Genetic algorithm for bi-criteria single machine scheduling problem of minimizing maximum earliness and number of tardy jobs (original) (raw)
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Single Machine Total Weighted Tardiness Problem with Genetic Algorithms
2007 IEEE/ACS International Conference on Computer Systems and Applications, 2007
Scheduling problems are important NP-hard problems. Genetic algorithms can provide good solutions for such optimization problems. In this paper, we present a genetic algorithm to solve the single machine total weighted tardiness scheduling problem, which is a strong NP-hard problem. The algorithm uses the natural permutation representation of a chromosome, heuristic dispatching rules combined with random method to create the initial population, position-based crossover and order-based mutation operators, and the best members of the population during generations. The computational results of problem examples with 10 and 25 jobs and general problems with 50, 100, 200 and 500 jobs show the good performance and the efficiency of the developed algorithm.
Genetic algorithms to minimize the weighted number of late jobs on a single machine
European Journal of Operational Research, 2003
The general one-machine scheduling problem is strongly NP-Hard when the objective is to minimize the weighted number of late jobs. Few methods exist to solve this problem. In an other paper, we developed a Lagrangean relaxation algorithm which gives good results on many instances. However, there is still room for improvement, and a metaheuristic might lead to better results. In this paper, we decided to use a genetic algorithm (GA). Although a GA is somewhat easy to implement, many variations exist, and we tested some of them to design the best GA for our problem. Three different engines to evaluate the fitness of a chromosome are considered, together with four types of crossover operators and three types of mutation operators. An improved GA is also proposed by applying local search on solutions determined from the chromosome by the engine. Numerical experiments on different tests of instances are reported. They show that starting from an initial population already containing a good solution is very effective.
International Journal of Production Management and Engineering
This article presents two combinatorial genetic algorithms (GA), unequal earliness tardiness-GA (UET-GA) and job-dependent earliness tardiness-GA (JDET-GA) for the single-machine scheduling problem to minimize earliness tardiness (ET) cost. The sequence of jobs produced in basic UET and JDET as a chromosome is added to the random population of GA. The best sequence from each epoch is also injected as a population member in the subsequent epoch. The proposed improvement seeks to achieve convergence in less time to search for an optimal solution. Although the GA has been implemented very successfully on many different types of optimization problems, it has been learnt that the algorithm has a search ability difficulty that makes computations NP-hard for types of optimization problems, such as permutation-based optimization problems. The use of a plain random population initialization results in this flaw. To reinforce the random population initialization, the proposed enhancement is u...
Genetic algorithm for job shop scheduling with earliness and tardiness penalties
2010
The job-shop scheduling problem with operators is a very interesting problem that generalizes the classic jobshop problem in such a way that an operation must be algorithm to solve this problem considering makespan minimization. The genetic algorithm uses permutations with repetition to encode chromosomes and a schedule generation scheme, termed OG&T, as decoding algorithm. This combination guaranties that at least one of the chromosomes represents and optimal schedule and, at the samhat machines and operators are idle while an operation is available to be processed. To improve the quality of the schedules for large instances, we use Lamarckian evolution and modify the OG&T algorithm to further reduce the idle time of the machines and operators, in this case at the risk of leaving all optimal schedules out of the search space. We conducted a large experimental study showing that these improvements allow the genetic algorithm to reach high quality solutions in very short time, and so it is quite competitive with the current state-of-the-art methods.
European Journal of Operational Research, 2010
We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer's position, and the latter reflects the manufacturer's perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.
International journal of multicriteria decision making, 2012
The bi-criterion problem of minimising the number of tardy jobs and maximum earliness on a single machine is investigated experimentally. Two approximate solution approaches are tested. The first one is based on transforming the bi-criterion problem into a series of single-objective sub-problems and then applying a deterministic, heuristic procedure to solve them iteratively. The second approach is based on a multi-objective evolutionary algorithm with random keys encoding scheme. A dataset of 180 problem instances with 50, 100, and 150 jobs was generated randomly in order to evaluate the performance of the two approaches. The Pareto optimal sets computed by the evolutionary approach were consistently under-populated when compared to those of the heuristic however; more than 60% of the solutions found by the heuristic in all instances were dominated by solutions generated by the evolutionary algorithm.
Minimizing earliness and tardiness penalties in a single-machine problem with a common due date
European Journal of Operational Research, 2005
Scheduling problems involving both earliness and tardiness costs became more important in recent years. This kind of problems include both earliness and tardiness penalties and tries to reduce them. In this study a case study from real world is investigated. Since the machine is bottle neck in the production line and all jobs have a common restrictive due date and different earliness and tardiness penalties, the problem is NPhard. In this study a discrete Genetic Algorithm (GA) is successfully implemented to find an optimum scheduling for the production line. The results show the effectiveness of the proposed algorithm in finding near optimal solution.
Weighted Tardiness Minimization in Job Shops with Setup Times by Hybrid Genetic Algorithm
Lecture Notes in Computer Science, 2011
In this paper we confront the weighted tardiness minimization in the job shop scheduling problem with sequence-dependent setup times. We start by extending an existing disjunctive graph model used for makespan minimization to represent the weighted tardiness problem. Using this representation, we adapt a local search neighborhood originally defined for makespan minimization. The proposed neighborhood structure is used in a genetic algorithm hybridized with a simple tabu search method. This algorithm is quite competitive with state-of-theart methods in solving problem instances from several datasets of both classical JSP and JSP with setup times.