Evolving priority scheduling heuristics with genetic programming

Abstract

This paper investigates the use of genetic programming in automated synthesis of scheduling heuristics for an arbitrary performance measure. Genetic programming is used to evolve the priority function, which determines the priority values of certain system elements (jobs, machines). The priority function is used within an appropriate meta-algorithm for a given environment, which forms the priority scheduling heuristic. The evolved solutions are compared with existing scheduling heuristics and found to perform similarly to or better than existing algorithms. We intend to show that this approach is particularly useful for combinations of scheduling environments and performance measures for which no adequate scheduling algorithms exist.

Introduction

Scheduling is a decision-making process concerned with allocating scarce resources to tasks over given time periods, aiming to optimize one or more objectives (performance measures) [1]. Scheduling problems are usually modeled based on a quantitative mathematical approach. The scheduling environment includes the resource set (the amount and the type of each resource), and the nature of the tasks. A model may contain one or more machines available in unit amounts or in parallel. Tasks may be described by their resource requirement, duration, and the start and due times. Precedence restrictions that may exist among the tasks and other processing characteristics and constraints are also considered as parts of task modeling. The manufacturing vocabulary is usually employed, as early developments in the scheduling field were related to the problems arising in manufacturing. Hence, resources are usually called machines and tasks are referred to as jobs.

Decision-making goals are modeled as objective functions. The objective to be minimized is a function of the completion times for the jobs. For example, the objective could be to minimize the completion time of the last job or the number of jobs completed after their respective due dates.

A solution to a scheduling problem includes resolving allocation and sequencing issues: which resource should be allocated to perform each task, and when each task should be performed. There are cases when scheduling is narrowed down to pure allocation resolution, and in other cases scheduling is purely sequencing. Depending on the model, the solution usually involves developing, applying and evaluating combinatorial methods, simulation techniques and heuristic approaches.

The combinatorial nature of most scheduling problems allows using search-based and enumerative techniques [2], including genetic algorithms, branch and bound, simulated annealing. These methods usually offer good quality solutions, but at the cost of a large amount of computational time required by a solution algorithm. Furthermore, search-based techniques are not applicable in dynamic or uncertain conditions, which may require frequent schedule modification or reaction to changing system requirements (i.e. resource failures or job parameter changes). Scheduling with simple but fast heuristic algorithms that directly build schedules (not searching the solution space) is therefore highly effective, and the only feasible solution, in many instances.

Due to the inherent problem complexity and variability, many scheduling systems employ such heuristic scheduling methods. Among the available heuristic algorithms, the question arises of which heuristic to use in a particular environment, given different performance criteria and user requirements. The problem of selecting the appropriate scheduling policy is an active research area [2], [3], and considerable effort is needed to choose or develop the algorithm best suited to the scheduling problem at hand. Recent approaches addressing this issue include inferring fuzzy rules to assign the appropriate scheduling strategy for parallel jobs on identical machines [4] and building a fuzzy rule base for a hypothetical manufacturing system [5]. Considering the vast variety of environments that may be encountered, an effective solution to this problem may be provided using machine learning, particularly genetic programming, to create problem-specific scheduling algorithms.

Genetic programming (GP) is rarely employed in scheduling [6], [7], mainly because it is unpractical to use it to search the space of potential solutions (i.e. schedules). It is, however, suitable for searching the space of algorithms that provide solution to the scheduling problem. Previous work in this area includes evolving scheduling policies for the single machine unweighted tardiness problem [8], [9], [10] and single machine scheduling subject to breakdowns [11]. Classic job shop tardiness scheduling is also addressed [12], [13], as well as airplane scheduling in air traffic control [14], [15]. In most cases, the authors observe performance comparable to human-made algorithms. The scheduling procedure is however defined only implicitly for a given scheduling environment, which leaves space for misunderstandings and affects reproducibility. Moreover, the scheduling paradigm is mostly reduced to list scheduling, where job ordering is determined only at the beginning of the process, which reduces the space of usable heuristics.

In this paper, we structure the scheduling algorithm in two components: a meta-algorithm, which uses priority values to perform scheduling, and a priority function, which defines priorities for different system elements. The priority function is evolved for a given scheduling environment using genetic programming, while the meta-algorithm is defined manually. This allows creating of various heuristics tailored to an arbitrary scheduling environment.

To illustrate this methodology, we address the problems in single machine and job shop scheduling environments, combined with several real-world properties that complicate the application of existing heuristics. The properties include job weights, dynamic job arrivals, precedence constraints, sequence dependent setup times and combinations of those. Other problems (not covered here) were also investigated, such as multiple proportional machine scheduling [16], dynamic identification of bottleneck resources [17] and resource constrained project scheduling [18].

The remainder of this paper is organized as follows: Section 2 describes the approach in more detail, and Sections 3 Single machine scheduling, 4 Job shop scheduling show its application on the single machine and job shop problems, respectively. Section 5 covers the choice of relevant parameters. Section 6 discusses the results, followed by a brief conclusion.