ABSTRACT. Multi-objective Capacitated Vehicle Routing Problem (MO-CVRP) is common in real-world logistics networks but remains challenging for large-scale road-network graphs. Evolutionary algorithms such as NSGA-II are widely used, yet they often suffer from high computational cost and limited scalability. This paper proposes a nonlinear savings-based greedy heuristic inspired by the Clarke–Wright method for solving bi-objective CVRP on general road graphs. The proposed approach extends classical savings formulations by integrating demand, radial balance, and angular similarity with tunable parameters, enabling efficient generation of Pareto-efficient solutions without population-based search. Computational results show that the proposed method significantly outperforms NSGA-II in terms of runtime, particularly on large-scale instances, while producing comparable solution quality on medium-sized problems.

ABSTRACT. Metaheuristic strategy based on chaotic dynamics is effective for escaping local optima by controlling local search through a chaotic neural network. While this approach is effective in avoiding premature convergence, its impact is limited when improvements are restricted to small-scale solution modifications. To expand the scope of chaotic search, this study presents a hybrid chaotic search approach that incorporates local search and destroy-and-repair operations. This adaptive mechanism enables the search to introduce large perturbations when progress stagnates while preserving promising structures when local improvements remain effective. Numerical experiments on CVRPLIB show that the proposed method achieves lower gap rates and greater robustness compared to the conventional chaotic search.

ABSTRACT. The objective of this paper is to introduce a new approach for solving the periodic traveling salesman problem (PTSP). The key idea is to transform the PTSP into a standard TSP, allowing it to be solved using TSP-specific algorithms, which have demonstrated advanced performance in recent years. Among the well-known algorithms, we use the latest version of the Lin-Kernighan-Helsgaun algorithm (LKH-3), which is specifically designed to solve TSP variants and vehicle routing problems. We have extended LKH-3 to handle the PTSP by incorporating a specific penalty function that calculates the degree of periodic constraint violation. This penalty function follows the same logic as those already implemented in LKH-3. The results show that, despite LKH-3 being a general-purpose algorithm, its performance is comparable to algorithms specifically designed for periodic problems reported in the literature. Moreover, we obtained several new best-known solutions for the PTSP benchmark instances.

ABSTRACT. Best Improvement (BI) is a local search strategy that evaluates all possible moves from a given solution and if one or more improving moves exist, applies the best among them. Consequently, after each move, BI requires a complete re-evaluation of the neighborhood, which makes it a highly time-consuming process. To accelerate BI, a previously proposed idea in the literature suggests avoiding the re-evaluation of the entire neighborhood after every move. Instead, a candidate list of improving moves is constructed from the initial solution, containing all of them. These moves are then sorted according to their potential contribution to the solution quality, and the candidate list is traversed and examined before re-evaluating the full neighborhood. As a result, multiple moves may be applied consecutively. In this work, we study the behavior of this strategy for the Traveling Salesman Problem using the 2-opt move. Our results show that the adapted version of BI requires significantly fewer solution evaluations to reach a local optimum, with a trade-off regarding the quality of the solution.

ABSTRACT. Classical Euclidean instances for the Vehicle Routing Problem with Time Windows (VRPTW) have floating-point arc costs derived from node coordinates. This raises reproducibility and numerical consistency issues. Hence, a common practice is to scale and round data to integer values, yet the impact of these choices is poorly understood. This paper studies the effect of integer scaling by a factor P and compares three rounding schemes with distinct feasibility and optimality guarantees. We analyze how scaling and rounding influence empirical performance of two well-known VRPTW solvers: Hybrid Genetic Search (HGS) and OR-Tools. We evaluate the quality of solutions mapped back to the original floating-point instances. Our results show that scaling and rounding can significantly affect both solver performance and solution quality. Based on these findings, we provide practical recommendations for scaling and rounding in VRPTW benchmarks to improve efficiency, robustness and reproducibility.

ABSTRACT. This short paper describes the contribution of the MAMUT project to the CVRPLIB BKS challenge, dedicated to the capacitated vehicle routing problem, and offers an analysis of the results achieved by our approach and by the other competitors. Our approach builds upon the Hybrid Genetic Search (HGS) framework and incorporates a clustering mechanism designed to partition the customer set into subsets of strongly related nodes. Each subset defines a reduced CVRP sub-instance, which is independently solved using lightweight HGS configurations. The underlying rationale is to exploit the high solution quality and robustness of HGS solutions on instances of limited to medium size. These solutions generate high-quality local structures that can be reintegrated into the solution of the original large-scale instance. The method is naturally amenable to parallel execution, as sub-instances are solved independently, enabling substantial reductions in wall-clock solving time.

