Research Interests

• Genetic algorithms
• Genetic programming
• Resource constrained project scheduling problem
• Container relocation 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

1. M. Đurasević, M. Đumić, R. Čorić, F.J. Gil-Gala, Automated design of relocation rules for minimising energy consumption in the container relocation problem, Expert systems with applications 237 (2024)
   Abstract

   The container relocation problem (CRP) is a combinatorial optimisation problem in which the sequence of container relocations must be determined to retrieve all containers from the yard while optimising a given objective. Prior to now, the primary objective of CRP was to minimise the number of container relocations; however, due to environmental concerns, optimising energy consumption is gaining importance. This criterion was not considered extensively in the literature about CRP; therefore, there is a lack of suitable methods to tackle this problem variant. Primarily, there is a lack of relocation rules (RRs), simple heuristics that efficiently solve large problems in negligible time. Unfortunately, RRs are challenging to design manually since this process requires significant domain knowledge and is time-consuming. Using hyperheuristics to evolve new RRs automatically is one way to circumvent this problem. In this study, we evolved new RRs that aim to minimise energy consumption using genetic programming. We consider both the scenario in which only energy consumption is optimised and a multi-objective scenario where energy consumption is optimised together with the number of container relocations. The proposed approach is compared with an existing approach from the literature that uses a genetic algorithm to design RRs. The results show that RRs designed using genetic programming perform significantly better than the existing method, especially in multi-objective scenarios.
2. M. Đurasević, M. Đumić, Designing relocation rules with genetic programming for the container relocation problem with multiple bays and container groups, Applied Soft Computing 150 (2024)
   Abstract

   The container relocation problem (CRP) is an NP-hard combinatorial optimisation problem that arises in yard management. The problem is concerned with loading all containers from the storage yard to the ship in a certain order. The yard layout consists of bays where containers are placed in stacks on top of each other, and each container has a due date that determines their retrieval order. Due to its complexity, heuristic methods are used to solve CRP, ranging from relocation rules to metaheuristics. Relocation rules (RRs) are used when the goal is to obtain a solution of acceptable quality in short time. Manually designing RRs is difficult and time-consuming, which motivates the use of different methods to automatically design RRs. In this study, we investigate the application of genetic programming (GP) to design RRs for CRP with multiple bays and container groups. The GP algorithm was adapted for generating RRs by proposing a new set of terminals and several solution construction methods. The proposed method was evaluated on an extensive benchmark of existing problems. The results obtained with automatically developed RRs were compared with the results of manually designed RRs and it was found that the automatically designed RRs performed significantly better in all cases.
3. M. Đurasević, M. Đumić, Automated design of heuristics for the container relocation problem using genetic programming, Applied Soft Computing 130 (2022)
   Abstract

   The container relocation problem is a challenging combinatorial optimisation problem tasked with finding a sequence of container relocations required to retrieve all containers by a given order. Due to the complexity of this problem, heuristic methods are often applied to obtain acceptable solutions in a small amount of time. These include relocation rules (RRs) that determine the relocation moves that need to be performed to efficiently retrieve the next container based on certain yard properties. Such rules are often designed manually by domain experts, which is a time-consuming and challenging task. This paper investigates the application of genetic programming (GP) to design effective RRs automatically. Experimental results show that RRs evolved by GP outperform several existing manually designed RRs. Additional analyses of the proposed approach demonstrate that the evolved rules generalise well across a wide range of unseen problems and that their performance can be further enhanced. Therefore, the proposed method presents a viable alternative to existing manually designed RRs and opens a new research direction in the area of container relocation problems.
4. M. Đumić, D. Jakobović, Using priority rules for resource-constrained project scheduling problem in static environment, Computers & Industrial Engineering 169 (2022)
   Abstract

   The resource-constrained project scheduling problem (RCPSP) is one of the scheduling problems that belong to the class of NP-hard 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.
5. M. Đumić, D. Jakobović, Ensembles of Priority Rules for Resource Constrained Project Scheduling Problem, Applied Soft Computing 110 (2021)
   Abstract

   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.
6. R. Čorić, M. Đumić, D. Jakobović, Genetic programming hyperheuristic parameter configuration using fitness landscape analysis, Applied Intelligence 51/10 (2021), 7402-7426
   Abstract

   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.
7. 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
   Abstract

   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.
8. 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
   Abstract

   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.

