Title
Примена метода комбинаторне оптимизације за решавање проблема формирања група у настави
Creator
Lazović, Bojana, 1979-
Copyright date
2018
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
Dozvoljavate samo preuzimanje i distribuciju dela, ako/dok se pravilno naznačava ime autora, bez ikakvih promena dela i bez prava komercijalnog korišćenja dela. Ova licenca je najstroža CC licenca. Osnovni opis Licence: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/deed.sr_LATN. Sadržaj ugovora u celini: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/legalcode.sr-Latn
Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 28. 9. 2018.
Other responsibilities
mentor
Marić, Miroslav, 1978-
član komisije
Mateljević, Miodrag, 1949-
član komisije
Božić, Milan, 1952-
član komisije
Stanimirović, Zorica, 1976-
član komisije
Dolićanin, Ćemal.
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Beogradu
Faculty
Matematički fakultet
Alternative title
Combinatorial optimization methods for solving the problems of group formation in classes
Publisher
[Б. Лазовић]
Format
XIII, 165 листова
description
математика - методика наставе математике и рачунарства / Mathematics - Methodology of teaching of mathematics and computer science
Abstract (sr)
The subject of this thesis is to present new mathematical methods and algorithms of combinatorial optimization, which could be applied for solving the problems of group formation in classes. Namely, there are various problems that require the selection of certain groups forming of individuals from the finite set, based on previously determined grouping criteria. Some of these are NP-hard problems of combinatorial optimization, which are taken into consideration in this thesis: Maximum Set Splitting Problem - MSSP, Well-Balanced Experimental and Control Group Formation Problem - WBECGFP, Balanced Multi-Weighted Attribute Set Partitioning problem – BMWASP, Collaborative Learning Groups Formation Problem - CLGFP and Minimum Hitting Set Problem - MHSP. The process of group formation represents a complex and time- consuming task, thus requiring a necessary software support for the efficient and successful completion of the task. Some of the problems that could come up in the course of teaching are equivalent to the aforementioned NP-hard problems and their special cases, especially when there is a need to take into consideration a large nunber of individuals, charactersitics and criteria for their assigning into groups.
The objective of the research presented in this thesis is solving combinatorial optimization problems: MSSP, WBECGFP, BMWASP, CLGFP и MHSP. The obtained results of the considered problems can be applied for: upgrading the process of the organization and performance of teaching, the process of splitting and the adoption of new knowledge, as well as to achive more successful performance of educational experimental researches, and to increase student’s motivation through group and team work. The objective is to achieve higher quality teaching of mathematics and computing. Taking into consideration various requests put forward by the organizers of teaching, in terms of number, size and group composition needed to be formed, as well as the criteria needed to be taken into account, this thesis provides a practical contribution to the methodology of optimal distribution of individuals into groups by applying mathematical
models and combinatorial optimization algorithms. The proposed algorithms are implemented in publicly available applications, such that users of all educational profiles are able to use them...
Abstract (sr)
Предмет овог рада је представљање нових математичких модела и алгоритама комбинаторне оптимизације, који се могу применити за решавање проблема формирања група у настави. Наиме, постоје разни проблеми који подразумевају издвајање одређених група индивидуа из коначног скупа, по унапред утврђеним критеријумима груписања. Неки од њих су NP-тешки проблеми комбинаторне оптимизације, разматрани у овој дисертацији: проблем максималне поделе скупа на два дела (енгл. Maximum Set Splitting Problem - MSSP), проблем формирања добро балансиране експерименталне и контролне групе (енгл. Well-Balanced Experimental and Control Group Formation Problem - WBECGFP), проблем формирања к добро балансираних група (енгл. Balanced Multi-Weighted Attribute Set Partitioning Problem - BMWASP), проблем формирања група за колаборативно учење (енгл. Collaborative Learning Groups Formation Problem - CLGFP) и проблем минималног репрезентативног скупа (енгл. Minimum Hitting Set Problem - MHSP). Сам процес формирања група представља комплексан и временски веома захтеван задатак, па је из тих разлога неопходна и софтверска подршка како би се он ефикасно и успешно извршио. Неки од проблема на које се може наићи у настави су еквивалентни наведеним NP-тешким проблемима и њиховим специјалним случајевима, посебно када је потребно узети у обзир велики број индивидуа, карактеристика и критеријума за њихово распоређивање у групе.
Циљ истраживања приказаног у овом раду је решавање проблема комбинаторне оптимизације: MSSP, WBECGFP, BMWASP, CLGFP и MHSP. Добијена решења разматраних проблема се могу применити за унапређивање процеса организовања и извођења наставе, процеса дељења и усвајања нових знања, за успешније извођење образовних експерименталних истраживања, за повећање мотивације код студената кроз групни и тимски рад, и све то у циљу што квалитетније наставе математике и рачунарства. С обзиром на разноврсне захтевe
који се постављају од стране организатора наставе у погледу броја, величина и састава група које треба формирати, као и критеријума које при томе треба узети у обзир, ова дисертација даје практични допринос методологији што бољег распоређивања индивидуа у групе применом математичких модела и алгоритама комбинаторне оптимизације. Предложени алгоритами су имплементирани у јавно доступне апликације, како би се омогућила што једноставнија примена од стране корисника свих образовних профила...
Authors Key words
комбинаторна оптимизација, проблеми формирања група у настави, математичко моделирање, метахеуристичке методе, генетски алгоритми, метода променљивих околина
Authors Key words
Combinatorial Optimization, Problems of Group Formation in Classes, Mathematical Modelling, Metaheuristics, Genetic Algorithms, Variable Neighborhood Search
Classification
519.1:371.3(043.3)
Type
Tekst
Abstract (sr)
The subject of this thesis is to present new mathematical methods and algorithms of combinatorial optimization, which could be applied for solving the problems of group formation in classes. Namely, there are various problems that require the selection of certain groups forming of individuals from the finite set, based on previously determined grouping criteria. Some of these are NP-hard problems of combinatorial optimization, which are taken into consideration in this thesis: Maximum Set Splitting Problem - MSSP, Well-Balanced Experimental and Control Group Formation Problem - WBECGFP, Balanced Multi-Weighted Attribute Set Partitioning problem – BMWASP, Collaborative Learning Groups Formation Problem - CLGFP and Minimum Hitting Set Problem - MHSP. The process of group formation represents a complex and time- consuming task, thus requiring a necessary software support for the efficient and successful completion of the task. Some of the problems that could come up in the course of teaching are equivalent to the aforementioned NP-hard problems and their special cases, especially when there is a need to take into consideration a large nunber of individuals, charactersitics and criteria for their assigning into groups.
The objective of the research presented in this thesis is solving combinatorial optimization problems: MSSP, WBECGFP, BMWASP, CLGFP и MHSP. The obtained results of the considered problems can be applied for: upgrading the process of the organization and performance of teaching, the process of splitting and the adoption of new knowledge, as well as to achive more successful performance of educational experimental researches, and to increase student’s motivation through group and team work. The objective is to achieve higher quality teaching of mathematics and computing. Taking into consideration various requests put forward by the organizers of teaching, in terms of number, size and group composition needed to be formed, as well as the criteria needed to be taken into account, this thesis provides a practical contribution to the methodology of optimal distribution of individuals into groups by applying mathematical
models and combinatorial optimization algorithms. The proposed algorithms are implemented in publicly available applications, such that users of all educational profiles are able to use them...
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