Solving multi-objective parallel machine scheduling problem by a modified NSGA-II

Bandyopadhyay, Susmita; Bhattacharya, Ranjan

doi:10.1016/j.apm.2013.01.050

“…Specifically in parallel machine scheduling under multiple objectives, heuristic approaches such as the GAP/EDD algorithm were combined with metaheuristics, such as Tabu Search, to solve the bicriteria Cmax and Max T problem [1]. In the recent years, new metaheuristic approaches have been proposed to solve the different multi-objective problems in parallel machine scheduling, such as the Nondominated Sorting Genetic Algorithm (NSGA) [9], the Particle Swarm Optimization Problem (PSO) [10], among others. On the other hand, agent-based approaches have also been approached for machine scheduling.…”

Section: Extant Workmentioning

confidence: 99%

A bi-criteria optimization model for parallel machine scheduling: game theoretic vs genetic algorithms

Rios¹,

Pinto²,

Martinez³

et al. 2016

IJMSOR

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Abstract--This paper considers a problem for scheduling jobs on two identical parallel machines, the aim was to minimize two criteria in particular, makespan and total flow time. In order to solve this problem, two approaches were considered. A mechanism was proposed as an approach to solve this type of problem with a setting of a 2-player non-cooperative game, under the framework of a 2x2 non-sum zero matrix; each player looking after one of the criteria suggested in the scheduling problem. On the other hand, a Genetic Algorithm, known as Strength Pareto Evolutionary Algorithm (SPEA), was applied to the problem. The comparison between both approaches suggests a complementarity among rational agents approach models and machine enforced solution approaches. The resulting Pareto Front set of points were plotted and curves were compared, showing promising results for game theoretic applications to scheduling under multiple objectives.Keywords-identical parallel machines, makespan, total flow time, non-cooperative game, SPEA, Pareto Front.Resumen--Este articulo contempla el problema de programación de la producción en una configuracion de maquinas en paralelo con el objetivo de minimizar dos criterios en particular: el lapso y el tiempo total de flujo. En este problema en particular, el incremento de uno de estos objetivos resulta en la reduccion del otro, por lo que se propone su solucion bajo enfoques metaheuristicos. Dos tipos de algoritmos fueron considerados: uno basado en la teoria de juegos y el otro en los algoritmos genéticos. Para el primero se diseña un mecanismo de juego no cooperativo entre dos jugadores, en donde cada jugador busca optimizar cada criterio de programación de las máquinas. Para el segundo enfoque se implementa el algortimo genético SPEA, en donde se seleccionan aquellas soluciones dominantes en ambos objetivos. Resultados de ambos enfoques resultan en un Frente de Pareto, las cuales representan las soluciones dominantes para ambos objetivos. Estos resultados demuestran que ambos enfoques son complementarios: SPEA arroja resultados que cubren todo el frente de Pareto, mientras que el algoritmo de Juegos No Cooperativo indica la programación mas conveniente para cada agente en particular.

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“…In practical engineering, multiple indicators may be involved in many optimization problems [15,16], e.g., the diaphragm spring requires that not only the absolute value of the pressing force |F b − F a | is the lowest value that ensures a reliable pressing force in the range of the wear limit but, in addition, the average value of the separation force of bearings in the separation process should be as small as possible to ensure light manipulation. These two or more design specifications achieve an optimal value that is termed multi-objective optimization.…”

Section: Nsga-ii Algorithm and Multi-objective Solutionmentioning

confidence: 99%

Multi-Objective Optimization of a Spring Diaphragm Clutch on an Automobile Based on the Non-Dominated Sorting Genetic Algorithm (NSGA-II)

Zhou

¹

,

Chun

²

,

Zhu

³

2016

MCA

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Abstract:The weight coefficients of the diaphragm spring depend on experiences in the traditional optimization. However, this method not only cannot guarantee the optimal solution but it is also not universal. Therefore, a new optimization target function is proposed. The new function takes the minimum of average compress force changing of the spring and the minimum force of the separation as total objectives. Based on the optimization function, the result of the clutch diaphragm spring in a car is analyzed by the non-dominated sorting genetic algorithm (NSGA-II) and the solution set of Pareto is obtained. The results show that the pressing force of the diaphragm spring is improved by 4.09% by the new algorithm and the steering separation force is improved by 6.55%, which has better stability and steering portability. The problem of the weight coefficient in the traditional empirical design is solved. The pressing force of the optimized diaphragm spring varied slightly during the abrasion range of the friction film, and the manipulation became remarkably light.

show abstract

“…In practical engineering, multiple indicators may be involved in many optimization problems [16,17], e.g., the diaphragm spring requires that not only the absolute value of the pressing force |Fb − Fa| is the lowest value that ensures a reliable pressing force in the range of the wear limit but, in addition, the average value of the separation force of bearings in the separation process should be as small as possible to ensure light manipulation. These two or more design specifications achieve an optimal value that is termed multi-objective optimization.…”

Section: Nsga-ii Algorithm and Multi-objective Solutionmentioning

confidence: 99%

Multi-Objective Optimization of Spring Diaphragm Clutch on Automobile Based on the Non-Dominated Sorting Genetic Algorithm (NSGA-II)

Zhou¹,

Wang²,

Zhu³

2016

Preprint

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Abstract:The weight coefficients of the diaphragm spring depend on experiences in the traditional optimization. However, this method not only cannot guarantee the optimal solution but it is also not universal. Therefore, a new optimization target function is proposed. The new function takes the minimum of average compress force changing of the spring and the minimum force of the separation as total objectives. Based on the optimization function, the result of the clutch diaphragm spring in a car is analyzed by the non-dominated sorting genetic algorithm (NSGA-II) and the solution set of Pareto is obtained. The results show that the pressing force of the diaphragm spring is improved by 4.09% by the new algorithm and the steering separation force is improved by 6.55%, which has better stability and steering portability. The problem of the weight coefficient in the traditional empirical design is solved. The pressing force of the optimized diaphragm spring varied slightly during the abrasion range of the friction film, and the manipulation became remarkably light.

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Solving multi-objective parallel machine scheduling problem by a modified NSGA-II

Cited by 69 publications

References 30 publications

A bi-criteria optimization model for parallel machine scheduling: game theoretic vs genetic algorithms

A bi-criteria optimization model for parallel machine scheduling: game theoretic vs genetic algorithms

Multi-Objective Optimization of a Spring Diaphragm Clutch on an Automobile Based on the Non-Dominated Sorting Genetic Algorithm (NSGA-II)

Multi-Objective Optimization of Spring Diaphragm Clutch on Automobile Based on the Non-Dominated Sorting Genetic Algorithm (NSGA-II)

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