The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Initially, trajectory metaheuristics used to shape the state of the art in many problems, whereas today, population-based mechanisms tend to be more effective.Such has been the case for the Linear Ordering Problem (LOP), a field in which strategies such as Iterated Local Search and Variable Neighborhood Search led the way during the 1990s, but which have now been surpassed by evolutionary and memetic schemes. This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions. On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months. Our analysis of this aspect relied on parallelization, and allowed us to conclude that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating. And on the other, the best-known results for today's most challenging set of instances (xLOLIB2) were significantly outperformed. Instances with sizes ranging from 300 to 1000 were analyzed, and new bounds were established that provide a frame of reference for future research.

翻译：启发式优化器的设计方式随着计算能力的提升而历经数十年的演变。最初，轨迹元启发式算法主导了许多问题的最优解方法，而如今基于群体的机制往往更具效能。线性排序问题（LOP）领域正是如此——迭代局部搜索和变邻域搜索等策略在20世纪90年代曾引领该领域，但如今已被进化算法和模因方案所超越。本文聚焦于探究计算能力持续增长背景下LOP优化器设计将如何演变，并取得两项主要贡献。其一，我们设计了一种能够有效利用大量计算资源的元启发式算法，具体而言，该算法可调用相当于现代处理器核在超过四个月的持续运行中所能产生的计算能力。我们基于并行化对该特性的分析表明：随着计算资源能力的提升，必须增强模因算法中强化方法的效能，以防止种群陷入停滞。其二，我们显著超越了当前最具挑战性的实例集（xLOLIB2）的最佳已知结果。研究分析了规模从300到1000的实例，并建立了新的基准，为未来研究提供了参照框架。