Evolving priority rules for on-line scheduling of jobs on a single machine with variable capacity over time

Abstract

On-line scheduling is often required in a number of real-life settings. This is the case of distributing charging times for a large fleet of electric vehicles arriving stochastically to a charging station working under power constraints. In this paper, we consider a scheduling problem derived from a situation of this type: one machine scheduling with variable capacity and tardiness minimization, denoted (1, Cap(t)|| P T i). The goal is to develop new priority rules to improve the results from some classical ones as Earliest Due Date (EDD) or Apparent Tardiness Cost (ATC). To this end, we developed a Genetic Programming (GP) approach. The e ciency of this algorithm relies on some smart representation of the expression trees. Besides, we restrict the search space to that of dimensionally compliant expressions, which allows GP to reach single and clear solutions. We conducted an experimental study showing that GP is able to evolve new rules that outperform ATC and EDD using the same problem attributes and operations.

Learning ensembles of priority rules for online scheduling by hybrid evolutionary algorithms

“…We conducted an experimental study, comparing the evolved ensembles to the best online and offline methods in the literature to solve the (1, Cap(t)|| T i ) problem. As far as we know, the best performing methods are a schedule builder guided by the priority rules evolved by GP in [12] and the memetic algorithm proposed in [32]. The results show that the solutions obtained from the evolved ensembles are better than those produced by the best rules obtained in [12] and that these solutions are actually close to those obtained offline in [32].…”

“…They capture some single features of the problem that may be exploited to devise heuristics; however there may be other complex features that are not evident to the human eye, which can only be captured by some automatic learning mechanism. Under this hypothesis, in [12], a Genetic Program (GP) was proposed to evolve new priority rules, which were shown to outperform the aforementioned EDD, SPT and ATC rules.…”

“…We propose a new benchmark set that consists of instances more realistic than those considered in [12]. More concretely, we have observed that in the instances considered in [12] the capacity intervals are in general very long compared to the processing times of the operations. As a result, most operations can be scheduled before the capacity of the machine begins to decrease, which is not realistic.…”

“…In this respect, several authors have adopted the classic GP paradigm proposed by Koza in [7] for learning rules for scheduling problems. These include job shop [8,9,10], single machine [11,12], unrelated parallel machines [13] or resource constrained project scheduling problems [14,15], among others. Other approaches have emerged such as cartesian genetic programming [16,17], single node genetic programming island model [18] or hybrid genetic programming [19].…”

“…The approach proposed herein starts from a large set of rules produced by GP [12] from a given training set in a number of runs. Due to the stochastic nature of GP, one may expect that this set will include quite different rules.…”