1. M. Đurasević, M. Đumić, F.J. Gil-Gala, Constructing Ensembles of Automatically Designed Relocation Rules for the Container Relocation Problem, 2024 IEEE Congress on Evolutionary Computation (CEC), Yokohama, Japan, 2024
   Abstract

   Automated design of heuristics with genetic programming (G P) has, in recent years, become an intensively researched research area. One of the most recent applications of this methodology is to generate relocation rules (RRs) for the container relocation problem (CRP). CRP is an important combinatorial optimisation problem that is found in ship ter-minals and warehouses. RRs are simple constructive heuristic methods that provide a good solution quickly, thus representing an alternative to computationally expensive exact or metaheuris-tic methods. Even though the RRs designed by GP provide an improvement over existing manually designed rules, they have limited performance. An efficient way to improve the performance of RRs generated by GP is to use ensemble learning. In this study, we apply ensemble learning on RRs generated by GP for CRP to improve the performance of individual rules. We investigate how different ensemble sizes and combination methods affect the quality of the results, as well as which rules are selected to form ensembles. The experimental study shows that ensembles constructed out of automatically designed RRs significantly improve performance compared to the individual rules.
2. M. Đurasević, M. Đumić, F.J. Gil-Gala, Designing Relocation Rules with Genetic Programming for the Online Container Relocation Problem, 2024 IEEE Congress on Evolutionary Computation (CEC), Yokohama, Japan, 2024
   Abstract

   The container relocation problem (CRP) in shipping terminals is becoming increasingly important due to the growing amount of transferred goods. Until now, the most commonly investigated problem variant has been the offline CRP, in which the order in which the containers need to be retrieved is known beforehand. However, in many real-world situations this is not the case, which is modelled using the online CRP variant. In this variant, not all information is available from the beginning, but rather, it becomes available as the problem is being solved. Unfortunately, many traditional metaheuristic solution methods can not be applied to such a problem variant, which prompts the application of problem-specific heuristics called relocation rules (RRs). However, RRs are challenging to design manually, which prompted the application of genetic programming (GP) to design them automatically. Since GP was used only to design RRs for the offline problem variant, we apply GP to design relocation rules for the online variant in this study. The performance of GP is investigated under different levels of information availability to measure its performance. The results demonstrate that GP can evolve RRs that perform better than existing manually designed ones. Furthermore, the results show that in certain cases, rules generated for one level of information availability perform well for other levels, demonstrating that the evolved rules exhibit a good generalisation capability.
3. M. Đurasević, M. Đumić, F.J. Gil-Gala, N. Frid, D. Jakobović, Improving the Performance of Relocation Rules for the Container Relocation Problem with the Rollout Algorithm, Parallel Problem Solving from Nature – PPSN XVIII: 18th International Conference, Hagenberg, Austria, 2024, 184-200
   Abstract

   Container relocation problems represent a significant challenge in maritime ports and terminals. To address this challenge, there is a growing demand for innovative and efficient solution methods. While exact and metaheuristic methods often yield superior results, they require a substantial time to reach good solutions. On the other hand, relocation rules (RRs) represent simple yet efficient constructive heuristics. Nevertheless, RRs suffer from two main issues, they are difficult to design for different problem variants and their performance is quite limited. To tackle the first issue, genetic programming is commonly used to automatically generate RRs. However, regarding the second issue, there is no single approach by which their performance can be improved. In this study, we investigate the application of the rollout algorithm in combination with manually and automatically generated RRs to improve their performance. The idea of using the rollout algorithm is to balance between an exhaustive and heuristic search, where RRs are used to determine the most appropriate decision in each step of the rollout algorithm. The results demonstrate that with the use of the rollout algorithm it is possible to significantly improve the performance of RRs, albeit with increased execution time. Nevertheless, even in this case, the method can still solve all the considered problems within seconds, underscoring its effectiveness.
4. F.J. Gil-Gala, M. Đurasević, M. Đumić, R. Čorić, D. Jakobović, An analysis of training models to evolve heuristics for the travelling salesman problem, GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation, Lisbon, Portugal, 2023, 575-578
   Abstract

