This paper addresses a special bin packing problem in which each item can only be assigned to a subset of the bins. We name this problem as the restricted bin packing problem (RBPP). This paper is designed to explore the relationships of RBPP with classic NP-complete problems, and to resolve the restrictions of assignment through heuristic and meta-heuristic algorithms. A new heuristic algorithm named ‘Max-fit Based on Zigzag Sorting with Retained Feasibility’ is proposed. In this heuristic algorithm, a feasibility retaining rule is constructed to assure the assignment of every item; a zigzag sorting method is designed to improve the performance of the algorithm. Our heuristic algorithm is able to generate better results in comparison with existing heuristics. Greedy Randomized Adaptive Search Procedure (GRASP) and Simulated Annealing (SA) are exploited to obtain better solutions for RBPP. A new construction method based on cliques and zigzag sorting are built for GRASP and SA. The proposed methods are shown to have higher efficiency than traditional ones through numeric examples.

中文翻译：

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限制装箱问题的启发式/元启发式方法

本文解决了一个特殊的垃圾箱包装问题，其中每个项目只能分配给垃圾箱的一个子集。我们将此问题称为受限装箱问题（RBPP）。本文旨在探讨RBPP与经典NP完全问题的关系，并通过启发式和元启发式算法解决分配的限制。提出了一种新的启发式算法，即“基于具有保留可行性的曲折排序的最大拟合”。在这种启发式算法中，构造了可行性保留规则以确保每个项目的分配。设计曲折排序方法以提高算法的性能。与现有的启发式算法相比，我们的启发式算法能够产生更好的结果。利用贪婪随机自适应搜索程序（GRASP）和模拟退火（SA）可以为RBPP获得更好的解决方案。针对GRASP和SA，建立了一种基于群体和锯齿排序的新构造方法。通过数值算例表明，所提出的方法具有比传统方法更高的效率。