İÇ NOKTA ALGORİTMALARI VE DOĞRUSAL PROGRAMLAMAYA UYGULANAMASI

Öz

Karmarkar’s Interior Point Algorithm is an algorithm developed by Narendra Karmarkar in 1984 and known the major algorithm of interior point algorithms. In Interior point algorithms, it is tried to reach for the optimum solution by starting from an available one and gradually continuing for better ones which lie in the interior points of the available area. The purpose of our study is to present the efficiency of Karmarkar’s Interior Point Algorithm and Mehrotra Predictor-Corrector Algorithm, which is an other effective interior point algorithm in solving the linear programming problem in a very short time. A linear programming model has been formulated that has 4500 decision variables and 180 constraints. This model has been solved by interior point algorithms and Simplex Algorithm and they have been compared. MOSEK, PCx, XPRESS-MP/Barrier and XPRESS-MP/Simplex softwares are used for the solution of the model

Anahtar Kelimeler

• Interior point algorithms, unit simplex

İÇ NOKTA ALGORİTMALARI VE DOĞRUSAL PROGRAMLAMAYA UYGULANAMASI

Öz

Karmarkar-İç Nokta Algoritması, 1984’te Narendra Karmarkar tarafından geliştirilmiş olup; iç nokta algoritmalarının ana algoritması olarak bilinen bir algoritmadır. İç nokta algoritmalarında, uygun bölge içerisindeki bir noktadan başlayıp; her bir adımda uygun bölgenin iç noktalarında var olan daha iyi bir çözüme gidilerek optimal çözüme ulaşılmaya çalışılır. Çalışmamızın amacı, doğrusal programlama probleminin kısa sürede çözülmesinde Karmarkar- İç Nokta Algoritmasının ve etkin bir iç nokta algoritması olan Mehrotra tahminci-düzeltici Algoritması’nın etkinliğinin gösterilmesidir. Bir üretim işletmesine ilişkin 4500 karar değişkeni ve 180 kısıtlayıcı içeren bir Doğrusal programlama modeli oluşturulmuştur. Model, iç nokta algoritmaları ve Simpleks algoritması ile çözülerek, çözüm sonuçları karşılaştırılmıştır. Modelin çözümü için MOSEK, PCx, XPRESS-MP/Barrier ve XPRESS-MP/Simplex yazılımlarından yararlanılmıştır

Anahtar Kelimeler

• İç nokta algoritmaları, Birim Simpleks

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