Ghassan Shobaki
ABSTRACT
In this paper, we describe how to combine a parallel branch-and-bound (B&B) algorithm and a strong heuristic to solve the Sequential Ordering Problem (SOP), which is an NP-hard optimization problem. A parallel B&B algorithm is run in parallel with the Lin-Kernighan-Helsgaun heuristic algorithm, which is known to be one of the strongest heuristic algorithms for solving the SOP. The best solutions found by each algorithm are shared with the other algorithm, and each algorithm benefits from the better solutions found by the other. With the better solutions found by B&B, LKH can find even better solutions. With the better solutions found by LKH, B&B will have a tighter upper bound that enables it to prune at shallower tree nodes and thus complete it search faster. The combined algorithm is evaluated experimentally on the SOPLIB and TSPLIB benchmarks. The results show that the combined algorithm gives significantly better performance than any of the B&B algorithm or the LKH heuristic individually. Significant improvements in both speed and solution quality are seen on both benchmark suites. For example, the proposed algorithm delivers a geometric-mean speedup of 10.17 relative to LKH on the medium-difficulty SOPLIB instances. On the hard SOPLIB instances, it improves the cost by up to 22% relative to B&B and up to 90% relative to LKH
- D. Anghinolfi, R. Montemanni, M. Paolucci, and L.M. Gambardella. 2011. A hybrid particle swarm optimization approach for the sequential ordering problem. Computers & Operations Research 38, 7 (2011), 1076–1085.Google Scholar
Digital Library
- N. Ascheuer, L.F. Escudero, M. Grötschel, and M. Stoer. 1993. A cutting plane approach to the sequential ordering problem (with applications to job scheduling in manufacturing). SIAM J. Optim. 3, 1 (1993), 25–42.Google ScholarDigital Library
- N. Ascheuer, M. Jünger, and G. Reinelt. 2000. A branch & cut algorithm for the asymmetric traveling salesman problem with precedence constraints. Comput. Optim. Appl. 17 (2000), 61–84.Google ScholarDigital Library
- A. Borisenko and S. Gorlatch. 2019. Optimal batch plants design on parallel systems: A comparative study. In IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). 549–558.Google Scholar
- I. Chakroun and N. Melab. 2015. Towards a heterogeneous and adaptive parallel branch-and-bound algorithm. J. Comput. System Sci. 81, 1 (2015), 72–84.Google ScholarDigital Library
- T.G. Crainic, B. Le Cun, and C. Roucairol. 2006. Parallel branch-and-bound algorithms. In Parallel Combinatorial Optimization. 1–28.Google Scholar
- A. Dabah, A. Bendjoudi, A. AitZai, D. El-Baz, and N.N. Taboudjemat. 2018. Hybrid multi-core CPU and GPU-based B&B approaches for the blocking job shop scheduling problem. J. Parallel and Distrib. Comput. 117 (2018), 73–86.Google ScholarDigital Library
- A. de Bruin, G.A.P. Kindervater, and H.W.J.M. Trienekens. 1995. Asynchronous parallel branch and bound and anomalies. In Parallel Algorithms for Irregularly Structured Problems. Lecture Notes in Computer Science, Vol. 980. 363–377.Google Scholar
- L.F. Escudero. 1988. An inexact algorithm for the sequential ordering problem. Eur. J. Oper. Res. 37, 2 (1988), 236–249.Google ScholarCross Ref
- L.F. Escudero, M. Guignard, and K. Malik. 1994. A Lagrangian relax-and-cut approach for the sequential ordering problem with precedence relationships. Ann. Oper. Res. 50, 1 (1994), 219–237.Google ScholarCross Ref
- L.M. Gambardella, R. Montemanni, and D. Weyland. 2012. An enhanced ant colony system for the sequential ordering problem. In Operations Research Proceedings 2011. 355–360.Google Scholar
- B. Gendron and T.G. Crainic. 1994. Parallel branch-And-bound algorithms: Survey and synthesis. Oper. Res. 42, 6 (1994), 1042–1066.Google ScholarDigital Library
- J. Gmys. 2017. Heterogeneous cluster computing for many-task exact optimization - Application to permutation problems. Ph. D. Dissertation. Université de Mons (UMONS) ; Université de Lille.Google Scholar
- J. Gmys, M. Mezmaz, N. Melab, and D. Tuyttens. 2020. A computationally efficient branch-and-bound algorithm for the permutation flow-shop scheduling problem. European Journal of Operational Research 284, 3 (2020), 814–833.Google ScholarCross Ref
- T. Gonggiatgul, G. Shobaki, and P. Muyan-Özçelik. 2022. A Parallel Branch-and-Bound Algorithm with History-Based Domination. In Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP). 439–440.Google Scholar
- T. Gonggiatgul, G. Shobaki, and P. Muyan-Özçelik. 2023. A parallel branch-and-bound algorithm with history-based domination and its application to the sequential ordering problem. J. Parallel and Distrib. Comput. 172 (2023), 131–143.Google ScholarDigital Library
- L. Gouveia and P. Pesneau. 2006. On extended formulations for the precedence constrained asymmetric traveling salesman problem. Networks 48, 2 (2006), 77–89.Google ScholarDigital Library
