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Combinatorial optimization problems (COPs) play an important role in both industrial production and theoretical research. As a classical class of optimization algorithms, evolutionary algorithms have shown good performance in COPs. However, as the size of the problem increases, it becomes difficult for evolutionary algorithms to produce satisfactory solutions within the specified time. In recent years, neural network algorithms have been applied to solve COPs and have shown superior effects. Inspired by this, this paper proposes a new algorithm based on graph structure for solving COPs. Through relaxation, COPs are transformed into their corresponding continuous optimization problems. The output state of our algorithm is converted to a discrete solution by approximation method. Compared with previous algorithms, our algorithm can not only solve COPs with general form such as binary quadratic programming (BQP), but also solve COPs with special form, which greatly expands the application scope of neural network algorithms. In addition, our algorithm can be embedded into other problem frameworks such as solving multi-objective combinatorial optimization problem (MOCOP) through scalarization method. A new penalty function is added to the objective function, which enables our algorithm to overcome the inconsistency between the optimal solution of the original problem and the corresponding continuous problem, so that our algorithm can perform well on various problems. Several numerical simulations are used to illustrate the effectiveness of our algorithm in solving COPs. Experimental results show that our algorithm can effectively solve COPs with general form and has a shorter solving time compared to traditional evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Quantization methods for convolutional neural network models can be broadly categorized into post-training quantization (PTQ) and quantization aware training (QAT). While PTQ offers the advantage of requiring only a small portion of the data for quantization, the resulting quantized model may not be as effective as QAT. To address this limitation, this paper proposes a novel quantization function named Attention Round. Unlike traditional quantization function that map 32 bit floating-point value w to nearby quantization levels, Attention Round allows w to be mapped to all possible quantization levels in the entire quantization space, expanding the quantization optimization space. The possibilities of mapping w to different quantization levels are inversely correlated with the distance between w and the quantization levels, regulated by a Gaussian decay function. Furthermore, to tackle the challenge of mixed precision quantization, this paper introduces a lossy coding length measure to assign quantization precision to different layers of the model, eliminating the need for solving a combinatorial optimization problem. Experimental evaluations on various models demonstrate the effectiveness of the proposed method. Notably, for ResNet18 and MobileNetV2, the PTQ approach achieves comparable quantization performance to QAT while utilizing only 1024 training data and 10 min for the quantization process. • Attention Round quantization function expands the quantization optimization space. • Mixed precision allocation method improves mixed precision quantization efficiency. • Enriched lightweight CNNs contribute to applications in resource-limited scenarios. [ABSTRACT FROM AUTHOR]

How to identify a small fraction of users with the best capacity to influence other users is central to the research of social network analysis. This problem is termed influence maximization (IM) and is known for its extensive applications. IM can be formulated as a combinatorial optimization problem, which has been shown to be NP -hard under some diffusion models. Therefore, seeking for high-accuracy IM algorithms with acceptable running time has attracted much attention in literature. However, most of existing IM algorithms only adopt a uniform mechanism in the whole solution search process, which lacks of flexible response when the algorithms trap in local optimum. This paper proposes a phased evaluation-enhanced (PHEE) approach for IM, which utilizes two distinct strategies to search the optimal solutions: The first one is a random range division-based evolutionary algorithm for improving solution quality; the second is a fast convergence strategy for searching an optimal solution. Two PHEE-based algorithms, MDD-PHEE and GCI-PHEE, are generated and are evaluated on 10 real-world social networks of different sizes and types. Experimental results demonstrate the effectiveness of PHEE; in particular, MDD-PHEE obtains the best influence spread on all networks compared with the state-of-the-art algorithms, and has a better performance than the time-consuming algorithm CELF on four datasets. [ABSTRACT FROM AUTHOR]