Epsilon Oscillation Algorithm for the bi-objective green identical parallel machine scheduling problem

This paper addresses the bi-objective optimization problem of scheduling jobs on multiple identical parallel machines to minimize both makespan and total energy consumption. The problem can be denoted as Pm, TOU divided by divided by C max , TEC . A Pipe Variable Neighborhood Descent approach with Dynamic Programming, employing an Epsilon Constraint method and incorporating an Epsilon Oscillation technique that consists of alternating between ascending and descending ways to vary the epsilon value. This technique improves the pareto front by exploring new search space. A comparison is provided between the proposed Epsilon Oscillation Algorithm (EOA) and the state-of-the-art solving techniques. The experimental results as well as the statistical tests show the significant superiority of the EOA, motivating its adaptation to solve other bi-objective scheduling problems.