- L. Gouveia and M. Ruthmair. 2015. Load-dependent and precedence-based models for pickup and delivery problems. Comput. Oper. Res. 63 (2015), 56–71.Google ScholarDigital Library
- K. Helsgaun. 2000. An effective implementation of the Lin–Kernighan traveling salesman heuristic. European Journal of Operational Research 126, 1 (2000), 106–130.Google ScholarCross Ref
- K. Helsgaun. 2009. General k-opt submoves for the Lin–Kernighan TSP heuristic. Math. Prog. Comp. 1 (2009), 119–163.Google ScholarCross Ref
- K. Helsgaun. 2017. An extension of the Lin-Kernighan-Helsgaun TSP Solver for constrained traveling salesman and vehicle routing problems. Technical Report. Roskilde Universitet.Google Scholar
- J. Jamal, G. Shobaki, V. Papapanagiotou, L.M. Gambardella, and R. Montemanni. 2017. Solving the sequential ordering problem using branch and bound. In IEEE Symposium Series on Computational Intelligence. 1–9.Google Scholar
- J. Kinable, A.A. Ciré, and W.-J. van Hoeve. 2017. Hybrid optimization methods for time-dependent sequencing problems. Eur. J. Oper. Res. 259, 3 (2017), 887–897.Google ScholarCross Ref
- M. E. Lalami and D. El-Baz. 2012. GPU implementation of the branch and bound method for knapsack problems. In IEEE International Parallel and Distributed Processing Symposium Workshops PhD Forum. 1769–1777.Google Scholar
- S. Lin and B. W. Kernighan. 1973. An effective heuristic algorithm for the Traveling-Salesman Problem. Operations Research 21, 2 (1973), 498–516.Google ScholarDigital Library
- C. McCreesh and P. Prosser. 2015. The shape of the search tree for the maximum clique problem and the implications for parallel branch and bound. ACM Trans. Parallel Comput. 2, 1 (2015), 8:1–8:27.Google ScholarDigital Library
- A. Mingozzi, L. Bianco, and S. Ricciardelli. 1997. Dynamic programming strategies for the traveling salesman problem with time window and precedence constraints. Oper. Res. 45, 3 (1997), 365–377.Google ScholarDigital Library
- M. Mojana, R. Montemanni, G.D. Caro, and L.M. Gambardella. 2012. A branch and bound approach for the sequential ordering problem. In Proceedings of the International Conference on Applied Operational Research. Lecture Notes in Management Science, Vol. 4. 266–273.Google Scholar
- R. Montemanni, D.H. Smith, and L.M. Gambardella. 2008. A heuristic manipulation technique for the sequential ordering problem. Computers & Operations Research 35, 12 (2008), 3931–3944.Google ScholarDigital Library
- V. Papapanagiotou, J. Jamal, R. Montemanni, G. Shobaki, and L.M. Gambardella. 2015. A comparison of two exact algorithms for the sequential ordering problem. In IEEE conference on systems, process and control (ICSPC). 73–78.Google Scholar
- G. Reinelt. 1991. TSPLIB—A traveling salesman problem library. INFORMS Journal on Computing 3, 4 (1991), 376–384.Google ScholarCross Ref
- Y. Salii. 2019. Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization. Eur. J. Oper. Res. 272, 1 (2019), 32–42.Google ScholarCross Ref
- Y.V. Salii and A.S. Sheka. 2020. Improving dynamic programming for travelling salesman with precedence constraints: Parallel Morin–Marsten bounding. Optimization Methods and Software (2020), 1–27.Google Scholar
- G. Shobaki and J. Jamal. 2015. An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers. Comput. Optim. Appl. 61, 2 (2015), 343–372.Google ScholarDigital Library
- R. Skinderowicz. 2017. An improved ant colony system for the sequential ordering problem. Computers & Operations Research 86 (2017), 1–17.Google ScholarCross Ref
Index Terms
- Combining a Parallel Branch-and-Bound Algorithm with a Strong Heuristic to Solve the Sequential Ordering Problem
Recommendations
A parallel branch-and-bound algorithm with history-based domination
PPoPP '22: Proceedings of the 27th ACM SIGPLAN Symposium on Principles and Practice of Parallel ProgrammingIn this paper, we describe a parallel Branch-and-Bound (B&B) algorithm with a history-based domination technique, and we apply it to the Sequential Ordering Problem (SOP). To the best of our knowledge, the proposed algorithm is the first parallel B&B ...
A parallel branch-and-bound algorithm with history-based domination and its application to the sequential ordering problem
AbstractIn this paper, we describe the first parallel Branch-and-Bound (B&B) algorithm with a history-based domination technique. Although history-based domination substantially speeds up a B&B search, it makes parallelization much more ...
Highlights- We propose the first parallel B&B algorithm that involves a history-based domination technique.
A cooperative parallel rollout algorithm for the sequential ordering problem
Special issue: Parallel computing in logisticsIn this paper we deal with the solution of the sequential ordering problem (SOP) in parallel environments. In particular, we present a parallel version of the rollout algorithm, an innovative heuristic method for solving NP-Hard combinatorial ...
Comments