Genetic algorithms for single machine scheduling with quadratic earliness and tardiness costs

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet, and present several algorithms based on this approach. These versions differ on the generation of both the initial population and the individuals added in the migration step, as well as on the use of local search. The proposed procedures are compared with the best existing heuristics, as well as with optimal solutions for the smaller instance sizes. The computational results show that the proposed algorithms clearly outperform the existing procedures, and are quite close to the optimum. The improvement over the existing heuristics increases with both the difficulty and the size of the instances. The performance of the proposed genetic approach is improved by the initialization of the initial population, the generation of greedy randomized solutions and the addition of the local search procedure. Indeed, the more sophisticated versions can obtain similar or better solutions, and are much faster. The genetic version that incorporates all the considered features is the new heuristic of choice for small and medium size instances.