ILS Heuristics for the Single-Machine Scheduling Problem with Sequence-Dependent Family Setup Times to Minimize Total Tardiness

Vinícius Vilar Jacob,José Elias C Arroyo

doi:10.1155/2016/9598041

Vinícius Vilar Jacob, José Elias C Arroyo

Open Access

https://doi.org/10.1155/2016/9598041

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Abstract

This paper addresses a single-machine scheduling problem with sequence-dependent family setup times. In this problem the jobs are classified into families according to their similarity characteristics. Setup times are required on each occasion when the machine switches from processing jobs in one family to jobs in another family. The performance measure to be minimized is the total tardiness with respect to the given due dates of the jobs. The problem is classified asNP-hard in the ordinary sense. Since the computational complexity associated with the mathematical formulation of the problem makes it difficult for optimization solvers to deal with large-sized instances in reasonable solution time, efficient heuristic algorithms are needed to obtain near-optimal solutions. In this work we propose three heuristics based on the Iterated Local Search (ILS) metaheuristic. The first heuristic is a basic ILS, the second uses a dynamic perturbation size, and the third uses a Path Relinking (PR) technique as an intensification strategy. We carry out comprehensive computational and statistical experiments in order to analyze the performance of the proposed heuristics. The computational experiments show that the ILS heuristics outperform a genetic algorithm proposed in the literature. The ILS heuristic with dynamic perturbation size and PR intensification has a superior performance compared to other heuristics.

Highlights

Scheduling is a very important decision-making process that occurs in manufacturing systems
To solve the 1|STsd,f| ∑ Tj problem, we propose three heuristics based on the Iterated Local Search (ILS) metaheuristic
In this paper we have considered a single-machine scheduling problem with sequence-dependent family setup times, so as to minimize the total tardiness

Summary

Introduction

Scheduling is a very important decision-making process that occurs in manufacturing systems. The SMTT problem with sequence-dependent setup times (without considering the grouping of jobs into families), denoted by 1|STsd| ∑ Tj, is one of the most researched topics in the scheduling literature. For this problem there are many studies on metaheuristics such as genetic algorithms [7,8,9,10], Simulated Annealing [11], Ant Colony Optimization [12, 13], Greedy Randomized Adaptive Search Procedure [14, 15], Iterated Local Search [16], and iterated greedy [17].

Problem Model

Proposed ILS Heuristics

Computational Experiments

Conclusions