Abordagem multiobjetivo para o problema de sequenciamento de tarefas em máquinas paralelas não-relacionadas com a deterioração da máquina dependente da sequência

Abstract

This work addresses a scheduling problem unrelated to parallel machines, in which jobs significantly impact machine deterioration. This deterioration, in turn, adversely affects machine performance, resulting in progressive increases in job processing times over time. To tackle this challenge, a mixed-integer nonlinear programming model is proposed, aiming to optimize two objectives simultaneously: minimizing the maximum job completion time, known as makespan, and minimizing the job total tardiness. An innovative approach is developed to extend the meta-heuristic Iterated Local Search (ILS) to multiobjective problems. The resulting algorithm, named Iterated Local Search Based on Decomposition (ILS/D), employs a decomposition strategy similar to that used by the Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D). In this context, ILS is utilized as a search mechanism to enhance the exploration process within the MOEA/D framework. One distinctive advantage of ILS/D is that a single-objective ILS can optimize each subproblem under the decomposition and aggregation framework, thus obviating the need for multiobjective local search. To evaluate the effectiveness of ILS/D, comparisons were made with other algorithms, including MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Pareto Iterated Local Search (PILS). The results demonstrate that ILS/D significantly outperforms the other mentioned algorithms. These findings highlight the decomposition strategy's effectiveness in evolutionary algorithms and illustrate the ILS algorithm's successful extension to complex multiobjective problem resolution. Furthermore, a multiobjective approach involving maintenance is proposed. In this approach, the integration of maintenance into production scheduling is sought, to mitigate machine deterioration and reduce the total processing time. The central purpose is to determine the strategic allocation of maintenance, or maintenance jobs, to maximize the overall system performance. When a machine fails within a production system or when its level of deterioration reaches a critical threshold, that machine becomes unable to continue production until it is restored to a fully operational state through maintenance intervention. In other words, the machine's performance must be restored to 100%. Machine downtime results in production time losses and can overload other machines in the system, causing them to become unavailable as well. In this context, three distinct strategies for scheduling maintenance jobs are developed, all operating within the ILS/D algorithm. A comprehensive set of numerical experiments is conducted on instances of various sizes, demonstrating that the developed algorithms can provide more precise solutions to the maintenance scheduling problem.