We study the general problem of orthogonally packing rectangles in a fixed size circular container. This is a computationally challenging combinatorial optimization problem with important real-world applications and has recently received much attention from the operations research community. We propose an effective evolutionary algorithm for four variants of the problem, which integrates an improved decoding procedure and several dedicated search operators for population initialization and new solution generation. Computational results on 108 popular benchmark instances show that the proposed algorithm advances the state of the art in practically solving these four variants of the problem by finding 53 new best solutions (26 for the variants of maximizing the area of the packed items and 27 for the variants of maximizing the number of the packed items). We perform experiments to verify the design of key algorithmic components.

中文翻译：

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一种将矩形打包到固定大小的圆形容器中的有效进化算法


我们研究了在固定尺寸的圆形容器中正交包装矩形的一般问题。这是一个在计算上具有挑战性的组合优化问题，具有重要的实际应用，最近受到了运筹学界的广泛关注。我们为该问题的四种变体提出了一种有效的进化算法，该算法集成了改进的解码程序和几个用于种群初始化和新解决方案生成的专用搜索运算符。对 108 个常用基准实例的计算结果表明，所提出的算法通过找到 53 个新的最佳解决方案（26 个用于最大化包装物品面积的变体，27 个用于最大化包装物品数量的变体）来推进实际解决这四种问题的最新技术。我们进行实验以验证关键算法组件的设计。