The template design problem (TDP) is a hard combinatorial problem with a high number of symmetries which makes solving it more complicated. A number of techniques have been proposed in the literature to optimise its resolution, ranging from complete methods to stochastic ones. However, although metaheuristics are considered efficient methods that can find enough-quality solutions at a reasonable computational cost, these techniques have not proven to be truly efficient enough to deal with this problem. This paper explores and analyses a wide range of metaheuristics to tackle the problem with the aim of assessing their suitability for finding template designs. We tackle the problem using a wide set of metaheuristics whose implementation is guided by a number of issues such as problem formulation, solution encoding, the symmetrical nature of the problem, and distinct forms of hybridisation. For the TDP, we also propose a slot-based alternative problem formulation (distinct to other slot-based proposals), which represents another option other than the classical variation-based formulation of the problem. An empirical analysis, assessing the performance of all the metaheuristics (i.e., basic, integrative and collaborative algorithms working on different search spaces and with/without symmetry breaking) shows that some of our proposals can be considered the state-of-the-art when they are applied to specific problem instances.

翻译：模板设计问题（TDP）是一个具有大量对称性的困难组合优化问题，其对称性使得求解更加复杂。文献中已提出多种技术来优化其求解过程，涵盖从完备方法到随机方法。然而，尽管元启发式方法被认为是能够在合理计算成本下找到足够优质解的高效方法，但这些技术尚未被证明能真正高效地处理该问题。本文探索并分析了广泛的元启发式方法以应对该问题，旨在评估它们寻找模板设计的适用性。我们通过一系列元启发式方法处理该问题，其实施受到问题表述、解编码、问题的对称性本质以及不同混合形式等多方面因素的指导。针对TDP，我们还提出了一种基于槽位的替代问题表述（不同于其他基于槽位的方案），这为经典基于变异的表述提供了另一种选择。通过实证分析评估所有元启发式方法（即在不同搜索空间运行、包含/不包含对称性破缺的基本算法、集成算法与协作算法）的性能，结果表明我们提出的部分方法在应用于特定问题实例时可被视为当前最优方法。