An adaptive genetic algorithm to solve the Single Machine Scheduling Problem with Earliness and Tardiness Penalties

This paper deals with the Single Machine Scheduling Problem with Earliness and Tardiness Penalties, considering distinct due windows and sequence-dependent setup time. Due to its complexity, an adaptive genetic algorithm is proposed for solving it. Five search operators are used to explore the solution space and the choice probability for each operator depends on the success in a previous search. The initial population is generated by the combination between construct methods based on greedy, random and GRASP techniques. For each job sequence generated, a polynomial time algorithm are used for determining the processing initial optimal date to each job. During the evolutive process, a group with the best five individuals generated by each crossover operator is built. Then, periodically, a Path Relinking module is applied taking as base individual the best one so far generated by the algorithm and as guide individual each one of the five best individuals generated by each crossover operator. Three variations of this algorithm were submitted to computational experiments. The results shows the effectiveness of the proposal.