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1.
Two-echelon drone–truck collaborative TSP-based routing for humanitarian logistics with time windows and stochastic demand
N. Xiao, H. Lan, 2025, original scientific article

Abstract: In humanitarian logistics emergency material transportation and distribution, trucks offer large load capacity and long driving range, whereas drone transportation is independent of ground road conditions but constrained by battery life and payload capacity. The coordination of the two can therefore provide complementary advantages. In this paper, the traveling salesman problem is formulated for a two-echelon emergency material distribution process, spanning transportation from the central warehouse to the distribution center and then to the demand points. In the first stage, transportation from the central warehouse to the distribution center is performed by trucks. In the second stage, trucks and drones collaboratively carry out material distribution from the distribution center to the demand points. Based on the above scenario, this paper aims to minimize the total cost of completing all distribution tasks. The model considers capacity constraints at distribution centers, time window constraints at demand points, and stochastic demand, and establishes a two-echelon traveling salesman problem for humanitarian logistics with truck–drone collaboration. Based on the particle swarm optimization (PSO) framework, a heuristic algorithm named PSO-VD is proposed, which transforms the discrete traveling salesman problem into a continuous encoding and integrates drone routes into truck routes using the 2-opt method. In small-scale instances, the solutions obtained by PSO-VD are compared with those of commercial solvers, demonstrating that the proposed algorithm achieves high accuracy with low computational time. For instances with up to 12 demand points, the algorithm obtains solutions within 150 seconds, with an accuracy deviation of less than 10 % compared to exact solution methods. The applicability of the algorithm proposed in this paper has been demonstrated through large-scale numerical examples. Sensitivity analyses are conducted on key parameters, including the time window penalty coefficient, drone speed, and drone battery capacity, yielding practical managerial insights.
Keywords: humanitarian logistics, two-echelon routing, drone–vehicle collaboration, stochastic demand, time windows, capacity constraint, vehicle routing problem, VRP, travelling salesman problem, TSP, heuristic algorithm, particle swarm optimization, PSO
Published in DKUM: 23.01.2026; Views: 0; Downloads: 0
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2.
Analysis of the Shortest Path Method Application in Social Networks
Boštjan Šumak, Maja Pušnik, 2023, independent scientific component part or a chapter in a monograph

Abstract: This paper analyzes the shortest path problem (SPP) in social networks, based on the investigation and implementation of different methods on a simulated example. The objectives of the paper include identification of the most commonly used methods for finding the shortest path in a social network as a strategic attempt to speed the search of network nodes, focusing on the application of the two most used SPP methods: the Dijkstra and Bellman-Ford algorithms. A comparative analysis is used as an investigation method for performance evaluation of different algorithms, based on their implementation and behavior, tested on a social network example. The research results indicate that the Dijkstra algorithm is faster, and therefore more suitable for searching the shortest connection in social networks.
Keywords: social networks, social networks analysis, shortest path problem, Dijkstra algorithm, Bellman-Ford algorithm, optimization of search
Published in DKUM: 20.01.2026; Views: 0; Downloads: 0
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3.
Multiparametric ▫$Cost–CO_2$▫ optimization of bored reinforced-concrete piles under combined loading in cohesive soils
Primož Jelušič, 2025, original scientific article

Abstract: Laterally loaded slender piles present a classic soil–structure interaction problem where pile displacements and flexural demands are governed by the mobilized lateral resistance of the surrounding soil and the axial-bending capacity of the reinforced concrete section. In response to increasing pressure to reduce embodied emissions, this study develops LAVERCO, an optimization framework for cost- and CO2-efficient design of bored reinforced-concrete piles in cohesive soils subjected to combined lateral and axial actions. The framework integrates Eurocode-based geotechnical checks with full N–M section verification of the RC pile and applies a genetic algorithm over a multi-parametric grid of lateral load, vertical load, and undrained shear strength, using economic cost and embodied CO2 as alternative single objectives. Rank-based (Spearman) sensitivity analysis quantifies how actions, soil strength, and design variables influence the optimal solutions. The results reveal two consistent geometry regimes: CO2-optimal piles are systematically longer and slimmer, while COST-optimal piles are shorter and thicker. In both cases, the objective is dominated by pile length and is reduced by higher undrained shear strength; vertical load has a moderate direct effect, while horizontal load contributes mainly through deflection and bending checks. Feasibility improves significantly in stronger clays, and CO2-optimal geometries generally incur higher costs, clarifying the trade-off between economic and environmental performance. The framework provides explicit geometry-level guidance for selecting bored pile designs that balance cost and embodied CO2 across a wide range of soil and loading conditions and can be directly applied in both preliminary and detailed designs.
Keywords: laterally loaded pile, reinforced-concrete piles, structural analysis, reinforced-concrete design, optimization, CO2 emissions, genetic algorithm, multiparametric analysis, civil engineering practice
Published in DKUM: 19.01.2026; Views: 0; Downloads: 4
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4.
Improving mutation strategies in differential evolution with a new pbest selection mechanism
Jan Popič, Borko Bošković, Janez Brest, 2025, original scientific article

