A simple genetic algorithm for a minimal overlapping scheduling problem

Abstract

This article introduces a new version of the Multiple Machine Scheduling Problem: the Scheduling Problem with Time Windows and Minimal Overlap (SPTWMO). Given a set of nonpreemptive jobs with time windows and a number of identical machines, the problem consists on finding a starting time for each job which satisfies time window constraints while minimizing a measure of resource infeasibility (the Total Overlap). The problem is NP-Complete even in the case when only one machine is considered. We present a simple genetic algorithm applied to the SPTWMO, reporting efficient numerical results according to lower bounds obtained solving the preemptive version of the problem.