Department for

Computer science and informatics

Modelling and optimization group

Researchers in this group work on mathematical modelling and solving of the complex optimization problems, as well as mathematical modeling and improving of the various metaheuristic optimization methods. Optimization problems (from combinatorial and global domain) that are considered have great practical importance and they are used (beside “pure” operational research) in various parts of computer science: machine learning, classification, case-based reasoning, bioinformatics, etc.

Problems from various groups are successfully solved (and still are solving):

• Location problems – problem is to decide where to locate warehouse or hub in order to achieve that all consumers are supplied and the overall cost is minimal;
• Transport problems – how to optimally visit all location with given vehicles in order to have minimal expenses;
• Job scheduling problems – for instance, how to achieve fast file transfer through computer network;
• Assignment problems – for instance, objective is to assign devices to locations so that the sum of products between flows and distances is minimal or to assign tasks to processor in order to achieve minimal overall costs;
• Selection problems – for instance, optimally select super-peers in P2P network;
• Graph partition problems – determining maximally balanced partition in graph; determining maximally connected partition in graph;
• Graph coloring problems – for instance, coloring graph vertexes (simple and multicolor) in respect to bandwidth;
• Set partition problems – how to create set partition so family of the subsets of that set have maximal intersection with the created partition;
• Satisfiability problems – more precisely, problem of probabilistic satisfiability p-SAT;
• Wireless sensor network problems - more precisely, how to design wireless sensor network in order to achieve minimal energy consumption;
• Case-based reasoning problems;
• Classification and data mining problems – classification method adjustment problem; dimensionality reduction problem; cluster analysis problem;
• Dimensional reduction problems - for instance, feature selection problem;
• Parameter selection problems - for instance, determination of parameters in kernel learning methods;
• Feature weighting problems - assignment of importance coefficients to features during classification process;
• etc.

There are two fundamental approaches in optimization:

• Exact problem solving, which incorporates creating of the mathematical model (it is usually an ILP model) for given optimization problem and implementation of created mathematical model in some modern solver (for instance, in CPLEX and GUROBI). Mathematical models for following problems are designed so far: Maximum set partition problem (MSSP), Two dimensional packing problem, Quadratic assignment problem (QAP), File transfer scheduling problem (FTSP), several domination problems in graphs, etc.
• For complex and/or high-dimensional problems, often is necessary to use (beside exact approach) the metaheuristics methods. These methods can be population methods (Genetic algorithms, Electromagnetism-like metaheuristics, Ant colonies etc.) and local search based methods (Variable neighborhood search, Tabu search etc.).

Researchers in this group are dealing with metaheuristics modifications and improvements:

• New operators are introduced – fine grained tournament selection in Genetic algorithms is proposed, its characteristics are described, as well as results that are obtained during solving various optimization problems.
• Cashing is introduced and successfully used – cashing of the individual’s genetic code and cashing of the objective function value for the points in search space within various metaheuristics optimization methods, including genetic algorithms and electromagnetism-like metaheuristics.
• Hybrid methods, that combine good features of different approaches, are designed and used. Those methods often achieve excellent results when they are applied to a practical problem.

Methods that are developed are used as auxiliary tool in solving various mathematical problems, dominantly for graph problems (for instance, determining of the metric dimension and domination numbers for various graph classes).

Members of the modelling and optimization group are intensively working on parallelization of previously mentioned methods, which also includes distributed optimization methods.

Scientific work

Monograph

1. Milutinović Veljko, Mitić Nenad, Kartelj Aleksandar, Kotlar Miloš, Implementation of Machine Learning Algorithms Using Control-Flow and Dataflow Paradigms , IGI Global, 2022. ISBN13: ISBN13: 9781799883500.
2. Stanimirović Zorica, Kratica Jozef, Filipović Vladimir, Tošić Dušan, Evolutionary approach for Solving Hab Location Problems (in Serbian), Zavod za udžbenike, Belgrade, 2011.

