we propose a distributed strategy to appropriately decompose the problem into small-scale sub-problems that address vehicle cooperation within limited temporal-spatial areas and meanwhile assure appropriate coordination between adjacent areas by specially designed information exchange. Simulation results demonstrate the efficiency-complexity balanced advantage of the proposed strategy under various traffic demand settings.

Distributed AC-DC Optimal Power Dispatch of VSC-Based Energy Routers in Smart Microgrids

This paper presents a novel model of voltage source converter (VSC) based energy routers (ERs) in microgrids. The proposed model explicitly describes the circuit laws within the ERs and captures the coupling of control variables among the AC/DC, DC/DC, DC/AC links. Therefore, the proposed model possesses unparalleled control capabilities in the operational parameters of both the AC and DC sides of ERs. By incorporating such a model into the AC-DC optimal power flow formulation, we not only optimize the power flows between the AC and DC sides of ERs, but also strategically schedule the flexible resources. To solve the ERs based AC-DC optimal power flow (ER-OPF) in a distributed fashion, we propose a hierarchical distributed optimization method that decouples the power grids into a master region and several sub-regions. In the master region, we propose a sequence of strong relaxations to transform the problem into a semidefinite program (SDP). We further show that this SDP relaxation is exact. For the sub-regions, we utilize sequential quadratic programming (SQP) to solve multiple small-scale subproblems with non-convex constraints in parallel. Case studies on the IEEE benchmark system show that fuel costs and power losses are reduced dramatically by utilizing ERs in microgrids. In addition, the proposed distributed algorithm can converge faster than alternating direction method of multipliers (ADMM).

A QCQP-based splitting SQP algorithm for two-block nonconvex constrained optimization problems with application

This paper discusses a class of two-block nonconvex smooth optimization problems with nonlinear constraints. Based on a quadratically constrained quadratic programming (QCQP) approximation, an augmented Lagrangian function (ALF), and a Lagrangian splitting technique into small-scale subproblems, we propose a novel sequential quadratic programming (SQP) algorithm. First, inspired by the augmented Lagrangian method (ALM), we penalize the quadratic equality constraints associated with the QCQP approximation subproblem in its objective by means of the ALF, and then split the resulting subproblem into two small-scale ones, but both of them are not quadratic programming (QP) due to the square of the quadratic equality constraints in the objective. Second, by ignoring the three-order infinitesimal arising from the squared term, the two small-scale subproblems are reduced to two standard QP subproblems, which can yield an improved search direction. Third, taking the ALF of the discussed problem as a merit function, the next iterate point is generated by the Armijo line search. As a result, a new SQP method, called QCQP-based splitting SQP method, is proposed. Under suitable conditions, the global convergence, strong convergence, iteration complexity and convergence rate of the proposed method are analyzed and obtained. Finally, preliminary numerical experiments and applications were carried out, and these show that the proposed method is promising.

Robust multiview feature selection via view weighted

In recent years, combining the multiple views of data to perform feature selection has been popular. As the different views are the descriptions from different angles of the same data, the abundant information coming from multiple views instead of the single view can be used to improve the performance of identification. In this paper, through the view weighted strategy, we propose a novel robust supervised multiview feature selection method, in which the robust feature selection is performed under the effect of l2,1-norm. The proposed model has the following advantages. Firstly, different from the commonly used view concatenation that is liable to ignore the physical meaning of features and cause over-fitting, the proposed method divides the original space into several subspaces and performs feature selection in the subspaces, which can reduce the computational complexity. Secondly, the proposed method assigns different weights to views adaptively according to their importance, which shows the complementarity and the specificity of views. Then, the iterative algorithm is given to solve the proposed model, and in each iteration, the original large-scale problem is split into the small-scale subproblems due to the divided original space. The performance of the proposed method is compared with several related state-of-the-art methods on the widely used multiview datasets, and the experimental results demonstrate the effectiveness of the proposed method.

A Three-Level Recursive Differential Grouping Method for Large-Scale Continuous Optimization

Cooperative co-evolution (CC) is widely used to solve large-scale continuous optimization problems, which divides a large-scale problem into several small-scale sub-problems via decomposition methods and then optimizes each sub-problem separately. However, the performance of CC mainly depends on the decomposition methods. A recently proposed bisection-based decomposition method, called recursive differential grouping (RDG), shows good performance when solving large-scale continuous optimization problems. In order to further improve the performance of RDG, this paper develops a novel decomposition method, called three-level recursive differential grouping (TRDG). In TRDG, when the interaction between two sets is detected, the variables in one of the sets are divided into three subsets based on the trichotomy method, and then the interaction between each subset and the other set is detected. Compared with RDG, TRDG can reduce the depth of recursion, thus saving the number of fitness evaluations (FEs). In addition, we devise a novel strategy to update adaptively the threshold for identifying the interactions between variables. The simulation experiment results on CEC’2010 and CEC’2013 benchmark functions show that the performance of TRDG is better than several existing decomposition methods in terms of the accuracy and the number of FEs. Furthermore, TRDG is embedded into two frameworks to tackle CEC’2010 large-scale continuous optimization problems.