Mateja Đumić
PhD Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests

Genetic algorithms
Genetic programming
Resource constrained project scheduling problem
Degrees

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.
Publications
 M. Đumić, D. Jakobović, Using priority rules for resourceconstrained project scheduling problem in static environment, Computers & Industrial Engineering 169 (2022)The resourceconstrained project scheduling problem (RCPSP) is one of the scheduling problems that belong to the class of NPhard problems. Therefore, heuristic approaches are usually used to solve it. One of the most commonly used heuristic approaches are priority rules (PRs). PRs are easy to use, fast and able to respond to system changes, which makes them applicable in a dynamic environment. The disadvantage of PRs is that when applied in a static environment, they do not achieve results of the same quality as heuristic approaches designed for a static environment. Moreover, a new PR must be evolved separately for each optimization criterion, which is a challenging process. Therefore, recently significant effort has been put into the automatic development of PRs. Although PRs are mainly used in a dynamic environment, they are also used in a static environment in situations where speed and simplicity are more important than the quality of the obtained solution. Since PRs evolved for a dynamic environment do not use all the information available in a static environment, this paper analyzes two adaptations for evolving PRs in a static environment for the RCPSP  iterative priority rules and rollout approach. This paper shows that these approaches achieve better results than the PRs evolved and used without these adaptations. The results of the approaches presented in the paper were also compared with the results obtained with the genetic algorithm as a representative of the heuristic approaches used mainly in the static environment.
 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 NPhard 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.
 R. Čorić, M. Đumić, D. Jakobović, Genetic programming hyperheuristic parameter configuration using fitness landscape analysis, Applied Intelligence 51/10 (2021), 74027426Fitness 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 treebased 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.
 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), 211221The 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 reallife 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, hyperheuristic 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.
 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), 419427The 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 branchandbound 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 userfriendly web application was made and is available to the public for testing purposes.
 R. Čorić, M. Đumić, S. Jelić, A clustering model for timeseries forecasting, 42nd International Convention  MIPRO 2019, Opatija, 2019, 12951299In this paper we consider a novel Integer programming approach for the clusterbased model used for timeseries 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 shortterm prediction of airborne pollen concentrations. We give experimental results about comparison of our method to some common approaches.
 R. Čorić, M. Đumić, S. Jelić, A Genetic Algorithm for Group Steiner Tree Problem, 41st International Convention  MIPRO 2018, Opatija, Hrvatska, 2018, 11131118In 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 minimumweight subgraph which contains at least one vertex from each group (groups do not have to be disjoint). GST is NPhard combinatorial optimization problem that arises from many complex reallife problems such as finding substratereaction pathways in protein networks, progressive keyword search in relational databases, team formation in social networks, etc. Heuristic methods are extremely important for finding the goodenough 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.
 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, 13941400Resource 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.
 M. Đumić, M. Jukić Bokun, Euklidov algoritam, Osječki matematički list 13 (2013), 121137
Projects
 GAMebased 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
Conferences 42th International ICT Convention  MIPRO 2019, Opatija, Croatia, May 2025, 2019
 23nd Young Statisticians Meeting, October 1214, 2018, Balatonfüred, Hungary
 41th International ICT Convention  MIPRO 2018, Opatija, Croatia, May 2125, 2018.
 40th International ICT Convention  MIPRO 2017, Opatija, Croatia, May 2226, 2017.
 15th International Conference on Operational Research KOI 2014, Osijek, Croatia, September 2426, 2014.
Workshops
 Time Verification of RealTime Systems, workshop organized as part of MERIDA research project HRZZ IP2016068350, on September 19, 2018 in Osijek, Croatia
 International Workshop on Optimal Control of Dynamical Systems and applications, 2022 June 2018 at Department of Mathematics, J. J. Strossmayer University of Osijek
 Mathematics for Big Data, Novi Sad, Serbia, May 31 June 1, 2017
Schools
 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 NatureInspired Optimisation Joining Theory and Practice, Paris, France, October 1824, 2017.
 7th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, July 2329, 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 uključivanjaisključivanja
2020. radionica  Formula uključivanjaisključivanja
 Zimska škola informatike:
2017. radionica  Multithreading i multiprocessing u Pythonu
Teaching
Nastavne aktivnosti u zimskom semestru akademske 2021./2022.
 Uvod u računalnu znanost
 Heuristički algoritmi
 Matematika (Građevinski fakultet)
Nastavne aktivnosti u ljetnom semestru akademske 2021./2022.
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 emailom.