Future Trends in the Design of Memetic Algorithms: the Case of the Linear Ordering Problem

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.