   Designing heuristics is an arduous task, usually approached with hyper-heuristic methods such as genetic programming (GP). In this setting, the goal of GP is to evolve new heuristics that generalise well, i.e., that work well on a large number of problems. To achieve this, GP must use a good training model to evolve new heuristics and also to evaluate their generalisation ability. For this reason, dozens of training models have been used in the literature. However, there is a lack of comparison between different models to determine their effectiveness, which makes it difficult to choose the right one. Therefore, in this paper, we compare different training models and evaluate their effectiveness. We consider the well-known Travelling Salesman Problem (TSP) as a case study to analyse the performance of different training models and gain insights about training models. Moreover, this research opens new directions for the future application of hyper-heuristics.
5. M. Đurasević, M. Đumić, R. Čorić, F.J. Gil-Gala, Automated design of relocation rules for minimising energy consumption in the container relocation problem, GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation, Lisbon, Portugal, 2023, 523-526
   Abstract

   The container relocation problem is a combinatorial optimisation problem aimed at finding a sequence of container relocations to retrieve all containers in a predetermined order by minimising a given objective. Relocation rules (RRs), which consist of a priority function and relocation scheme, are heuristics commonly used for solving the mentioned problem due to their flexibility and efficiency. Recently, in many real-world problems it is becoming increasingly important to consider energy consumption. However, for this variant no RRs exist and would need to be designed manually. One possibility to circumvent this issue is by applying hyperheuristics to automatically design new RRs. In this study we use genetic programming to obtain priority functions used in RRs whose goal is to minimise energy consumption. We compare the proposed approach with a genetic algorithm from the literature used to design the priority function. The results obtained demonstrate that the RRs designed by genetic programming achieve the best performance.
6. R. Čorić, M. Đumić, S. Jelić, A clustering model for time-series forecasting, 42nd International Convention - MIPRO 2019, Opatija, 2019, 1295-1299
   Abstract

   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.
7. R. Čorić, M. Đumić, S. Jelić, A Genetic Algorithm for Group Steiner Tree Problem, 41st International Convention - MIPRO 2018, Opatija, Hrvatska, 2018, 1113-1118
   Abstract

   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.
8. 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
   Abstract

   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

Projects

• Hyper-Heuristic Design for Container Relocation, funded by Croatian Science Foundation, duration:31.12.2023.-30.12.2027. Project leader: ass.prof. Marko Đurasević from University of Zagreb.
• Učeničko poduzetništvo – 404: teorija, Osječko-baranjska županija, Program poticanja poduzetništva, Duration: 15.12.2022.-30.5.2023. Project leader at Department of mathematics: ass.prof. Domaogj Ševerdija
• 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

Conferences

8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024.
10th VOCAL Optimization Conference: Advanced Algorithms, Budapest, Hungary, June, 5-7, 2024.
GECCO 2023, Lisbon, Portugal, July 15-19, 2023.
19th International Conference on Operational Research KOI 2022, Amadria Park, Croatia, September 28-30, 2022.
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.

Workshops

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

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 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.

LTTA (Learning/Teaching/Training Activities)

LTTA in Athens, Greece, June 6-9, 2022
LTTA in Amsterdam, Netherlands, November, 7-10, 2022
LTTA in Pori, Finland, January, 16-20, 2023

Service Activities

• Festival znanosti:

2011. radionica – Primjena Sunčeve svjetlosti pri određenim izračunavanjima2012. 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

Teaching

Nastavne aktivnosti u zimskom semestru akademske 2023./2024.

Uvod u računalnu znanost
Heuristički algoritmi

Nastavne aktivnosti u ljetnom semestru akademske 2023./2024.
Moderni sustavi baza podataka
Objektno orijentirano programiranje

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)
Matematika (Građevinski fakultet)

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