scholarly journals Optimisasi Program Linear Integer Murni Dengan Metode Branch And Bound

2018 ◽  
Vol 1 (2) ◽  
pp. 175-181
Author(s):  
Tondi Marulizar ◽  
Ujian Sinulingga ◽  
Esther Nababan
Keyword(s):  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Simplex Method ◽  
Optimization Problem ◽  
Linear Program ◽  
Integer Linear Program ◽  
Branch And Bound Method ◽  
A Value ◽  
Calculation Process ◽  
Lower Limits

Program Linier Integer Murni merupakan optimisasi kombinatorial yang tidak mudah untuk diselesaikan secara efisien. Metode yang sering digunakan untuk menyelesaikan Program Linier Integer Murni diantaranya adalah metode merative, yang merupakan salah satunya metode Branch and Bound. Metode ini menggunakan hasil dari metode simpleks yang belum bernilai integer sehingga dilakukan pencabangan dan batasan terhadap variabel x_j yang bernilai pecahan terbesar. Metode Branch and Bound dapat menyelesaikan masalah optimisasi suatu produk, tetapi membutuhkan waktu yang lebih lama dalam proses perhitungannya dikarenakan dalam setiap tahap perhitungan harus dicari nilai dari batas atas dan batas bawah yang ditentuan berdasarkan suatubatasandankriteria tertentu. Pure Integer Linear Program is combinatorial optimization that is not easy to solve efficiently. The method that is often used to complete the Pure Integer Linear Program is the merative method, which is one of the Branch and Bound methods. This method uses the results of the simplex method that is not yet an integer value so that the branching and limitation of the x_j variable is the largest fraction. The Branch and Bound method can solve the optimization problem of a product, but requires a longer time in the calculation process because in each calculation phase, a value must be sought from the upper and lower limits determined based on the boundary and certain criteria. 

scholarly journals A Branch-and-Bound Algorithm for Team Formation on Social Networks

2020 ◽  
Author(s):  
Nihal Berktaş ◽  
Hande Yaman
Keyword(s):  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Optimization Problem ◽  
Exact Algorithm ◽  
Combinatorial Optimization Problem ◽  
Branch And Bound Algorithm ◽  
Team Formation ◽  
Set Covering ◽  
Covering Problem ◽  
Linear Set

This paper presents an exact algorithm for the team formation problem, in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems, and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modeling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application and a new algorithm to solve a quadratic version of a classical combinatorial optimization problem.

Application of Combinatorial Optimization and Fuzzy Scheduling to Pipe Assembly Process

2007 ◽  
Vol 23 (03) ◽  
pp. 142-146
Author(s):  
Yasuhisa Okumoto
Keyword(s):  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Evaluation Method ◽  
Search Algorithm ◽  
High Reliability ◽  
Computer Time ◽  
Optimization Techniques ◽  
Branch And Bound Method ◽  
Original Process ◽  
Fuzzy Scheduling

The combinatorial optimization of the sequence for pipe assembly was studied to mass produce the pipe units efficiently using the branch-and-bound method in the previous report by the authors. As a result of the simulation, shortening of the total working hours and a reduction in the middle stock were achieved. However, two problems remained: It was difficult to get an optimization solution in the case of many combinations due to computer time, and only the average time of each working process was taken. For the former problem, the tabu search algorithm has been introduced in addition to the branch-and-bound method, and the revised process of the production has been proposed as a simulation result using this algorithm. For the latter problem, the technique of fuzzy scheduling has been adopted to take into account the variation in working time for each process and in the resulting delivery period. These have been formalized using the fuzziness, and the reliability of the completion time has been calculated for the original process and the improved process. As a result, the proposed process that was calculated by the optimization program has been evaluated as having high reliability, comparing to the original process. According to these studies, it was confirmed that these optimization techniques and the evaluation method of reliability using the fuzzy scheduling technique were quite effective.

Inverse version of the kth maximization combinatorial optimization problem

2018 ◽  
Vol 54(5) ◽  
pp. 72
Author(s):  
Quoc, H.D. ◽  
Kien, N.T. ◽  
Thuy, T.T.C. ◽  
Hai, L.H. ◽  
Thanh, V.N.
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem
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