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# Article K-OPT in JSSP

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Este artigo apresenta de forma inédita a utilização da heurística do k-opt para o Job Shop Schedule Problem

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### Article K-OPT in JSSP

1. 1. K-OPT heuristic for TSP and JSSP Adriano Patricksábado, 16 de junho de 2012
2. 2. Work Proposal Traveling Salesman Problem Job Shop Scheduling Problemsábado, 16 de junho de 2012
3. 3. Traveling Salesman Problem The Traveling Salesman Problem consists in ﬁnding a circuit that has the shortdistance, starting in any city, among many, visiting each city exactly once and returning to the starting city (Nilsson, 1982).sábado, 16 de junho de 2012
4. 4. Job Shop Scheduling Problem “Allocating machines and tasks to minimize the total time (makespan) manufacturing a production line.”sábado, 16 de junho de 2012
5. 5. Job Shop Scheduling Problem Make n tasks: J1, J2, ... , Jn (as wires), as follows: Each task is processed by "m" machines M1, ..., Mm The processing ﬂow of the "n" tasks in "m" machines is the same for all tasks. A machine processes only one operation at a time, and should not be interrupted until its completion. Are known processing times for each task by machine. A task => "m" operations. Objective: To minimize the completion time of all tasks. There are n! different possible sequencessábado, 16 de junho de 2012
6. 6. K-OPT Lin and Kernighan in 1973 developed the k-optsábado, 16 de junho de 2012
7. 7. K-OPT In this proposal, k arcs are replaced in the circuit, other k arcs with the objective of reduce the total distance traveled. The higher the value of k, the better the accuracy of the method, but higher is the computational effort.sábado, 16 de junho de 2012
8. 8. K-OPT in TSPsábado, 16 de junho de 2012
9. 9. K-OPT in TSPsábado, 16 de junho de 2012
10. 10. K-OPT in JSSPsábado, 16 de junho de 2012
11. 11. K-OPT in JSSPsábado, 16 de junho de 2012
12. 12. K-OPT in JSSPsábado, 16 de junho de 2012
13. 13. K-OPT in JSSPsábado, 16 de junho de 2012
14. 14. K-OPT in JSSPsábado, 16 de junho de 2012
15. 15. K-OPT in JSSPsábado, 16 de junho de 2012
16. 16. Conclusions 3-OPT generates a limited number of threads in a short time As the time passes increases the difﬁculty of ﬁnding new threads heuristics But with the implementation of the method for generating new Shufﬂe random sequences based on sequence before showing the solution to more effectively the resultssábado, 16 de junho de 2012
17. 17. Bibliography Branco Ceron, Fábio José (2011); Um novo método heurístico construtivo de alto desempenho para o problema no idle ﬂow shop. Oliveira, José Fernando e Carravilla, Combinatória:Modelos e Algoritmos. De Paula, Mateus Rocha (2008); Heurísticas para a minimização dos atrasos emsequenciamento de máquinas paralelas com temposde preparação dependentes da sequência. Lin, S. e B. W. Kernighan (1973). An Effective Heuristic Algorithm for the Traveling Salesman Problem, Operations Research, v.21, p.498-516. Laporte, G.; M. Gendreau; J.Y. Potvin e F. Semet (2000) Classical and modern heuristics for the vehicle routing problem, International Transactions in Operational Research, v.7, n4/5, p.285-300. Novaes, A. G. (2001). Logística e Gerenciamento da Cadeia de Distribuição. Rio de Janeiro: Campus. Reinelt, G. (1994) The Traveling Salesman – Computational Solutions for TSP Applications. Berlin: Springer - Verlag. Souza, P.S. (1993) Asynchronous organizations for multi-algorithms problems. Pittsburgh: Carnegie Mellow University, Department of Electrical and Computer Engineering. 139p. (Tese de Doutoramento). Helsgaun, K. (2000). An effective implementation of the Lin-Kernigham Traveling Salesman Heuristic, European Journal of Operational Research, v.126, p.106-130.sábado, 16 de junho de 2012