A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

2012 ◽  
Vol 3 (2) ◽  
pp. 24-45 ◽  
Author(s):  
Deniz Mungan ◽  
Junfang Yu ◽  
Bhaba R. Sarker ◽  
Mohammad Anwar Rahman
Keyword(s):  
Objective Function ◽  
Single Machine ◽  
Pareto Optimality ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Neighborhood Search ◽  
Pareto Optimal ◽  
Scheduling Problem ◽  
Objective Functions ◽  
Periodic Maintenance

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

On Pareto Optimal Solution for Production and Maintenance Jobs Scheduling Problem in a Job Shop and Flow Shop with an Immune Algorithm

2014 ◽  
Vol 1036 ◽  
pp. 875-880 ◽  
Author(s):  
Iwona Paprocka ◽  
Wojciech M. Kempa ◽  
Krzysztof Kalinowski ◽  
Cezary Grabowik
Keyword(s):  
Job Shop ◽  
Flow Shop ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Immune Algorithm ◽  
Flow Shop Scheduling ◽  
Pareto Optimal ◽  
Scheduling Problem ◽  
Shop Scheduling ◽  
Mean Time

In the paper a job shop and flow shop scheduling problems with availability time constraint for maintenance are considered. Unavailability time due to maintenance is estimated basing on information about predicted Mean Time To Failure/To First Failure and Mean Time of Repair of a machine. Maintenance actions are introduced into a schedule to keep the machine available in a good operation condition. The efficiency of predictive schedules (PS) is evaluated using criteria: makespan, flow time, total tardiness, idle time. The efficiency of reactive schedules (RSs) is evaluated using criteria: solution and quality robustness. For basic schedule generation Multi Objective Immune Algorithm is applied. For predictive scheduling Minimal Impact of Disturbed Operation on the Schedule is applied. After doing computer simulations for the job shop scheduling problem following question arises: do dominated Pareto optimal basic schedules achieve better PSs? Although a single Pareto-optimal solution is achieved on Pareto-optimal frontier three different schedules have the same quality in the flow shop scheduling problem. The question is: which schedule is the most robust solution?

scholarly journals A variable neighborhood search algorithm for solving the single machine scheduling problem with periodic maintenance

2019 ◽  
Vol 53 (1) ◽  
pp. 289-302 ◽  
Author(s):  
Hanane Krim ◽  
Rachid Benmansour ◽  
David Duvivier ◽  
Abdelhakim Artiba
Keyword(s):  
Single Machine ◽  
Variable Neighborhood Search ◽  
Search Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Computational Time ◽  
Neighborhood Search ◽  
Scheduling Problem ◽  
Periodic Maintenance ◽  
Neighborhood Search Algorithm

In this paper we propose to solve a single machine scheduling problem which has to undergo a periodic preventive maintenance. The objective is to minimize the weighted sum of the completion times. This criterion is defined as one of the most important objectives in practice but has not been studied so far for the considered problem. As the problem is proven to be NP-hard, and a mathematical model is proposed in the literature, we propose to use General Variable Neighborhood Search algorithm to solve this problem in order to obtain near optimal solutions for the large-sized instances in a small amount of computational time.

scholarly journals Matrix Maxima Method to Solve Multi-objective Transportation Problem with a Pareto Optimality Criteria

2019 ◽  
Vol 8 (11) ◽  
pp. 1929-1932
Keyword(s):  
Pareto Optimality ◽  
Transportation Problem ◽  
Geometric Mean ◽  
Optimal Solution ◽  
Optimality Criteria ◽  
Pareto Optimal Solution ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Pareto Optimal ◽  
Fast Method

In this paper we proposed a new method (Matrix Maxima Method) using Geometric mean approach to solve multiobjective transportation problem with a Pareto Optimality Criteria. Fuzzy membership function is used to convert objectives into membership values and then we take Geomertic mean of membership values. We used a different criteria to find Pareto Optimal Solution. This is an easy and fast method to find the Pareto Optimal solution. The method is illustrated by numerical examples. The result is compared with some other available methods in the literature.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

Sign in / Sign up

Export Citation Format

Share Document