A NEW MATHEMATICAL MODEL AND RANDOM KEY BASED METAHEURISTIC SOLUTION APPROACH FOR COURSE-ROOM-TIME ASSIGNMENT PROBLEM

Year 2019, , 67 - 76, 15.08.2019

Zehra Kamışlı Öztürk , Müjgan Sağır

https://doi.org/10.31796/ogummf.549986

Cited By: 3

Abstract

This study presents a newly developed mixed-integer mathematical model for university course-room-time assignment problem. Optimal results with no soft constraint violations are obtained for some type of problem instances. As problem complexity increases it becomes more difficult to find feasible solution for this problem in a reasonable time. Therefore, a heuristic approach is often needed for such problems. In this study, a random key based genetic algorithm (RKGA) is developed. RKGA encoding is used in order to encode the chromosomes with a length of just the number of courses and not to use problem specific genetic operators and/or repair mechanisms. Well-known problem instances from the literature are selected to evaluate the outcome. The performance of RKGA is competitive to that of other algorithms especially for big size problems.

Keywords

Course-room-time, assignment problem, Mathematical modelling, Random key based genetic algorithms

DERS-DERSLİK-ZAMAN DİLİMİ ATAMA PROBLEMİ İÇİN YENİ BİR MATEMATİKSEL MODEL VE RASSAL ANAHTAR TEMELLİ METASEZGİSEL ÇÖZÜM YAKLAŞIMI

Abstract

Bu çalışmada üniversite ders-derslik-zaman dilimi atama problemi için yeni bir karma tam sayılı matematiksel model önerilmiştir. Geliştirilen karma tam sayılı matematiksel model ile literatürde yer alan test problemleri çözdürülmüş ve bir kısmı için tüm esnek kısıtlar sağlanarak en iyi çözüm elde edilmiştir. Problem karmaşıklığı arttıkça makul sürelerde uygun çözüm bulmak zorlaştığından, bu tür problemlerin çözümü için sezgisel bir yaklaşıma ihtiyaç duyulmaktadır. Çalışmada, rassal anahtar temelli bir genetik algoritma (RKGA) geliştirilmiştir. Probleme özgü özel genetik operatörler ve/veya onarma mekanizmaları kullanmamak için sadece ders sayısı uzunluğundaki kromozomları kodlamak için RKGA kodlaması kullanılmıştır. Çıktıların
değerlendirilmesi için literatürde iyi bilinen test problemleri seçilmiştir. Özellikle büyük boyutlu problemlerde RKGA’nın performansının diğer algoritmalar ile rekabet edebilir düzeyde olduğu görülmüştür.

Keywords

Ders-derslik-zaman dilimi atama problemi, Matematiksel modelleme, Rassal anahtar temelli genetik algoritma

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