Lagrangian Particle Swarm Optimization for a resource constrained machine scheduling problem

Recently a novel hybrid heuristic combining various Lagrangian heuristic ideas with Particle Swarm Optimization has been proposed and tested in the context of degree constrained minimum spanning trees. This paper investigates the applicability of the new hybrid meta-heuristic to a challenging scheduling problem. The resource constrained scheduling problem involves a set of jobs that need to be scheduled on multiple machines so as to minimise total weighted tardiness in the presence of precedence constraints and release dates. This is further complicated by the need for the jobs to consume a shared resource with limited capacity. The paper shows that the Lagrangian Particle Swarm Optimization approach can produce both high quality upper bounds (heuristic solutions) and useful lower bounds giving a performance guarantee for these heuristic solutions. Computational results are presented to show that the new method can outperform previous approaches in the literature for this problem.