Biased random-key genetic algorithms using path-relinking as a progressive crossover strategy

In a biased random-key genetic algorithm, a deterministic decoder algorithm takes a solution represented by a vector of real numbers (random-keys) and builds a feasible solution for the problem at hand. Selection is said to be biased not only because one parent is always a high-quality solution, but also because it has a higher probability of passing its characteristics to its offspring. Path-relinking is a search intensification strategy to explore trajectories connecting high-quality solutions. In this work, we show how path-relinking can be applied in the space of the random-keys and successfully explored as a progressive crossover strategy in biased random-key genetic algorithms. The efficiency of the newly proposed improved crossover strategies, combining multiple crossover operators with the progressive crossover strategy by path-relinking, is illustrated by applications on two problems: the single-round divisible load scheduling problem and the multi-round divisible load scheduling problem. The computational results show that the improved crossover strategies, combining multiple crossover operators with the progressive crossover strategy by path-relinking, are able not only to improve the running times of the original BRKGA, but also to find better solutions in the same running times.