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The end-to-end learning approaches possess the advantages of high efficiency, rapidity and superior solving precision for combinatorial optimization problems, while exploring generalization to instances different from training scale is an open question. In this paper, we focus on the knapsack problem (KP) and employ an end-to-end data-driven approach based on attention model incorporated with different forms of baseline of policy gradient algorithm to solve KP. We first investigate the generalization performance of the proposed approach for KP on various problem scales with different capacities. The experimental results show that the end-to-end model possesses certain learning and generalization abilities to discover the intrinsic characteristics between instances, then guides to solve other instances of different scales. [ABSTRACT FROM AUTHOR]

In this paper, a multiobjective root system growth algorithm-based p-optimality (p-MORSGA) is proposed. The proposed p-MORSGA extended original root system growth algorithm with multiobjective nondomination strategy. To enhance its effect of convergence of solution groups, the p-optimality criterion is employed to determine the solutions of last nondominated front into the next generation group. In the evolution process, global general (GG), concerning the margin information and population density, is selected as the suitable optimality criterion of evaluating the performance of solutions. Application of the new p-MORSGA on several multiobjective benchmark functions shows a marked improvement in performance over the modified classical MOEAs with such criterion. Finally, the proposed p-MORSGA is applied to solve two real-world problems, multiobjective portfolio optimization problems (MOPOPs) and multiobjective optimal power flow (OPF) problems. The experimental results demonstrate that p-MORSGA is extremely effective for real-world application problems. [ABSTRACT FROM AUTHOR]

• The generation method of digital camouflage image is studied based on several background images. • The K-harmonic means clustering algorithm is combined with the color histogram to optimize the clustering algorithm. • The edge contour of regular hexagon digital camouflage basic unit is more blurred and broken. Since the digital camouflage generation method based on fixed single background image cannot fully meet the hidden need of maneuvering targets. In this paper, a method of generating digital camouflage image based on several background images is proposed. Firstly, according to the active range of the maneuvering target, several background images are collected. Secondly, in order to resolve the problem that the clustering algorithm is sensitive to the initial clustering center and easy to fall into local optimum, K-harmonic means (KHM) clustering algorithm is introduced and initial clustering center is determined based on color histogram. Again, KHM clustering is used to extract color features from several background images, the first clustering is extracted from a single background image, and the second clustering is extracted with several color features sets extracted from the first clustering of background images as input. Finally, the regular hexagon is used as the basic unit of the digital camouflage image to construct the spot template, and the digital camouflage image is generated by the lowest horizontal line algorithm. Example verification and camouflage effect detection show that the digital camouflage image generated by this method can effectively realize the concealment of maneuvering targets and has good camouflage effect. [ABSTRACT FROM AUTHOR]