Abstract: Differential evolution, which belongs to a group of population-based algorithms, has received a lot of research attention since its introduction in 1995. A population-based algorithm is required to guide individuals to visit potentially better basins of attraction in the search space when searching for a globally optimal solution. Additionally, individuals need to interact with each other during an evolutionary process to explore the search space effectively. In this paper, we propose a novel pbest selection mechanism for DE/current-to-pbest mutation strategy and its variants designed to enhance the potential for exploration of different attraction basins. The proposed mechanism enforces a minimal distance between the selected pbest individual and all other better individuals. This means that possible candidates for the pbest individual, used in mutation, are further spaced apart. As a result, the likelihood that the new trial vector will be generated in a different attraction basin of the search space is increased. The mechanism is incorporated into the L-SHADE, jSO, and L-SRTDE algorithms, and its effectiveness is evaluated using CEC’24 benchmark functions. Experimental results demonstrate improvements in the performance of the selected algorithms, particularly in higher-dimensional problem instances.
Keywords: population-based algorithm, differential evolution, gobal optimization, mutation strategies, exploration–exploitation
Published in DKUM: 29.10.2025; Views: 0; Downloads: 7
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5.
Performance comparison of single-objective evolutionary algorithms implemented in different frameworks
Miha Ravber, Marko Šmid, Matej Moravec, Marjan Mernik, Matej Črepinšek, 2025, original scientific article

Abstract: Fair comparison with state-of-the-art evolutionary algorithms is crucial, but is obstructed by differences in problems, parameters, and stopping criteria across studies. Metaheuristic frameworks can help, but often lack clarity on algorithm versions, improvements, or deviations. Some also restrict parameter configuration. We analysed source codes and identified inconsistencies between implementations. Performance comparisons across frameworks, even with identical settings, revealed significant differences, sometimes even with the authors’ own code. This questions the validity of comparisons using such frameworks. We provide guidelines to improve open-source metaheuristics, aiming to support more credible and reliable comparative studies.
Keywords: metaheuristics, evolutionary algorithm, metaheuristic optimization framework, algorithm comparison, benchmarking
Published in DKUM: 02.10.2025; Views: 0; Downloads: 5
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6.
Controllability-oriented method to improve small-signal response of virtual synchronous generators
Antonija Šumiga, Boštjan Polajžer, Jožef Ritonja, Peter Kitak, 2025, original scientific article

Abstract: This paper presents a method for optimizing the inertia constants and damping coefficients of interconnected virtual synchronous generators (VSGs) using a genetic algorithm. The goal of optimization is to find a balance between minimizing the rate of change of frequency (RoCoF) and enhancing controllability. Five controllability-based metrics are tested: the minimum eigenvalue, the sum of the two smallest eigenvalues, the maximum eigenvalue, the trace, and the determinant of the controllability Gramian matrix. The approach includes the oscillatory modes’ damping ratio constraints to ensure the small-signal stability of the entire system. The results of optimization on the IEEE 9-bus system with three VSGs show that the proposed method improves controllability, reduces RoCoF, and maintains the desired oscillation damping. The proposed approach was tested through time-domain simulations.
Keywords: virtual synchronous generator, inertia constant, damping coefficient, small-signal stability, multi-objective optimization, genetic algorithm
Published in DKUM: 12.08.2025; Views: 0; Downloads: 12
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7.
Tackling blind spot challenges in metaheuristics algorithms through exploration and exploitation
Matej Črepinšek, Miha Ravber, Luka Mernik, Marjan Mernik, 2025, original scientific article

