One of the research topics was Developing metaheuristic algorithms for optimization problems
from the Operations research and management science discipline.

Short description: The main research topics are directed towards the development of mathematical models and (meta)heuristic optimization methods for various world-known optimization problems (optimization on graphs, scheduling, transportation, location, etc). Beside the application of different general purpose exact solution methods (CPLEX, Gurobi, LINGO, etc.), problem specific exact and heuristic algorithms will be developed. Although working with various metaheuristic methods, we particularly promote the ones developed by Serbian researchers: Variable Neighborhood Search (VNS) and Bee Colony Optimization (BCO). In addition, our current research project investigates parallelization, theoretical and empirical evaluation of metaheuristics. Our interest is also directed towards the integration of Artificial Intelligence (AI) and optimization methods to deal with real-life optimization problems that occur in science and industry.

Supervisors: Tatjana Davidović, tanjad@mi.sanu.ac.rs; Dragan Urošević draganu@mi.sanu.ac.rs; and Tatjana Jakšić-Krüger tatjana@mi.sanu.ac.rs;
Dušan Ramljak, Penn State University, Great Valey, Philadelphia, USA;
Raka Jovanović, Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar;
Milica Anđelić, Department of Mathematics, Kuwait University;
Slobodan Jelić, Faculty of Civil Engineering, University of Belgrade, Serbia.

Prerequisites: Good programming skills, C(C++), Java, Python.

Suggested material:

• Talbi, El-Ghazali, Metaheuristics: from design to implementation, John Wiley and Sons, 2009.
• Hansen, Pierre, et al., Variable neighborhood search: basics and variants, EURO Journal on Computational Optimization 5(3):423-454, 2017.
• Davidović, T., Bee Colony Optimization: Recent Developments and Applications, (plenary talk), Proc. Balkan Conference on Operational Research, BALCOR 2015, Constanta, Romania, Sept. 9-12, 2015. Mircea cel Batran Naval Academy Scientific Bulletin, 18(2):225-235, 2015.

2020     2021     2022     2023     2024

1. List of atendees in Year 2020:
   • Petar Ćirković and Predrag Đorđević, Faculty of Science and Mathematics, University of Niš
     Subject: Variable neighborhood Search for Spectral Reconstruction of Graphs (in Serbian).
   • Marija Erić, Faculty of Mathematics, University of Belgrade
     Subject: Bee Colony Optimization for Training of Artificial Neural networks (in Serbian).
   • Jovana Rađenović, Faculty of Mathematics, University of Belgrade
     Subject: Automatic Tunig of Parameters for Metaheuristic Methods (Manual for irace in Serbian).
   • Magdalena Tarajić, Faculty of Mathematics, University of Belgrade
     Subject: Ant Colony Optimization for Clustering Incomplete Data (in Serbian).
   • Jana Vučković, Faculty of Mathematics, University of Belgrade
     Subject: Bee Colony Optimization for Feature Selection Problem.

   Presentation of the obtained results at Seminar on Computer Science and Applied Mathematics is available here.

   The students and their supervisors would like to thank the professors included in this internship: accademician Dragoš Cvetković, and Nataša Milosavljević. Your valuable help made our work easier and more successful.

2. List of atendees in Year 2021:
   • Miloš Milićević, Faculty of Mathematics, University of Belgrade
     Subject: Metaheuristic Approach to Spectral Reconstruction of Graphs (co-authored with P. Ćirković, P. Đorđević, and T. Davidović, published in the Proceedings of MOTOR 2022 conference).
   • Dragutin Ostojić, Faculty of Science and Mathematics, University of Kragujevac
     Subject: Comparative Analysis of Heuristic Approaches to P||Cmax, Proc. 11th International Conference on Operations Research and Enterprise Systems, ICORES 2022 (virtual), Feb. 3-5, 2022, pp. 259-266.
     DOI: 10.5220/0011008500003117 (co-authored with T. Davidović, T. Jakšić-Krüger, and D. Ramljak).

3. List of atendees in Year 2022:
   • Uroš Maleš, School of Electrical Engineering, University of Belgrade
     Subject: Difficulty Esimation of Combinatorial Optimization Problems using Machine Learning (co-authored with D. Ramljak, T. Jakšić-Krüger, T. Davidović, D. Ostojić, and A. Haridas, published in Symmetry 2023, 15(1), 140:1-32,
     DOI: 10.3390/sym15010140).
   • Andrija Urošević, Faculty of Mathematics, University of Belgrade
     Subject: Lower Bounds for P||Cmax, (in preparation, co-authored with D. Ostojić, T. Jakšić-Krüger, T. Davidović, and D. Ramljak).
   • Spomenka Milić, Faculty of Mathematics, University of Belgrade
     Subject: Neighborhood Management in Variable Intensity Neighborhood Search, (presented at SMSCG 2023, co-authored with T. Davidović).

