Odjel za matematiku


Mateja Đumić


Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-805
fax: +385-31-224-801
email:  mdjumic @ mathos.hr
office:  7 (ground floor)


Research Interests

Genetic algorithms
Genetic programming
Resource constrained project scheduling problem


PhD in Computing, Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia, 2020. 
MSc in Mathematics, Department of Mathematics, University of Osijek,Croatia, 2014.
BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2011.



Journal Publications

  1. M. Đumić, D. Jakobović, Ensembles of Priority Rules for Resource Constrained Project Scheduling Problem, Applied Soft Computing 110 (2021)
    Resource constrained project scheduling problem is an NP-hard problem that attracts many researchers because of its complexity and daily use. In literature there are a lot of various solving methods for this problem. The priority rules are one of the prominent methods used in practice. Because of their simplicity, speed, and possibility to react to changes in the system, they can be used in a dynamic environment. In this paper, ensembles of priority rules were created to improve the performance of priority rules created with genetic programming. For ensemble creation, four different methods will be considered: simple ensemble combination, BagGP, BoostGP, and cooperative coevolution. The priority rules that are part of the ensemble will be combined with the sum and vote methods in reaching the final decision. Additionally, the ensemble subset search method will be applied to the created ensembles to find the optimal subset of priority rules. The results achieved in this paper show that ensembles of priority rules can achieve significantly better results than those achieved when using only a single priority rule.
  2. R. Čorić, M. Đumić, D. Jakobović, Genetic programming hyperheuristic parameter configuration using fitness landscape analysis, Applied Intelligence 51/10 (2021), 7402-7426
    Fitness landscape analysis is a tool that can help us gain insight into a problem, determine how hard it is to solve a problem using a given algorithm, choose an algorithm for solving a given problem, or choose good algorithm parameters for solving the problem. In this paper, fitness landscape analysis of hyperheuristics is used for clustering instances of three scheduling problems. After that, good parameters for tree-based genetic programming that can solve a given scheduling problem are calculated automatically for every cluster. Additionally, we introduce tree editing operators which help in the calculation of fitness landscape features in tree based genetic programming. A heuristic is proposed based on introduced operators, and it calculates the distance between any two trees. The results show that the proposed approach can obtain parameters that offer better performance compared to manual parameter selection.
  3. M. Đumić, D. Šišejković, R. Čorić, D. Jakobović, Evolving priority rules for resource constrained project scheduling problem with genetic programming, Future Generation Computer Systems 86 (2018), 211-221
    The main task of scheduling is the allocation of limited resources to activities over time periods to optimize one or several criteria. The scheduling algorithms are devised mainly by the experts in the appropriate fields and evaluated over synthetic benchmarks or real-life problem instances. Since many variants of the same scheduling problem may appear in practice, and there are many scheduling algorithms to choose from, the task of designing or selecting an appropriate scheduling algorithm is far from trivial. Recently, hyper-heuristic approaches have been proven useful in many scheduling domains, where machine learning is applied to develop a customized scheduling method. This paper is concerned with the resource constrained project scheduling problem (RCPSP) and the development of scheduling heuristics based on Genetic programming (GP). The results show that this approach is a viable option when there is a need for a customized scheduling method in a dynamic environment, allowing the automated development of a suitable scheduling heuristic.
  4. N. Čerkez, R. Čorić, M. Đumić, D. Matijević, Finding an optimal seating arrangement for employees traveling to an event, Croatian Operational Research Review 6/2 (2015), 419-427
    The paper deals with modelling a specific problem called the Optimal Seating Arrangement (OSA) as an Integer Linear Program and demonstrated that the problem can be efficiently solved by combining branch-and-bound and cutting plane methods. OSA refers to a specific scenario that could possibly happen in a corporative environment, i.e. when a company endeavors to minimize travel costs when employees travel to an organized event. Each employee is free to choose the time to travel to and from an event and it depends on personal reasons. The paper differentiates between using different travel possibilities in the OSA problem, such as using company assigned or a company owned vehicles, private vehicles or using public transport, if needed. Also, a user-friendly web application was made and is available to the public for testing purposes.

