Xiaojun Zhou
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived. Integrating the dual solutions with the KKT conditions, we are able to obtain the approximate solutions or global solutions easily.
Xiaojun Zhou
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be solved easily by the well-developed optimization methods. Considering that there may exist no critical points in the dual feasible domain, a reduction technique is used gradually to guarantee the feasibility of the reduced solution, and a compensation technique is utilized to strengthen the robustness of the solution. The similar strategy is also applied to the maxcut problem with linear perturbation and its hybrid with quadratic perturbation. Experimental results demonstrate the effectiveness of the proposed algorithms when compared with other approaches.
Yang Wu, Jing Yang, Xiaojun Zhou et al.
Automatic detecting rumors on social media has become a challenging task. Previous studies focus on learning indicative clues from conversation threads for identifying rumorous information. However, these methods only model rumorous conversation threads from various views but fail to fuse multi-view features very well. In this paper, we propose a novel multi-view fusion framework for rumor representation learning and classification. It encodes the multiple views based on Graph Convolutional Networks (GCN), and leverages Convolutional Neural Networks (CNN) to capture the consistent and complementary information among all views and fuse them together. Experimental results on two public datasets demonstrate that our method outperforms state-of-the-art approaches.
Xiaojun Zhou
For boolean quadratic programming (BQP), we will show that there is no duality gap between the primal and dual problems under some conditions by using the classical Lagrangian duality. A benchmark generator is given to create random BQP problems which can be solved in polynomial time. Several numerical examples are generated to demonstrate the effectiveness of the proposed method.
Xiaojun zhou, Chunna Zhao, Yaqun Huang et al.
Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due to insufficient theoretical research, at present, there is no fractional-order matrix differentiation method that is perfectly compatible with automatic differentiation (Autograd) technology. Therefore, we propose a fractional-order matrix differentiation calculation method. This method is introduced by the definition of the integer-order Jacobian matrix. We denote it as fractional-order Jacobian matrix differentiation (${\bf{J}^α}$). Through ${\bf{J}^α}$, we can carry out the matrix-based fractional-order chain rule. Based on the Linear module and the fractional-order differentiation, we design the fractional-order Autograd technology to enable the use of fractional-order differentiation in hidden layers, thereby enhancing the practicality of fractional-order differentiation in deep learning. In the experiment, according to the PyTorch framework, we design fractional-order Linear (FLinear) and replace nn.Linear in the multilayer perceptron with FLinear. Through the qualitative analysis of the training set and validation set $Loss$, the quantitative analysis of the test set indicators, and the analysis of time consumption and GPU memory usage during model training, we verify the superior performance of ${\bf{J}^α}$ and prove that it is an excellent fractional-order gradient descent method in the field of deep learning.
Xiaojun Zhou
In the evolutionary computation community, it is widely believed that stagnation impedes convergence in evolutionary algorithms, and that convergence inherently indicates optimality. However, this perspective is misleading. In this study, it is the first to highlight that the stagnation of an individual can actually facilitate the convergence of the entire population, and convergence does not necessarily imply optimality, not even local optimality. Convergence alone is insufficient to ensure the effectiveness of evolutionary algorithms. Several counterexamples are provided to illustrate this argument.
Jingyi He, Xiaojun Zhou, Rundong Zhang et al.
The classification problem is a significant topic in machine learning which aims to teach machines how to group together data by particular criteria. In this paper, a framework for the ensemble learning (EL) method based on group decision making (GDM) has been proposed to resolve this issue. In this framework, base learners can be considered as decision-makers, different categories can be seen as alternatives, classification results obtained by diverse base learners can be considered as performance ratings, and the precision, recall, and accuracy which can reflect the performances of the classification methods can be employed to identify the weights of decision-makers in GDM. Moreover, considering that the precision and recall defined in binary classification problems can not be used directly in the multi-classification problem, the One vs Rest (OvR) has been proposed to obtain the precision and recall of the base learner for each category. The experimental results demonstrate that the proposed EL method based on GDM has higher accuracy than other 6 current popular classification methods in most instances, which verifies the effectiveness of the proposed method.
Xiaolin Tang, Chunhua Yang, Xiaojun Zhou et al.
Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for GTSP is proposed, where a new local search operator named \textit{K-circle}, directed by neighborhood information in space, has been introduced to DSTA to shrink search space and strengthen search ability. A novel robust update mechanism, restore in probability and risk in probability (Double R-Probability), is used in our work to escape from local minima. The proposed algorithm is tested on a set of GTSP instances. Compared with other heuristics, experimental results have demonstrated the effectiveness and strong adaptability of DSTA and also show that DSTA has better search ability than its competitors.
Xiaojun Zhou, Chunhua Yang, Weihua Gui
In terms of the concepts of state and state transition, a new algorithm-State Transition Algorithm (STA) is proposed in order to probe into classical and intelligent optimization algorithms. On the basis of state and state transition, it becomes much simpler and easier to understand. As for continuous function optimization problems, three special operators named rotation, translation and expansion are presented. While for discrete function optimization problems, an operator called general elementary transformation is introduced. Finally, with 4 common benchmark continuous functions and a discrete problem used to test the performance of STA, the experiment shows that STA is a promising algorithm due to its good search capability.
Xiaojun Zhou, Chunhua Yang, Weihua Gui
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.