Abstract In the Quadratic Assignment Problem (QAP), facilities are assigned to sites in order to minimize interactions between pairs of facilities. Although easy to define, it is among the hardest problems in combinatorial optimization, due to its non-linear nature. After decades of research on the QAP, many variants of this problem arose to deal with different applications. Along with the QAP, we consider four variants – the Quadratic Bottleneck Assignment Problem, the Biquadratic Assignment Problem, the Quadratic Semi-Assignment Problem, and the Generalized QAP – and develop a single framework to solve them all. Our parallel memetic iterated tabu search (PMITS) extends the most successful heuristics to solve the QAP. It combines the diversification phase of generating new local optima found after solutions modified by a new crossover operator that is biased towards one of the parents, with the intensification phase of an effective tabu search which uses a simplified tabu list structure to reduce the number of parameters and a new long-term memory that saves solutions previously visited to speed up the search. Solutions are improved concurrently using parallelism, and a convergence criterion determines whether the search stops according to the best solutions in each parallel search. Computational experiments using the hardest benchmark instances from the literature attest the effectiveness of the PMITS, showing its competitiveness when compared to the state-of-the-art methods, sequential and parallel, to solve the QAP. We also show that PMITS significantly outperforms the best methods found for all four variants of the QAP, significantly updating their literature.

中文翻译：

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二次分配问题变体：调查和有效的并行模因迭代禁忌搜索

摘要 在二次分配问题 (QAP) 中，将设施分配给站点以最小化设施对之间的交互。尽管很容易定义，但由于其非线性性质，它是组合优化中最难的问题之一。经过对 QAP 的数十年研究，出现了该问题的许多变体以处理不同的应用。除了 QAP，我们还考虑了四种变体——二次瓶颈分配问题、双二次分配问题、二次半分配问题和广义 QAP——并开发了一个单一的框架来解决它们。我们的并行模因迭代禁忌搜索 (PMITS) 扩展了最成功的启发式方法来解决 QAP。它结合了生成新的局部最优解后发现的新的局部最优解的多样化阶段，该解决方案被一个偏向父母之一的新交叉算子修改，与一个有效禁忌搜索的强化阶段，它使用简化的禁忌列表结构来减少参数的数量以及一个新的长期记忆，可以保存以前访问过的解决方案以加快搜索速度。使用并行性同时改进解，收敛标准根据每次并行搜索中的最佳解来确定搜索是否停止。使用文献中最难的基准实例的计算实验证明了 PMITS 的有效性，与最先进的顺序和并行方法相比，它显示了它的竞争力，以解决 QAP。