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A new branch and bound algorithm for cell formation problem

机译：解决细胞形成问题的新分支定界算法

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摘要

Cell formation (CF) is the first and the most important problem in designing cellular manufacturing systems. Due to its non-polynomial nature, various heuristic and metaheuristic algorithms have been proposed to solve CF problem. Despite the popularity of heuristic algorithms, few studies have attempted to develop exact algorithms, such as branch and bound (B&B) algorithms, for this problem. We develop three types of branch and bound algorithms to deal with the cell formation problem. The first algorithm uses a binary branching scheme based on the definitions provided for the decision variables. Unlike the first algorithm, which relies on the mathematical model, the second one is designed based on the structure of the cell formation problem. The last algorithm has a similar structure to the second one, except that it has the ability to eliminate duplicated nodes in branching trees. The proposed branch and bound algorithms and a hybrid genetic algorithm are compared through some numerical examples. The results demonstrate the effectiveness of the modified problem-oriented branch and bound algorithm in solving relatively large size cell formation problems.
机译：细胞形成（CF）是设计细胞制造系统时的第一个也是最重要的问题。由于其非多项式性质，已经提出了各种启发式和元启发式算法来解决CF问题。尽管启发式算法很受欢迎，但很少有研究尝试针对此问题开发精确的算法，例如分支定界（B＆B）算法。我们开发了三种类型的分支定界算法来处理细胞形成问题。第一种算法基于为决策变量提供的定义使用二进制分支方案。与第一种算法依赖于数学模型不同，第二种算法是基于细胞形成问题的结构设计的。最后一种算法与第二种算法具有相似的结构，只是它具有消除分支树中重复节点的能力。通过数值算例比较了提出的分支定界算法和混合遗传算法。结果证明了改进的面向问题的分支定界算法在解决相对较大的单元格形成问题方面的有效性。

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