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Abstract.A hybrid heuristic algorithm for the two-dimensional rectangular packing problem is presented. This algorithm is mainly based on divide-andconquer and greedy strategies. The computational results on a class of benchmark problems have shown that the performance of the heuristic algorithm can outperform that of quasi-human heuristics.

The use of computer aided diagnosis (CAD) systems, which are computer based tools for the automatic analysis of medical images such as mammogram and prostate MRI, can assist in the early detection and diagnosis of developing cancer. In the process of CAD for mammogram, the task of image processing (IP) plays a fundamental role in providing promising diagnostic results, by exploiting high-quality features extracted from the mammographic images. Normally, an IP procedure for mammographic images involves three mechanisms: region of interest (ROI) extraction, image enhancement (IE) and feature extraction (FE). However, an improper utilisation of IE may lead to an inferior composition of the features due to unexpected enhancement of any irrelevant or useless information in ROI. In order to overcome this problem, a fuzzy-rough refined IP (FRIP) framework is presented in this paper to improve the quality of mammographic image features hierarchically. Following the proposed framework, the ROI of each mammographic image is segmented and enhanced locally in the area of the block which is of the highest value of fuzzy positive region (FPR). Here, FPR implies a positive dependency relationship between the block and the decision with regard to the given feature set. The higher a block's FPR value the more certain its underlying image category. To attain a high quality of the image enhancement procedure, the winner block will be further improved by a multi-round strategy to create a pool of IE results. As such, for a mammographic image,

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