Abstract: This paper defines blind spots in continuous optimization problems as global optima that are inherently difficult to locate due to deceptive, misleading, or barren regions in the fitness landscape. Such regions can mislead the search process, trap metaheuristic algorithms (MAs) in local optima, or hide global optima in isolated regions, making effective exploration particularly challenging. To address the issue of premature convergence caused by blind spots, we propose LTMA+ (Long-Term Memory Assistance Plus), a novel meta-approach that enhances the search capabilities of MAs. LTMA+ extends the original Long-Term Memory Assistance (LTMA) by introducing strategies for handling duplicate evaluations, shifting the search away from over-exploited regions and dynamically toward unexplored areas and thereby improving global search efficiency and robustness. We introduce the Blind Spot benchmark, a specialized test suite designed to expose weaknesses in exploration by embedding global optima within deceptive fitness landscapes. To validate LTMA+, we benchmark it against a diverse set of MAs selected from the EARS framework, chosen for their different exploration mechanisms and relevance to continuous optimization problems. The tested MAs include ABC, LSHADE, jDElscop, and the more recent GAOA and MRFO. The experimental results show that LTMA+ improves the success rates for all the tested MAs on the Blind Spot benchmark statistically significantly, enhances solution accuracy, and accelerates convergence to the global optima compared to standard MAs with and without LTMA. Furthermore, evaluations on standard benchmarks without blind spots, such as CEC’15 and the soil model problem, confirm that LTMA+ maintains strong optimization performance without introducing significant computational overhead.
Keywords: optimization, metaheuristics algorithm, algorithmic performance, duplicate solutions, nonrevisited solutions, blind spots, LTMA
Published in DKUM: 19.05.2025; Views: 0; Downloads: 6
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8.
The MINLP approach to topology, shape and discrete sizing optimization of trusses
Simon Šilih, Zdravko Kravanja, Stojan Kravanja, 2022, original scientific article

Abstract: The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.
Keywords: structural synthesis, topology optimization, discrete sizing optimization, mixed-integer non-linear programming, MINLP, modified OA/ER algorithm, multi-level MINLP strategies, steel structures, trusses
Published in DKUM: 11.03.2025; Views: 0; Downloads: 15
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9.
Radiotherapy department supported by an optimization algorithm for scheduling patient appointments
Marcela Chavez, Silvia Gonzalez, Ruiz Alvaro, Duflot Patrick, Nicolas Jansen, Izidor Mlakar, Umut Arioz, Valentino Šafran, Philippe Kolh, Van Gasteren Marteyn, 2025, original scientific article

Abstract: Prompt administration of radiotherapy (RT) is one of the most effective treatments against cancer. Eachday, the radiotherapy departments of large hospitals must plan numerous irradiation sessions, con-sidering the availability of human and material resources, such as healthcare professionals and linearaccelerators. With the increasing number of patients suffering from different types of cancers, manuallyestablishing schedules following each patient’s treatment protocols has become an extremely difficultand time-consuming task. We propose an optimization algorithm that automatically schedules andgenerates patient appointments. The model can rearrange fixed appointments to accommodate urgentcases, enabling hospitals to schedule appointments more efficiently. It respects the different treatment Prompt administration of radiotherapy (RT) is one of the most effective treatments against cancer. Eachday, the radiotherapy departments of large hospitals must plan numerous irradiation sessions, con-sidering the availability of human and material resources, such as healthcare professionals and linearaccelerators. With the increasing number of patients suffering from different types of cancers, manuallyestablishing schedules following each patient’s treatment protocols has become an extremely difficultand time-consuming task. We propose an optimization algorithm that automatically schedules andgenerates patient appointments. The model can rearrange fixed appointments to accommodate urgentcases, enabling hospitals to schedule appointments more efficiently. It respects the different treatment.
Keywords: appointments, hospital management, optimization algorithm, patient satisfaction, planning, radiotherapy
Published in DKUM: 25.02.2025; Views: 0; Downloads: 11
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10.
Optimization of embedded retaining walls under the effects of groundwater seepage using a reliability-based and partial factor design approach
Rok Varga, Bojan Žlender, Primož Jelušič, 2024, original scientific article

Abstract: In this paper, a comparative analysis of the effects of groundwater, seepage and hydraulic heave on the optimal design of embedded retaining walls is carried out. The optimization model for an optimal retaining wall (ORW) minimizes the total length of the retaining wall considering design constraints. The model is extended to include the probability of failure as an additional constraint. This overcomes the limitations of the partial safety factor approach, which does not fully account for uncertainties in the soil. In contrast, the reliability-based design (RBD) approach integrates these uncertainties and enables an assessment of the impact of seepage and hydraulic heave on the reliability of the structure. A real-coded genetic algorithm was used to determine optimal designs for both optimization methods. The results of the case study show that the addition of seepage (groundwater flow) to the hydrostatic conditions has a modest effect on the embedment depth. The design based on partial safety factors, which takes seepage into account, leads to a slight increase in the embedment depth of 0.94% compared to a retaining wall design that only takes the hydrostatic conditions of the groundwater into account. When designing on the basis of probability failure, the percentage increase in embedment depth due to seepage is between 2.19% and 6.41%, depending on the target probability of failure. Furthermore, the hydraulic heave failure mechanism did not increase the required embedment depth of the retaining wall, which means that the failure mechanism of rotation near the base was decisive for the design.
Keywords: embedded retaining wall, reliability-based design, partial safety factor design, optimization, genetic algorithm
Published in DKUM: 10.12.2024; Views: 0; Downloads: 17
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