Selected journal papers

1. Đukanović Marko, Kartelj Aleksandar, Blum Christian, Self-adaptive CMSA for solving the multidimensional multi-way number partitioning problem , Expert Systems with Applications, Vol. 232, 2023, DOI: 10.1016/j.eswa.2023.120762. IF2021=8.665, M21 (Q1) in Computer Science, Artificial Intelligence.
2. Kartelj Aleksandar., Đukanović Marko, RILS-ROLS: robust symbolic regression via iterated local search and ordinary least squares , Journal of Big Data, Vol. 10, No. 1, p. 71, 2023, DOI: 10.1186/s40537-023-00743-2.
3. Kapunac Stefan, Kartelj Aleksandar, Djukanović Marko, Variable neighborhood search for weighted total domination problem and its application in social network information spreading , Applied Soft Computing, Vol. 143, p. 110387, 2023, DOI: 10.1016/j.asoc.2023.110387.
4. Ciccolella Simone, Della Vedova Gianluca, Filipović Vladimir, Soto Gomez Mauricio, Three Metaheuristic Approaches for Tumor Phylogeny Inference: An Experimental Comparison, Algorithms, Vol. 16, No. 7, pp. 333, 2023.
5. Kartelj Aleksandar, Grbić Milana, Matić Dragan, Filipović Vladimir, The Roman Domination Number of Some Special Classes of Graphs - Convex Polytopes , Applicable Analysis and Discrete Mathematics - AADM, , Vol. 15, Iss. 2, pp. 393-412, DOI 10.2298/AADM171211019K, 2021.
6. Grbić Milana, Matić Dragan, Kartelj Aleksandar, Janković Savka, Filipović Vladimir, A three-phase method for identifying functionally related protein groups in weighted PPI networks, Computational Biology and Chemistry 86, DOI 10.1016/j.compbiolchem.2020.107246, 2020.
7. Kratica Jozef, Matić Dragan, Filipović Vladimir Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs, Revista de la Unión Matemática Argentina, Vol. 61, Iss. 2, pp. 441-455, 2020.
8. Grbić Milana, Kartelj Aleksandar, Janković Savka, Matić Dragan, Filipović Vladimir, Variable Neighborhood Search for Partitioning Sparse Biological Networks into the Maximum Edge-Weighted $k$k-Plexes, IEEE/ACM Transactions on Computational Biology and Bioinformatics, Vol. 17, Iss. 5, pp. 1822-1831, DOI 10.1109/TCBB.2019.2898189, 2019.
9. Filipović Vladimir, Kartelj Aleksandar, Kratica Jozef, Edge metric dimension of some generalized Petersen graphs, Results in Mathematics 74: 182, 2019.
10. Matić Dragan, Kratica Jozef, Filipović Vladimir, Variable Neighborhood Search for solving Bandwidth Coloring Problem , Computer Science and Information Systems, Vol. 14, Iss. 2, pp. 309-327, 2017.
11. Kartelj Aleksandar, An Improved Electromagnetism-like Method for Feature Selection, Journal of Multiple Valued Logic and Soft Computing, Vol. 25, Iss. 2/3, pp. 169-187, 2015.
12. Kartelj Aleksandar, Šurlan Nebojša, Cekić Zoran, Case-based Reasoning and Electromagnetism-like Algorithm in Construction Management, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 42, No. 2, pp. 265-280, 2014.
13. Dražić Zorica, Savić Aleksandar, Filipović Vladimir, An integer linear formulation for the file transfer scheduling problem, TOP, Vol. 22, Iss. 3, pp. 1062-1073, 2014.
14. Filipović Vladimir, Kartelj Aleksandar, Matić Dragan, An electromagnetism metaheuristic for solving the Maximum Betweenness Problem , Applied Soft Computing, Vol. 13, Iss. 2, pp. 1303–1313, 2013.
15. Nikolić Zorana, Brajušković Goran, Savić Dušanka, Kojić Aleksandra, Vujović Vinka, Tomović Saša, Cerović Snežana, Filipović Vladimir, Mišljenović Đuro, Romac Stanka, Assessment of possible association between rs3787016 and prostate cancer risk in Serbian population, International Journal of Clinical and Experimental Medicine, Vol. 6, No. 1, pp. 57-66, 2013.
16. Kartelj Aleksandar, Mitić Nenad, Filipović Vladimir, Tošić Dušan, Electromagnetism-like Algorithm for Support Vector Machine Parameter Tuning, Soft Computing, Vol. 18, Iss. 10, pp. 1985-1998, 2013.
17. Savić Aleksandar, Kratica Jozef, Filipović Vladimir, A New Nonlinear Model for the Two-Dimensional Rectangle Packing Problem , Publications de l'Institut Mathématique, Vol. 93, Iss. 107, pp. 95-107, 2013.
18. Lazović Bojana, Marić Miroslav, Filipović Vladimir, Savić Aleksandar, An integer linear programming formulation and genetic algorithm for the maximum set splitting problem , Publications de l'Institut Mathématique, Vol. 92, Iss. 106, pp. 25-34, 2012.
19. Kratica Jozef, Kostić Tijana, Tošić Dušan, Dugošija Đorđe, Filipović Vladimir, A genetic algorithm for the routing and carrier selection problem , Computer Science and Information Systems – COMSIS, Vol. 9 No 1, pp. 49-62, 2012.
20. Filipović Vladimir, Kratica Jozef, Tošić Dušan, Dugošija Đorđe, GA Inspired Heuristic for Uncapacitated Single Allocation Hub Location Problem, Applications of Soft Computing - Advances in Soft Computing, Vol. 58/2009, pp. 149-158, Springer, 2009.
21. Kratica Jozef, Kojić Jelena, Tošić Dušan, Filipović Vladimir, Dugošija Đorđe, Two Hybrid Genetic Algorithms for Solving the Super-Peer Selection Problem, Applications of Soft Computing - Advances in Soft Computing, Vol. 58/2009, pp. 337-346, Springer, 2009.
22. Đurić Brankica, Kratica Jozef, Tošić Dušan, Filipović Vladimir, Solving the maximally balanced connected partition problem in graphs by using genetic algorithm, Computing and Informatics, Vol. 27 No 3, pp. 341-354, 2008.
23. Kratica Jozef, Stanimirović Zorica, Tošić Dušan, Filipović Vladimir, Two Genetic Algorithms for Solving the Uncapacitated Single Allocation p-Hub Median Problem , European Journal of Operational Research – EJOR, 182, pp. 15-28, 2006.
24. Kratica Jozef, Stanimirović Zorica, Tošić Dušan, Filipović Vladimir, Genetic Algorithm for Solving Uncapacitated Multiple Allocation Hub Location Problem, Computing and Informatics, Vol. 24 No 4, pp. 415-426, 2005.
25. Filipović Vladimir, Fine-grained Tournament Selection Operator in Genetic Algorithms, Computers and Informatics, Vol. 22, No. 2, pp. 143-162, 2003.
26. Kratica Jozef, Tošić Dušan, Filipović Vladimir, Ljubić Ivana, A Genetic Algorithm for the Uncapacitated Network Design Problem, Soft Computing in Industry – Recent Applications, pp. 329-338, Springer, 2002.
27. Kratica Jozef, Tošić Dušan, Filipović Vladimir, Ljubić Ivana, Solving the Simple Plant Location Problem by Genetic Algorithms, RAIRO - Operations Research, Vol. 35, No. 1, pp. 127-142, 2001.