ABSTRACT. The Minimum k-Dominating Set (MKDS) is a hard combinatorial optimization problem with real-world applications ranging from communication networks to facility location problems. Given a graph, the goal involves finding a subset of vertices with minimum cardinality such that every vertex not in the subset is adjacent to at least k dominant vertices. Due to its NP-Hardness, the MKDS problem is tackled from a metaheuristic perspective, proposing a Variable Neighborhood Search (VNS). The different decisions taken are validated through computational experiments which includes a competitive testing with the best method in the literature, a Restart Local Search with Relaxed Configuration Checking. The proposed VNS obtains competitive results (an average deviation of 0.71%) showing potential for future works.

ABSTRACT. The Subgraph Sampling Scheme (SSS) is a technique originally intro- duced for Markov Random Fields. In combinatorial optimization, it was employed by Selby [3] to solve the Max-Cut problem on a special class of graphs known as Chimera graphs, which constitute the underlying topol- ogy of certain quantum annealing systems. SSS operates by contracting a randomly selected subset of nodes so that the Max-Cut problem on the re- sulting graph becomes solvable in polynomial time. The obtained solution is then lifted to a feasible solution for the original graph. This procedure is iterated until a prescribed computational time limit is reached, and the best solution found across all iterations is retained. In Selby [3], the node subset is chosen so that the contracted graph has small treewidth, enabling an efficient dynamic-programming solution of the Max-Cut problem. In this work, we introduce two new SSS algorithms. The first, termed NN-SSS, is designed for general graphs and relies on contracted graphs that are nearly negative. The second, termed P-SSS, targets toroidal grid graphs and is based on contracted graphs that are planar. In a nearly negative graph, all edges with positive weight are incident to a designated node set; in our implementation, this set consists of a single node. Max-Cut on such graphs can be solved in polynomial time using min-cut/max-flow computations. For toroidal grid graphs, we contract the nodes of one randomly se- lected column and one randomly selected row. The resulting contractedgraph is planar, and the Max-Cut problem can then be solved by com- puting a maximum weight matching. We conducted an extensive computational study to evaluate the ef- fectiveness of our SSS heuristics, following the experimental methodology proposed in [1]. In these tests, the NN-SSS heuristic outperformed all 37 algorithms surveyed in [1], which were selected from the most highly cited Max-Cut heuristic methods. Furthermore, on large toroidal grid graphs, the P-SSS heuristic outperformed both the 37 reference algorithms and NN-SSS. These results have recently been published in a journal article [2].

[1] Iain Dunning, Swati Gupta, and John Silberholz. What works best when? a systematic evaluation of heuristics for Max-Cut and QUBO. INFORMS Journal on Computing, 30(3):608–624, 2018. [2] Claudio Gentile, Giovanni Rinaldi, and Esteban Salgado. SSS Algorithms for Max-Cut. INFORMS Journal on Computing, 2025. Articles in Advance. [3] Alex Selby. Efficient subgraph-based sampling of Ising-type models with frustration. arXiv e-prints, page arXiv:1409.3934, 2014.

ABSTRACT. The Minimum Vertex Cover Problem (MVC) is a fundamental NP-hard problem in graph optimization, commonly used as a benchmark for evaluating greedy heuristics and metaheuristic frameworks. In this paper, we investigate the application of the Data-Dependent Carousel Greedy (DDCG) algorithm to the MVC. The DDCG is an extension of the Carousel Greedy framework that incorporates adaptive, data-dependent selection criteria derived from the structure of the problem and from solution-related information, with the aim of improving solution quality while maintaining low computational effort. The performance of DDCG is evaluated through computational experiments from the BHOSLIB and DIMACS benchmark instances. The results are compared against those obtained by the classical CG, using identical constructive procedures and comparable computational budgets. The experimental results show that the DDCG consistently produces more compact vertex covers on the majority of the tested instances, while preserving the efficiency of the original framework.

