Simulated annealing and metaheuristic for randomized priority search algorithms for the aerial refuelling parallel machine scheduling problem with due date-to-deadline windows and release times

Abstract

This article addresses the aerial refuelling scheduling problem (ARSP), where a set of fighter jets (jobs) with certain ready times must be refuelled from tankers (machines) by their due dates; otherwise, they reach a low fuel level (deadline) incurring a high cost. ARSP is an identical parallel machine scheduling problem with release times and due date-to-deadline windows to minimize the total weighted tardiness. A simulated annealing (SA) and metaheuristic for randomized priority search (Meta-RaPS) with the newly introduced composite dispatching rule, apparent piecewise tardiness cost with ready times (APTCR), are applied to the problem. Computational experiments compared the algorithms’ solutions to optimal solutions for small problems and to each other for larger problems. To obtain optimal solutions, a mixed integer program with a piecewise weighted tardiness objective function was solved for up to 12 jobs. The results show that Meta-RaPS performs better in terms of average relative error but SA is more efficient.

Keywords:

• parallel machine scheduling
• total weighted tardiness
• due date-to-deadline window
• release time
• simulated annealing
• Meta-RaPS