Grasp with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times

Abstract

This paper addresses the problem of scheduling jobs in a single machine with sequence dependent setup times in order to minimize the total tardiness with respect to job due dates. We propose variants of the GRASP metaheuristic that incorporate memorybased mechanisms for solving this problem. There are two mechanisms proposed in the literature that utilize a long-term memory composed of an elite set of high quality and sufficiently distant solutions. The first mechanism consists of extracting attributes from the elite solutions in order to influence the construction of an initial solution. The second one makes use of path relinking to connect a GRASP local minimum with a solution of the elite set, and also to connect solutions from the elite set. Reactive GRASP, which probabilistically determines the degree of randomness in the GRASP construction throughout the iterations, is also investigated. Computational tests for instances involving up to 150 jobs are reported, and the proposed method is compared with heuristic and exact methods from the literature.

GRASP to minimize total weighted tardiness in a permutation flow shop environment

“…For instance, Caballero-Villalobos and Alvarado-Valencia (2010) and Vega-Mejía and Caballero-Villalobos (2010) used GRASP to minimize TWT in a single machine environment. Similarly Armentano and Araujo (2006) minimized total tardiness considering setup times and Armentano and de França Filho (2007) also used for a parallel machine problem. Moreover, Arroyo and de Souza Pereira (2010) and Shahul Hamid Khan et al (2007) solved multi-objective PFS problems and Rajkumar et al (2011) solved a flexible job shop problem.…”

A framework to minimise total energy consumption and total tardiness on a single machine

“…Note that the total processing energy (Power processing * n j=1 p j ) is not included in the optimization problem, since it is a fixed constant regardless of the sequence. The second objective involves the total tardiness objective, equation (2). In the mathematical formulation, equation (3 states that a job cannot be processed before it is released.…”

“…In another application, it is utilized to minimize total earliness (Laguna and Velarde 1991). It is also applied to minimize total tardiness on a single machine with setup times (Armentano and Araujo 2006). Although there are a significant number of GRASP applications to solve combinatorial optimization problems, utilizing this procedure in a multiobjective programming is not very common (Jones et al 2002).…”

Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times

“…For example, in Rios-Mercado and Bard (1999) the authors propose a heuristic for the Flow Shop Scheduling problem which is based on TSP relaxations and compare their results with a GRASP algorithm. Also, there are approaches to Single Machine Scheduling such as the hybrid genetic algorithm proposed by Miller et al (1999), or the GRASP algorithm proposed by Armentano and Basi de Araujo (2006).…”