ABSTRACT. This work is focused on solving the Partial Set Covering Problem using metaheuristic approaches. This problem emerges as a more realistic and generic variant of the classical Set Covering Problem that can be directly applied in logistics, facility location, and network analysis, among others. The problem has been mainly tackled from exact perspectives and the aim of this work is to evaluate the performance of the mathematical model implemented in Gurobi testing its limits. Then, the metaheuristic proposal will be compared with the exact approach in those instances in which it is able to find the optimal value and it will also be tested in a more complex set of instances in which the model is not able to find the optimal result. The computational experimentation evidences the necessity of heuristic algorithms since the exact approach is not able to find any optimal value in the complex instances, presenting a large deviation with respect to the results obtained by the metaheuristic algorithm.

ABSTRACT. The hub location problem (HLP) is widely used in network design and trans-portation planning. In this study, we consider multi-objective hub location problem (MOHLP) for rail network design. The first objective is to minimize the total transportation cost through the rail hub network, where a discount factor is applied to inter-hub transportation. The second objective is to min-imize transfer cost at hubs, particularly by minimizing the total transporta-tion cost associated with 2-stop routes. To solve the problem, we develop a simulated annealing (SA)-based algorithms, including weighted-sum SA (WS-SA), -constraint SA (-SA), and multi-objective SA (MOSA). A com-parative study of these algorithm is presented for solving a real-world railway network design case. Computational results indicate that MOSA yields the most solution diversity, while WS-SA and -SA are effective in identifying solutions for specific objectives, where solution quality depends on the level of grid refinement.

ABSTRACT. This tutorial presents the Random-Key Optimizer (RKO), a flexible metaheuristic framework that represents solutions as vectors in a continuous random-key space and maps them to feasible solutions through problem-specific decoders. We describe the fundamental components of RKO, including encoding and decoding schemes, elite solution pools, hybridization of multiple metaheuristics, and parallel search with solution sharing. Emphasis is placed on the separation between problem-independent search and problem-dependent decoding, enabling reusable optimization engines across diverse applications. We also discuss recent extensions of RKO to mixed-integer programming models, where carefully designed decoders naturally enforce integrality, variable bounds, and complex constraints, with illustrative applications to portfolio optimization and time-dependent routing problems. In addition, the tutorial introduces emerging research on automating decoder design using large language models (LLMs). This approach employs an iterative cycle of code generation, compilation, validation, and refinement, significantly reducing the expertise required to develop high-quality decoders while maintaining strong solution performance. The session combines theoretical insights, computational results, and implementation guidance, providing participants with practical tools for applying RKO to large-scale, highly constrained optimization problems across domains.

ABSTRACT. This work investigates the use of simulated annealing as an optimization algorithm in problems where the objective function is defined by a machine learning model. The framework is demonstrated in the context of beam angle optimization in proton therapy, aiming to mitigate radiation-induced lymphopenia (RIL). RIL is a prevalent and clinically significant adverse effect of radiotherapy that limits systemic anti-tumor immune response and arises from irradiation of lymphoid organs and circulating lymphocytes, even at low and intermediate dose levels. Given its capacity to limit the low-dose bath, proton therapy offers a potential means to spare immune system organs-at-risk and thus reduce RIL incidence. In this work, simulated annealing is used to solve a large-scale, constrained, and combinatorial optimization problem in which the objective function is defined by a machine learning–based lymphopenia risk prediction model trained to estimate post-treatment absolute lymphocyte count (ALC). The optimization task aims to maximize the predicted ALC while maintaining clinical dose constraints for target coverage and organ-at-risk (OAR) sparing. The objective function incorporates patient-specific and dosimetric parameters that influence RIL probability. The non-convex nature of the problem precludes the use of traditional deterministic solvers, motivating the adoption of simulated annealing as a global optimization strategy. The algorithm explores the multidimensional search space defined by potential beam angle configurations and evaluates each candidate plan based on the machine learning model’s predicted ALC output. Evaluation across ten esophageal cancer cases demonstrated that the proposed framework can improve sparing of lymphocyte-rich tissues. These findings indicate that integrating a machine learning–based objective function within a simulated annealing optimization framework provides an effective approach for data-driven treatment personalization.

