Eş Maliyetli Küme Kapsama Problemi İçin Adaptif Gözlem Ağırlıklandırmaya Dayalı Bir Yerel Arama Algoritması Önerisi

Öz

Gerçek hayatta işletmelerin karşılaştığı birçok problemin modellenebildiği eş maliyetli küme kapsama problemi, temel bir matematiksel problemdir. Problemde, veri setinde yer alan gözlemlerin tamamını barındıracak şekilde en az sayıda küme seçilmesi amaçlanmaktadır. Tam sayılı programlama şeklinde ifade edilen problemin çözümünde, klasik ve kesin sonuç veren yöntemlerin yetersiz kalması nedeniyle çeşitli iteratif yaklaşımlar kullanılmaktadır. Bu yaklaşımlardan biri ise yerel arama algoritmalarıdır. Çalışma kapsamında problemin kendi yapısına uygun ve gözlemleri adaptif ağırlıklandırmaya dayalı bir yerel arama algoritması önerilmiştir. Adaptif yapı kullanılarak oluşturulan değişkenler için, optimizasyon sürecinde elde edilen çıktılar girdi parametreleri olarak ele alınmıştır. Bu sayede yerel arama yaklaşımının daha akıllı hale getirilmesi amaçlanmıştır. Önerilen adaptif metot, örnek eş maliyetli küme kapsama problemlerinin çözümünde kullanılmış ve performansı literatürde yer alan diğer adaptif yöntemlerle kıyaslanmıştır. Sonuçlar incelenerek, geliştirilen metodun etkinliği ortaya konmuştur.

Anahtar Kelimeler

• Eş Maliyetli Küme Kapsama Problemi
• Yerel Arama Algoritması
• Adaptif Parametre

A Local Search Algorithm Proposal Based on Adaptive Row Weighting for Unicost Set Covering Problem

Öz

The Unicost Set Covering Problem is a basic mathematical problem with which many problems faced by businesses in real life can be modeled. In the problem, it is aimed to select the least number of clusters to contain all of the observations in the data set. In the solution of the problem expressed in the form of integer programming, various iterative approaches are used due to the inadequacy of classical and exact methods. One of these approaches is local search algorithms. Within the scope of the study, a local search algorithm suitable for the problem's own structure and based on adaptive weighting of the observations is proposed. For the variables created using the adaptive structure, the outputs obtained during the optimization process are considered as input parameters. In this way, it is aimed to make a smarter local search approach. The proposed adaptive method is used in solving the examples of unicost set covering problem and its performance is compared with other adaptive methods in the literature. By examining the results, the efficiency of the developed method is revealed.

Anahtar Kelimeler

• Unicost Set Covering Problem
• Local Search Algorithm
• Adaptive Parameter

Kaynakça

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