A comprehensive review of Branch-and-Bound algorithms: Guidelines and directions for further research on the flowshop scheduling problem

Tomazella, Caio Paziani; Nagano, Marcelo Seido

doi:10.1016/j.eswa.2020.113556

Cited by 34 publications

(15 citation statements)

References 186 publications

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“…That's why Branch-and-Bound algorithms are very popular. In their review, Tomazella and Nagano [87] enumerate about 120 Branch and Bound algorithms, only for flowshop problems. 1967 Burns [13] 1980 Bansal [4] 1983 Potts and Van Wassenhove [75] 1985 Posner [73] 1987 Bagchi and Ahmadi [3] 1988 Abdul-Razaq and Potts [1] 2003 Pan [63] 2004 T'kindt et al [85] 2021 Shang et al [81] (b) The F |prmu|C max problem year reference 1965 Ignall and Schrage [37] 1965 Lomnicki [52] 1966 Brown and Lomnicki [11] 1967 McMahon and Burton [54] 1970 Ashour [2] 1978 Lageweg et al [46] 1980 Potts [74] 1991 Brah and Hunsucker [10] 1996 Carlier and Rebaï [15] 1997 Cheng et al [16] 2005 Ladhari and Haouari [45] 2016 Ritt [76] 2020 Gmys et al [30] Branch-and-Bound is very successful when applied to sequencing problems, i.e.…”

Section: Branching Algorithmsmentioning

confidence: 99%

Contributions of Inclusion-Exclusion to exact or approximate solution of scheduling problems

Ploton

2023

4OR-Q J Oper Res

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Les études forment un long cheminement parsemé d'incertitudes et de rebondissements. Chaque étape, chaque projet est une aventure en soi, partagée entre un étudiant et son professeur. Il arrive que la transmission du savoir du professeur à l'étudiant s'opère de manière tellement naturelle que la motivation s'en trouve décuplée et permette des efforts et des réussites inimaginables.En tant qu'étudiant j'ai vécu cette situation idéale par deux fois. La première, c'était avec mon professeur de mathématiques d'hypotaupe, Michel Quercia, le professeur le plus époustouflant que j'aie connu, parmi une concurrence pourtant très relevée. La seconde, c'est avec Vincent T'kindt au cours de cette thèse. Je mesure toute l'audace dont il a fait preuve en me prenant en thèse, et tout le respect qu'il m'a témoigné au cours de ces trois années ponctuées d'efforts et de difficultés, d'espoirs et de déceptions, d'avancées et de circonvolutions. J'en suis très honoré. J'ai effectué cette thèse tout en enseignant les Mathématiques et l'Informatique en tant que PRAG à L'université de Tours. Cette thèse est donc auto-financée, mais j'ai bénéficié de décharges de service pour un total équivalent à une année complète. Je remercie le Conseil Académique de m'avoir accordé ces avantages matériels, et par là même de m'avoir accordé sa confiance.Je remercie Hubert Cardot, Emmanuel Humbert et Sandrine Dallet-Choisy de m'avoir appuyé auprès du Conseil Académique et de m'avoir constamment soutenu.Je remercie mes collègues Boris Andreianov, Thierry Brouard et Florent Malrieu d'avoir créé un contexte favorable à cette thèse par leurs conseils avisés.Je remercie Hélène Tison pour sa patience, ainsi que tous les membres de l'équipe de recherche ROOT pour leur bienveillance à mon égard :

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Section: Branching Algorithmsmentioning

confidence: 99%

Contributions of Inclusion-Exclusion to exact or approximate solution of scheduling problems

Ploton

2023

4OR-Q J Oper Res

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“…Classical PN generally employs an RNN [26] as the encoder, which can aggregate both the input information and the input order, such as the words in a sentence and the order of the words. However, the inputs to many COPs are mutually independent entities with no temporal relationship, such as cities in TSP and VRP [23], items in knapsack problem [24], and jobs in scheduling problem [25], etc. For solving such problems, the RNN in encoder is no longer appropriate.…”

Section: B Framework Of Mopnmentioning

confidence: 99%

Multi-objective Pointer Network for Combinatorial Optimization

Le-yang¹,

Wang²,

Liu³

et al. 2022

Preprint

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Multi-objective combinatorial optimization problems (MOCOPs), one type of complex optimization problems, widely exist in various real applications. Although meta-heuristics have been successfully applied to address MOCOPs, the calculation time is often much longer. Recently, a number of deep reinforcement learning (DRL) methods have been proposed to generate approximate optimal solutions to the combinatorial optimization problems. However, the existing studies on DRL have seldom focused on MOCOPs. This study proposes a singlemodel deep reinforcement learning framework, called multiobjective Pointer Network (MOPN), where the input structure of PN is effectively improved so that the single PN is capable of solving MOCOPs. In addition, two training strategies, based on representative model and transfer learning, respectively, are proposed to further enhance the performance of MOPN in different application scenarios. Moreover, compared to classical meta-heuristics, MOPN only consumes much less time on forward propagation to obtain the Pareto front. Meanwhile, MOPN is insensitive to problem scale, meaning that a trained MOPN is able to address MOCOPs with different scales. To verify the performance of MOPN, extensive experiments are conducted on three multi-objective traveling salesman problems, in comparison with one state-of-the-art model DRL-MOA and three classical multiobjective meta-heuristics. Experimental results demonstrate that the proposed model outperforms all the comparative methods with only 20% to 40% training time of DRL-MOA.

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“…This method searches for local optimum based on a certain deterministic strategy, and tries to jump the local optimum obtained to achieve a global optimum, which can make full use of the analytical properties of the problem and thus has high computational efficiency. For example, the filled function method 6 7 , the tunneling function method 8 , the D. C. optimization algorithm 9 , the interval method 10 , the monotone programming 11 , the branch and bound method 12 , and the integral-level set method 13 . The construction of these algorithms involves some local or global properties of the known objective function.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Granular Sieving Algorithm for Global Optimization

Lin

Chen

2023

Preprint

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Global optimization problems widely exist in the fields of economic model, finance, engineering design and control. Since it is easy to fall into multiple local optimal solutions that are different from the global optimal solution, how to obtain the global optimal solution is a very important subject. Inspired by the recently proposed deterministic global optimization method – Granular Sieving (GrS) algorithm, this paper proposes a parallel method for global optimization – P-GrS. Supported by the mathematical theory of GrS, P-GrS can theoretically guarantee to find the global optimum and the complete set of global optimal solutions through the parallel design of GrS. The method has better performance than the traditional GrS in most bench mark functions, and the results show the feasibility and effectiveness of the algorithm.

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A comprehensive review of Branch-and-Bound algorithms: Guidelines and directions for further research on the flowshop scheduling problem

Cited by 34 publications

References 186 publications

Contributions of Inclusion-Exclusion to exact or approximate solution of scheduling problems

Contributions of Inclusion-Exclusion to exact or approximate solution of scheduling problems

Multi-objective Pointer Network for Combinatorial Optimization

A Parallel Granular Sieving Algorithm for Global Optimization

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