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. Such has been the case for the Linear Ordering Problem (LOP), a field in which trajectory-based strategies led the way during the 1990s, but which have now been surpassed by 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 analyses show 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. New bounds were established in this benchmark, which provides a new frame of reference for future research.