In this paper, the two-dimensional cutting problem with defects is discussed. The objective is to cut some rectangles in a given shape and direction without overlapping the defects from the rectangular plate and maximize some profit associated. An Improved Heuristic-Dynamic Program (IHDP) is presented to solve the problem. In this algorithm, the discrete set contains not only the solution of one-dimensional knapsack problem with small rectangular block width and height, but also the cutting positions of one unit outside four boundaries of each defect. In addition, the denormalization recursive method is used to further decompose the sub problem with defects. The algorithm computes thousands of typical instances. The computational experimental results show that IHDP obtains most of the optimal solution of these instances, and its computation time is less than that of the latest literature algorithms.

Over the last few decades, reliability analysis has gained more and more attention as it can be beneficial in lowering the maintenance cost. Time between failures (TBF) is an essential topic in reliability analysis. If the TBF can be accurately predicted, preventive maintenance can be scheduled in advance in order to avoid critical failures. The purpose of this paper is to research the TBF using deep learning techniques. Deep learning, as a tool capable of capturing the highly complex and nonlinearly patterns, can be a useful tool for TBF prediction. The general principle of how to design deep learning model was introduced. By using a sizeable amount of automobile TBF dataset, we conduct an experiential study on TBF prediction by deep learning and several data mining approaches. The empirical results show the merits of deep learning in performance but comes with cost of high computational load.

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