4. List of atendees in Year 2023:
   • Robert Doža, Faculty of Mathematics, University of Belgrade and
     Marko Milenković, Faculty of Science and Mathematics, University of Niš
     Subject: General Variable neighborhood Search for Spectral Reconstruction of Graphs (co-authored with P. Đorđević, M. Anđelić, and T. Davidović, presented at EURO 2024 conference, paper in preparation).
   • Ana Mijović, Luka Radanović, and Vladimir Janković, Faculty of Mathematics, University of Belgrade
     Subject: Maximum Diversity Problem with Capacity and Budget Constraints
     Publications: Bee Colony Optimization for Maximum Diversity Problem with Capacity and Budget Constraints, 4th International Conference on Smart Grid and Renewable Energy (SGRE 2024), Doha, Qatar, Jan. 08-10, 2024, pp. 1-6.
     DOI: 10.1109/SGRE59715.2024.10428871 and
     General Variable Neighborhood Search for Maximum Diversity Problem with Capacity and Budget Constraints, (under review, co-authored with D. Urošević, T. Davidović, and R. Jovanović).
   • Ognjen Nešković and Pavle Sekešan, Faculty of Mathematics, University of Belgrade
     Subject: A Framework for Proof-of-Useful-Work Consensus Protocol (co-authored with D. Ramljak, B. Sharma, M. Todorović, T. Davidović, published in Proc. 2nd Blockchain and Cryptocurrency Conference (B2C' 2023), Corfu, Greece, Oct. 18-20, 2023, pp. 68-71.).
   • Marija Jolović and Radovan Drašković, Faculty of Science and Mathematics, University of Kragujevac
     Subject: Heuristics for P||Cmax Scheduling problem (co-authored with D. Ostojić, D. Ramljak, T. Jakšić-Kruger, and T. Davidović, paper in preparation).
   • Igor Pavlović, Lazar Stanarević, and Pavle Čulafić, Scool of Electrical Engineering, University of Belgrade
     Subject: Mashine Learning and Metaheuristics (supervised by T. Jakšić-Kruger and T. Davidović).
   • Jana Živković and Momčilo Tošić, Faculty of Mathematics, University of Belgrade
     Subject: Difficulty Estimation for P||Cmax problem instances (so-authored with S. Jelić, T. Jakšić-Kruger, and T. Davidović, presented at Artificial Intelligence conference, Belgrade, Dec. 26-27, 2023, paper in preparation).
   • Tijana Jakšić, Faculty of Mathematics, University of Belgrade
     Subject: Minimum Steiner Tree Problem (supervised by S. Jelić, R. Jovanović, D. Urošević, and T. Davidović).
   • Irena Šević, Faculty of Mathematics, University of Belgrade
     Subject: Fixed Set Search Applied to the Max-Cut Problem, (co-authored with R. Jovanović, D. Urošević, and T. Davidović, published in Proc. IEEE 8th International Energy Conference (ENERGYCON 2024), Doha, Qatar, March 04-07, 2024, pp. 1-6.
     DOI: 10.1109/ENERGYCON58629.2024.10488777).

5. List of atendees in Year 2024:
   • Iva Šuša, School of Electrical Engineering, University of Belgrade,
     Radoš Jojić, Faculty of Mathematics, University of Belgrade, and
     Natalija Ranđelović, Faculty of Science and Mathematics, University of Niš
     Subject: Sustainability and fairness of Blockchain Consensus Protocol (co-authored with D. Ramljak, M. Todorović, and T. Davidović).
     Presentations:
     Balancing Efficiency and Fairness in Blockchain: A Proof-Of-Useful-Work-Based Blockchain Consensus Protocol, Artificial Intelligence Conference, Dec. 26-27, 2024, Belgrade, Serbia
   • Jovan Benigin and Uroš Svilar, Faculty of Mathematics, University of Belgrade, and
     Aleksa Đorđević, Oxford University
     Subject: Price-Collecting Group Steiner Tree Problem (co-authored with S. Jelić, R. Jovanović, D. Urošević, and T. Davidović), paper in preparation).
   • Marko Rašković, Dimitrije Rađenović, Faculty of Mathematics, University of Belgrade
     Subject: Colored Travelling Salesmen Problem, ( co-authored with D. Urošević, R. Jovanović, and T. Davidović, paper in preparation).