Other publications

1. Filipović Vladimir, Optimization, classification and dimensionality reduction in biomedicine and bioinformatics, Biologia Serbica, Vol. 39, No. 1, pp. 83-98, 2017.
2. Kartelj Aleksandar, Electromagnetism Metaheuristic Algorithm for Solving The Strong Minimum Energy Topology Problem, , Yugoslav Journal of Operations Research – YUJOR, Vol. 23, pp. 43-57, 2013.
3. Filipović Vladimir, Zagarčanin Mladen, Tošić Dušan, Stanišić Sanja, Digitalization in the Bar County Museum – Pilot Project, Review of the National Center for Digitization, Vol. 23, pp. 57-66, 2013.
4. Matić Dragan, Kratica Jozef , Filipović Vladimir, Dugošija Đorđe, Variable neighborhood search for Multiple Level Warehouse Layout Problem , Electronic Notes in Discrete Mathematics, Vol. 39, pp. 161-168, 2012.
5. Matić Dragan, Filipović Vladimir, Savić Aleksandar, Stanimirović Zorica, A Genetic Algorithm for Solving Multiple Warehause Layout Problem, Kragujevac Journal of Mathematics, Issue 35 Vol. 1, pp. 119-138, 2011.
6. Savić Aleksandar, Šukilović Tijana, Filipović Vladimir, Solving the Two-Dimensional Packing Problem With m-M Calculus , Yugoslav Journal of Operations Research – YUJOR, Vol. 21 No. 1, pp. 93-102, 2011.
7. Kratica Jozef, Tošić Dušan, Filipović Vladimir, Dugošija Đorđe, A New Genetic Representation for Quadratic Assignment Problem , Yugoslav Journal of Operations Research – YUJOR, Vol. 21 No. 2, pp. 225-238, 2011.
8. Filipović Vladimir, An Electromagnetism Metaheuristic for the Uncapacitated Multiple Allocation Hub Location Problem, Serdica Journal of Computing, Vol. 5 No. 3, pp. 261-272, 2011.
9. Kratica Jozef, Savić Aleksandar, Filipović Vladimir, Milanović Marija, Solving the Task Assignment Problem with a Variable Neighborhood Search, Serdica Journal of Computing, Vol. 4 No. 4, pp. 435-446, 2010.
10. Kartelj Aleksandar, Classfication of Smoking Cessation Status Using Various Data Mining Methods, Mathematica Balkanica, Vol. 24, pp. 199-205, 2010.
11. Tošić Dušan, Filipović Vladimir, Kratica Jozef, Using SVG–XML for representation of historical graphical data, Review of the National Center for Digitization, Vol. 9, pp. 39-45, 2006.

Collaboration

Gecko

Collaboration with engineers within company in designing algorithm for transportation problem.

CeSID

Statistical Processing and Analysis Software (SPAS).

Sampling and statistical analysis in elections.

Software for automated recognition and analysis of paper inquiries (RECO).

Direct Media agency

Media Mix Optimizer - marketing investment portfolio optimization (MMO)