ABSTRACT. Chaotic neural networks offer efficient search capabilities for combinatorial optimization by exploiting the intrinsic chaotic dynamics. Recent studies have shown that such dynamics can be preserved even when the conventional sigmoid activation function is replaced with the computationally inexpensive rectified linear unit (ReLU) function. Motivated by these findings, this study proposes a solution approach for the Steiner tree problem in graphs using a ReLU-based chaotic neural network. The method initializes a solution with a shortest path heuristic and determines transitions among node-based neighborhood solutions through ReLU-driven chaotic dynamics. Numerical experiments were conducted on benchmark instances from SteinLib. For the B-type instances, the proposed method achieved optimal solutions for all test cases while reducing computation time to approximately 80% of that required by the original method. For the more challenging C-type instances, solution quality deteriorated, indicating sensitivity to parameter settings. These findings suggest that the ReLU-based model is an efficient alternative for small to moderately sized instances; however, further investigation of parameter control is required to enable scalability to large problems.

ABSTRACT. The challenges of the three-dimensional pose estimation of a human body by use of monocular cameras has been a long-standing issue in the computer vision community, which is largely due to intrinsic depth ambiguity, self-occlusions and the incredibly complex behaviour of human motion. Even with the current improvement in 2D estimation, with recent development of efficient 2D-to-3D lifting methods, both joint- level and time dynamics remain highly challenging to capture.In this paper, we present the 3DHybrid Spatio-Temporal Transformer model in the estimation of human pose in monocular 3D. The suggested method combines a spatial transformer, which is trained on the global association between body joints at every single frame, and a temporal transformer, which is trained on the consistency of motions between frames. We also add to the temporal reason a Cross-Frame Interaction (CFI) module that explicitly reasons about the relationship between frames. Notably, the framework directly compares 2D joint coordinates, which are obtained by conventional pose detectors, eliminating recurrent networks or custom kinematic constraints.We compare the suggested technique on popular benchmark datasets, such as Human3.6M, HumanEva-I -I, MPII and Leeds Sports Pose (LSP). Through experiments, it has been shown that our structure is more accurate and robust in reconstruction, particularly in difficult cases, where occlusions and noisy 2D detections are involved. The results highlight the practical value of spatio-temporal modeling using transformers to the monocular 3D human pose estimation, which provides reliable performance gains over the existing procedures.

ABSTRACT. The increasing demand for digital services has driven the adoption of network virtualization, which enables flexible and scalable network infrastructures by allowing multiple virtual networks to be deployed over a single physical substrate. This, naturally leads to the Virtual Network Embedding Problem (VNEP), which involves deciding how virtual nodes and links should be mapped onto physical resources to satisfy capacity constraints while effectively utilizing the underlying network. However, exact solutions to the VNEP are impractical for realistically sized instances due to the NP-hard nature of the problem. To overcome this limitation, this work adopts a fully heuristic perspective, where solution construction is directly guided by different topology-aware heuristics that exploit the structural properties of the substrate network and resource constraints. The experimental results are then contrasted with the state-of-the-art method, showing that the proposed approach constitutes a competitive alternative for certain instances.

ABSTRACT. Leveraging the potential of quantum machines to retrieve all optimal solutions, we explore a hybrid quantum-classical approach designed to enumerate feasible or optimal solutions to decision and optimization problems. While classical machines remain effective at verifying feasibility in NP problems, quantum machines offer the potential to exhaustively explore relaxed versions of these problems. We propose QonSAll, a general method that first relaxes hard constraints, solves the relaxed problem on a quantum computer to generate all candidate solutions, and then filters those that satisfy the original problem constraints using a classical computer. This strategy is applicable to decision problems, where the feasible set is expanded, as well as to optimization problems, which fall into one of three scenarios depending on how the optimal solution sets relate between the relaxed and original formulations. We illustrate the method with several examples, including Job-Shop Scheduling, SAT, and Max-Cut.

ABSTRACT. Models of software systems provide valuable abstractions for developers. However, model inference is a challenging task. In this work, we address the multi-objective optimization problem of model inference from user-reported activities. We propose a method based on MO-BVNS, a multi-objective extension of Basic Variable Neighborhood Search. The method combines two operators: one designed to extend models to represent missing behaviors; and another one designed to simplify those models to reduce their complexity. These operators provide a balance that enables the method to perform an effective exploration of the search space. We evaluate the proposed MO-BVNS on a benchmark of real-world instances derived from software projects and compare its performance with state-of-the-art evolutionary approaches, including NSGA-II, NSGA-III, and MOEA/D. Experimental results show that MO-BVNS achieves competitive performance, particularly in terms of Pareto front size and hypervolume, indicating its ability to generate diverse and well-distributed solutions. Although convergence is slightly inferior to some evolutionary methods, the results demonstrate that MO-BVNS is a promising alternative for multi-objective model inference in software engineering contexts.