A parallel branch-and-bound algorithm for integer linear programming and its implementation on a distributed multiprocessor

In branch and bound algorithm for integer linear programming the usual approach is incorporating dual simplex method to achieve feasibility for each sub-problem. Although one can also employ the phase 1 simplex method but the simplicity and easy implementation of the dual simplex method bounds the users to use it. In this paper a new technique for handling sub-problems in branch and bound method has been presented, which is an efficient alternative of dual simplex method.

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An integer linear programming model and a modified branch and bound algorithm for the project material requirements planning problem

Journal of Information and Optimization Sciences ◽

10.1080/02522667.2003.10699561 ◽

2003 ◽

Vol 24 (1) ◽

pp. 151-196

Author(s):

Huan Neng Chiu ◽

Deng Maw Tsai

Keyword(s):

Linear Programming ◽

Branch And Bound ◽

Integer Linear Programming ◽

Programming Model ◽

Branch And Bound Algorithm ◽

Linear Programming Model ◽

Planning Problem ◽

Material Requirements Planning ◽

Integer Linear Programming Model ◽

Material Requirements

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A Parallel Branch-and-Bound Algorithm for the Classification Problem

Lecture Notes in Computer Science - High Performance Computing – HiPC’99 ◽

10.1007/978-3-540-46642-0_40 ◽

1999 ◽

pp. 274-278

Author(s):

Stefan Balev ◽

Rumen Andonov ◽

Arnaud Freville

Keyword(s):

Branch And Bound ◽

Classification Problem ◽

Branch And Bound Algorithm ◽

Parallel Branch And Bound

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Penjadwalan Integer Linear Programming pada Penjadwalan Produksi Tipe Flowshop dan Program Optimasi Waktu dengan Metode Branch and Bound

JMT : Jurnal Matematika dan Terapan ◽

10.21009/jmt.3.1.5 ◽

2021 ◽

Vol 3 (1) ◽

pp. 44-51

Author(s):

Ismawati Khotimah ◽

Hagni Wijayanti ◽

Sri Setyaningsih

Keyword(s):

Linear Programming ◽

Branch And Bound ◽

Integer Linear Programming

Penjadwalan merupakan pengalokasian sumber daya yang tersedia untuk menyelesaikan sejumlah pekerjaan dengan mempertimbangkan batasan yang ada. Hal yang cukup penting dalam perusahaan adalah menentukan penjadwalan yang optimal agar kegiatan produksi dapat berjalan dengan lancar, efisien, dan sistematis. PT Unitex merupakan perusahaan yang bergerak dalam bidang tekstil. Perusahaan ini menerapkan penjadwalan yang kurang efisien sehingga menyebabkan permasalahan seperti keterlambatan waktu dalam penyelesaian produksi akibat terlalu banyaknya permintaan konsumen yang tidak menentu. Perusahaan melakukan penjadwalan hanya diperkirakan saja dan tidak menggunakan metode ilmiah. Metode Branch and Bound dapat diterapkan pada permasalahan tersebut karena dapat menentukan penjadwalan yang tepat dengan waktu optimal. Metode Branch and Bound adalah metode pencarian dalam menentukan solusi optimal pada penjadwalan dengan menentukan nilai batas atas dan nilai batas bawah untuk menghasilkan nilai makespan dari tiap job yang dikerjakan. Penjadwalan menggunakan Metode Branch and Bound menghasilkan urutan penjadwalan produksi dengan job 1-5-3-6-7-2-4 dengan makespan sebesar 17290.73 menit. Nilai ini lebih kecil dibandingkan hasil makespan perusahaan yaitu 19278.13 menit. Hal tersebut meminimumkan makespan sebesar 10.31%.

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Bit-Parallel Branch and Bound Algorithm for Transposition Invariant LCS

String Processing and Information Retrieval - Lecture Notes in Computer Science ◽

10.1007/978-3-540-30213-1_10 ◽

2004 ◽

pp. 74-75

Author(s):

Kjell Lemström ◽

Gonzalo Navarro ◽

Yoan Pinzon

Keyword(s):

Branch And Bound ◽

Branch And Bound Algorithm ◽

Parallel Branch And Bound

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A Deterministic Method for Solving the Sum of Linear Ratios Problem

Mathematical Problems in Engineering ◽

10.1155/2020/6174352 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Zhenping Wang ◽

Yonghong Zhang ◽

Paolo Manfredi

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Branch And Bound ◽

Nonconvex Programming ◽

Real Life ◽

Branch And Bound Algorithm ◽

Separation Technique ◽

Linear Programming Relaxation ◽

Deterministic Method ◽

Linearization Technique

Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.

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