A New Approach to the Solution of Facility Layout Problems with Filled Function Method

Year 2024, Volume: 19 Issue: 2, 475 - 483, 30.09.2024

Ahmet Sahiner , Ayşe Başağaoğlu Fındık , Emine Rumeysa Kocaer , Gültekin Özdemir

https://doi.org/10.55525/tjst.1366299

Abstract

Facility layout problems are generally solved by stochastic methods in the literature. The large number of iterations used in these methods is quite costly in terms of solution time. In this study, in order to get rid of this disadvantage, the facility layout problem was solved using the filled function method, which is known to be very successful in solving global optimization problems. In order to demonstrate the effectiveness of the filled function method, the classical linear facility layout problem was handled in a non-linear manner and the problem was deliberately made more difficult. In order to use the filled function method, the facility layout problem was transformed into an unconstrained and multimodal (including more than one local minima) global optimization problem by using the hyperbolic smoothing technique and the penalty function method. Thus, in this first study in the literature where a deterministic method is combined with the solution of the facility layout problem, it is shown that the non-convex facility layout problem can be solved with the filled function method with very few iterations and short solution times.

Keywords

Facility layout problem, global optimization, filled function method

Tesis Yerleşim Probleminin Çözümüne Doldurulmuş Fonksiyon Yöntemi ile Yeni Bir Yaklaşım

Abstract

Literatürdeki tesis yerleşim problemleri genellikle stokastik yöntemlerle çözülmektedir. Bu yöntemlerde kullanılan iterasyon sayısının fazlalığı çözüm süresi açısından oldukça maliyetlidir. Bu çalışmada, bu dezavantajdan kurtulmak adına tesis yerleşim problemi, global optimizasyon problemlerini çözmede oldukça başarılı olduğu bilinen doldurulmuş fonksiyon yöntemi kullanılarak çözülmüştür. Doldurulmuş fonksiyon yönteminin etkinliğini göstermek için klasik doğrusal tesis yerleşim problemi, doğrusal olmayacak şekilde ele alınmış ve problem bilinçli olarak zorlaştırılmıştır. Doldurulmuş fonksiyon yöntemini kullanabilmek adına hiperbolik yumuşatma tekniği ve ceza fonksiyonu yöntemi kullanılarak tesis yerleşim problemi kısıtsız ve multimodal (birden fazla yerel minimumun içerilmesi) bir global optimizasyon problemi haline dönüştürülmüştür. Böylece, tesis yerleşim probleminin çözümü ile deterministik bir yöntemin bir araya getirildiği literatürdeki bu ilk çalışmada, konveks olmayan tesis yerleşim problemi doldurulmuş fonksiyon yöntemi ile oldukça küçük iterasyonlar ve kısa çözüm süreleri ile çözülebileceği gösterilmiştir.

Keywords

Tesis yerleşim problemi, global optimizasyon, doldurulmuş fonksiyon metodu

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