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"Salah satu dari masalah-masalah dominan pada komputasi biologi molekuler adalah penyejajaran barisan berganda (Multiple Sequence Alignment - MSA) dari DNA. Banyak metode yang telah diajukan untuk menyelesaikan masalah MSA seperti pemrograman dinamik dan heuristik. Satu metode telah diajukan oleh Althaus et al. untuk menyelesaikan masalah MSA yang didasarkan pada pemrograman linear bilangan bulat (Integer Linear Programming - ILP). Formulasi ILP umum dari masalah MSA diturunkan dari representasi graf dari masalah MSA. Walaupun formulasi ILP umum dari masalah MSA diketahui, membentuk model ILP dari suatu masalah MSA yang dapat diselesaikan langsung menggunakan suatu solver ILP tidaklah mudah. Sebuah program yang dapat membangun dan menyelesaikan model ILP dari sebuah masalah MSA menggunakan MATLAB telah dibuat. Metode yang digunakan untuk menyelesaikan model ILP tersebut adalah branch-and-bound. Program yang telah dibuat dapat menghasilkan model ILP dari sembarang masalah MSA yang diberikan tetapi hanya dapat menyelesaikan masalah MSA dari sejumlah kecil barisanbarisan DNA yang pendek. Hasil dari program tersebut adalah penejajaran barisan-barisan DNA dari masalah MSA yang diberikan.

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One of the dominant problems in computational molecular biology is multiple sequence alignment (MSA) of DNA. Many methods have been proposed to solve MSA problem such as dynamic programming and heuristic. A method has been proposed by Althaus et al. to solve MSA problem which is based on integer linear programming (ILP). The general ILP formulation of the MSA is derived from the graph representation of the MSA problem. Although we have the general ILP formulation of the MSA problem, constructing the ILP model of an MSA that can be solved directly using an ILP solver is not straightforward. We develop a MATLAB program that can generate and solve the ILP model of an MSA problem. The method that is used to solve the ILP model is branch-and-bound. The constructed program can generate the ILP model of any given MSA problem but can only solve an MSA problem of a small number of short DNA sequences. The result of the program is the aligned sequences of the MSA problem."

"One of the dominant problems in computational molecular biology ismultiple sequence alignment (MSA) of DNA. Many methods have beenproposed to solve MSA problem such as dynamic programming and heuristic.A method has been proposed by Althaus et al. to solve MSA problem which isbased on integer linear programming (ILP). The general ILP formulation ofthe MSA is derived from the graph representation of the MSA problem.Although we have the general ILP formulation of the MSA problem,constructing the ILP model of an MSA that can be solved directly using anILP solver is not straightforward. We develop a MATLAB program that cangenerate and solve the ILP model of an MSA problem. The method that isused to solve the ILP model is branch-and-bound. The constructed programcan generate the ILP model of any given MSA problem but can only solve anMSA problem of a small number of short DNA sequences. The result of theprogram is the aligned sequences of the MSA problem."

"Pemrograman linier (PL) bilangan bulat merupakan bentuk khusus dari pemrograman linier dengan seluruh variabel keputusan berupa bilangan bulat. Salah satu metode yang digunakan dalam menyelesaikan masalah PL bilangan bulat adalah metode branch and bound (B&B). Tugas akhir ini membahas metode perbaikan B&B, yaitu melakukan beberapa tahapan sebelum mengimplementasikan metode B&B. Tahapan yang dilakukan dalam metode perbaikan B&B adalah memperkecil daerah layak dan menghilangkan kendala redundant. Metode ini bekerja secara efisien saat menyelesaikan masalah PL bilangan bulat dengan banyaknya kendala jauh lebih besar dibandingkan banyaknya variabel. Percobaan numerik yang dilakukan menunjukkan tingkat efisiensi dari metode perbaikan B&B sebesar 85% dalam menyelesaikan permasalahan PL bilangan bulat dengan banyaknya kendala 235 lebih besar dari banyaknya variabel.

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Integer linear programming problem is a special form of linear programming with all the decision variables are integers. Branch and bound is one of the methods for solving an integer linear programming problem. This skripsi discusses an improved branch and bound method, which adding several steps before implementing the branch and bound method. New steps in the improved branch and bound method are narrowing down the feasible solution range and removing the redundant constraints.

This method works efficiently in solving an integer linear programming problem with the number of constraints are much more than the number of variables. Numerical experiments show that the efficiency of improved B&B method is about 85% for solving an integer linear programming problem with the number of constraints 235 more than the variables."

"Multiple sequence alignment (MSA) is a sequence alignment of three or more biological sequences, which are assumed to have an evolutionary relationship. Because three or more sequences of biologically relevant length can be difficult and are almost always time-consuming to align by hand, computational algorithm are used to produce and analyze the alignments. Computational algorithm can be constructed by transforming multiple sequence alignment problems into graph problems. The problem of finding anoptimal alignment turns into finding a gapped trace of a gapped extended alignment graph. However, this process is difficult to be done manually. Hence, we study the properties of a gapped trace and using these properties to build a general integer linear programming formulation for MSA problem."