Hybrid heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs

In this paper we present three hybrid heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. Our heuristic is a combination of a steady-state genetic algorithm and three improvement procedures. The two computationally less expensive of these three improvement procedures are used inside the genetic algorithm to improve the schedule obtained after the application of genetic operators, whereas the more expensive one is used to improve the best solution returned by the genetic algorithm. We have compared our hybrid approaches against existing recovering beam search and genetic algorithms. The computational results show the effectiveness of our hybrid approaches. Indeed, our hybrid approaches outperformed the existing heuristics in terms of solution quality as well as running time.