Refereed Proceedings

  1. R. Čorić, M. Đumić, S. Jelić, A clustering model for time-series forecasting, 42nd International Convention - MIPRO 2019, Opatija, 2019, 1295-1299
    In this paper we consider a novel Integer programming approach for the cluster-based model used for time-series forecasting. There are several approaches in literature that aim to find a set of patterns which represent similar situations in the time series. In order to predict target variable, different types of fitting methods can be applied to set of data that belongs to the same pattern. We propose method that uses clustering of patterns and prediction of target value as the mean of values in the same cluster, in order to minimize total squared deviation between predicted and real values of target variable. We also propose a heuristic method that achieves good solution in practice. Our approach is applied to short-term prediction of airborne pollen concentrations. We give experimental results about comparison of our method to some common approaches.
  2. R. Čorić, M. Đumić, S. Jelić, A Genetic Algorithm for Group Steiner Tree Problem, 41st International Convention - MIPRO 2018, Opatija, Hrvatska, 2018, 1113-1118
    In Group Steiner Tree Problem (GST) we are given a weighted undirected graph and family of subsets of vertices which are called groups. Our objective is to find a minimum-weight subgraph which contains at least one vertex from each group (groups do not have to be disjoint). GST is NP-hard combinatorial optimization problem that arises from many complex real-life problems such as finding substrate-reaction pathways in protein networks, progressive keyword search in relational databases, team formation in social networks, etc. Heuristic methods are extremely important for finding the good-enough solutions in short time. In this paper we present genetic algorithm for solving GST. We also give results of computational experiments with comparisons to optimal solutions.
  3. R. Čorić, M. Đumić, D. Jakobović, Complexity Comparison of Integer Programming and Genetic Algorithms for Resource Constrained Scheduling Problems , 40th International ICT Convention - MIPRO 2017, Opatija, 2017, 1394-1400
    Resource constrained project scheduling problem (RCPSP) is one of the most intractable combinatorial optimization problems. RCPSP belongs to the class of NP hard problems. Integer Programming (IP) is one of the exact solving methods that can be used for solving RCPSP. IP formulation uses binary decision variables for generating a feasible solution and with different boundaries eliminates some of solutions to reduce the solution space size. All exact methods, including IP, search through entire solution space so they are impractical for very large problem instances. Due to the fact that exact methods are not applicable to all problem instances, many heuristic approaches are developed, such as genetic algorithms. In this paper we compare the time complexity of IP formulations and genetic algorithms when solving the RCPSP. In this paper we use two different solution representations for genetic algorithms, permutation vector and vector of floating point numbers. Two formulations of IP and and their time and convergence results are compared for the aforementioned approaches.


  1. M. Đumić, M. Jukić Bokun, Euklidov algoritam, Osječki matematički list 13 (2013), 121-137


  • GAMe-based learning in MAthematics, Erasmus+, Cooperation for innovation and the exchange of good practices, Strategic Partnerships for school education. Duration: 01.10.2020.-30.09.2022.
  • Hyperheuristic Design of Dispatching Rules, funded by Croatian Science Foundation, duration:01.01.2020.-31.12.2023. Project leader: prof. Domagoj Jakobović from University of Zagreb. 
  • Application of optimization methods in biomedicine, bilateral project with Serbia, Duration: 01.01.2019. - 31.12. 2020. Project leaders: ass.prof. Slobodan Jelić from University of Osijek (croatian side) and ass.prof. Dušan Jakovetić from University of Novi Sad (serbian side).


Professional Activities

  • 42th International ICT Convention - MIPRO 2019, Opatija, Croatia, May 20-25, 2019
  • 23nd Young Statisticians Meeting, October 12-14, 2018, Balatonfüred, Hungary
  • 41th International ICT Convention - MIPRO 2018, Opatija, Croatia, May 21-25, 2018.
  • 40th International ICT Convention - MIPRO 2017, Opatija, Croatia, May 22-26, 2017.
  • 15th International Conference on Operational Research KOI 2014, Osijek, Croatia, September 24-26, 2014.



  • Time Verification of Real-Time Systems, workshop organized as part of MERIDA research project HRZZ IP-2016-06-8350, on September 19, 2018 in Osijek, Croatia
  • International Workshop on Optimal Control of Dynamical Systems and applications, 20-22 June 2018 at Department of Mathematics, J. J. Strossmayer University of Osijek
  • Mathematics for Big Data, Novi Sad, Serbia, May 31- June 1, 2017


  • COST Action Training School ImAPPNIO, 25th–29th November 2019, Coimbra, Portugal.
  • Second Edition of the Summer School on Optimization, Big Data and Applications (OBA), 30th June - 06th July, 2019, Veroli, Italy
  • COST Action Training School: Improving Applicability of Nature-Inspired Optimisation Joining Theory and Practice, Paris, France, October 18-24, 2017.
  • 7th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, July 23-29, 2017.


Service Activities
  • Festival znanosti:

2011. radionica - Primjena Sunčeve svjetlosti pri određenim izračunavanjima

2012. radionica - 10 u svijetu matematike

2013. radionica - Zamisli jedan broj

2015. radionica - Kakve veze ima Sunce s matematikom?

  • Zimska škola matematike:

2011. predavanje - Euklidov algoritam

2019. predavanje - Formula uključivanja-isključivanja

2020. radionica - Formula uključivanja-isključivanja

  • Zimska škola informatike:

2017. radionica - Multi-threading i multi-processing u Pythonu



Nastavne aktivnosti u zimskom semestru akademske 2021./2022.


Nastavne aktivnosti u ljetnom semestru akademske 2020./2021.


Nastavne aktivnosti u prošlosti:

  • Analitička geometrija
  • Dizajniranje i modeliranje baza podataka
  • Kombinatorna i diskretna matematika
  • Osnove baza podataka
  • Uvod u računarstvo
  • Učenička matematička natjecanja
  • Matematika (Ekonomski fakultet)
  • Matematika (Poljoprivredni fakultet)


Konzultacije (Office Hours): Po dogovoru e-mailom.