Algoritmo genético para solucionar el problema de dimensionamiento y programación de lotes con costos de alistamiento dependientes de la secuencia

The main purpose of this paper is to develop a hybrid genetic algorithmin order to determine the lot sizes and their production scheduling in asingle machine manufacturing system for multi-item orders, the objectivefunction minimizes the sum of holding costs, tardy costs and setup costs.The problem considers a set of orders to be processed each one with itsown due date. Each order must be delivered complete. In the schedulingare considered sequence dependent setup times. The proposed hybridgenetic algorithm has embedded a heuristic that is used to calculate itsfitness function. The heuristic method presents a modification on theoptimal timming algorithm in which are involved sequence dependentset up times. A design of experiments is developed in order to assess thealgorithm performance, which is also tested using random-generateddata and results are compared with those generated by an exact method.The results show that the algorithm achieves a good performance in bothsolution quality and time especially for large instances.El objetivo de este artículo es desarrollar un algoritmo genético el cualpermita determinar los tamaños de lote de producción y su programaciónen un sistema de manufactura de una máquina para órdenesmultiproducto, cuya función objetivo minimiza la suma de los costosde inventario por terminaciones tardías y de alistamiento. El problemacontempla un conjunto de órdenes a ser procesadas con sus respectivasfechas de entrega. Cada orden debe ser entregada en su totalidad. Dentrode la programación de los trabajos se consideran tiempos de alistamientodependientes de la secuencia. En la metaheurística implementada se utilizade manera embebida un método heurístico para el cálculo de la funciónde adaptación. El método heurístico presentado es una variación delOptimal Timming Algorithm el cual involucra los tiempos de alistamientodependientes de la secuencia. Se desarrolla un diseño de experimentospara probar el desempeño del algoritmo utilizando instancias generadasde forma aleatoria y comparando sus soluciones contra las encontradaspor un método exacto. Los resultados muestran que el algoritmo lograun buen desempeño tanto en tiempo de ejecución como en calidad de lasolución especialmente en instancias grandes.

Artificial Chromosomes with Genetic Algorithm 2 (ACGA2) for Single Machine Scheduling Problems with Sequence-Dependent Setup Times

[[abstract]]Artificial chromosomes with genetic algorithm (ACGA) is one of the latest versions of the estimation of distribution algorithms (EDAs). This algorithm has already been applied successfully to solve different kinds of scheduling problems. However, due to the fact that its probabilistic model does not consider variable interactions, ACGA may not perform well in some scheduling problems, particularly if sequence-dependent setup times are considered. This is due to the fact that the previous job will influence the processing time of the next job. Simply capturing ordinal information from the parental distribution is not sufficient for a probabilistic model. As a result, this paper proposes a bi-variate probabilistic model to add into the ACGA. This new algorithm is called the ACGA2 and is used to solve single machine scheduling problems with sequence-dependent setup times in a common due-date environment. A theoretical analysis is given in this paper. Some heuristics and local search algorithm variable neighborhood search (VNS) are also employed in the ACGA2. The results indicate that the average error ratio of this ACGA2 is half the error ratio of the ACGA. In addition, when ACGA2 is applied in combination with other heuristic methods and VNS, the hybrid algorithm achieves optimal solution quality in comparison with other algorithms in the literature. Thus, the proposed algorithms are effective for solving the scheduling problems.[[notice]]補正完

Artificial chromosomes with genetic algorithm 2 (ACGA2) for single machine scheduling problems with sequence-dependent setup times

[[abstract]]Artificial chromosomes with genetic algorithm (ACGA) is one of the latest versions of the estimation of distribution algorithms (EDAs). This algorithm has already been applied successfully to solve different kinds of scheduling problems. However, due to the fact that its probabilistic model does not consider variable interactions, ACGA may not perform well in some scheduling problems, particularly if sequence-dependent setup times are considered. This is due to the fact that the previous job will influence the processing time of the next job. Simply capturing ordinal information from the parental distribution is not sufficient for a probabilistic model. As a result, this paper proposes a bi-variate probabilistic model to add into the ACGA. This new algorithm is called the ACGA2 and is used to solve single machine scheduling problems with sequence-dependent setup times in a common due-date environment. A theoretical analysis is given in this paper. Some heuristics and local search algorithm variable neighborhood search (VNS) are also employed in the ACGA2. The results indicate that the average error ratio of this ACGA2 is half the error ratio of the ACGA. In addition, when ACGA2 is applied in combination with other heuristic methods and VNS, the hybrid algorithm achieves optimal solution quality in comparison with other algorithms in the literature. Thus, the proposed algorithms are effective for solving the scheduling problems