ABSTRACT. We study a variant of the Capacitated Facility Location Problem in which customers may be assigned to multiple facilities, subject to customer-incompatibility constraints that forbid incompatible customer pairs from being served by the same facility. To address this challenging setting, we propose a competitive matheuristic framework that combines an effective construction phase with a Fix-and-Optimize intensification strategy.

The construction phase relies on reducing the decision space to identify high-quality feasible solutions. Building on this initial solution, the intensification phase iteratively solves a sequence of carefully designed subproblems in which selected subsets of variables are optimized while the remaining ones are fixed. This strategy efficiently explores the neighborhood of high-quality solutions without sacrificing computational tractability.

Extensive computational experiments demonstrate the robustness and effectiveness of the proposed approach. The matheuristic consistently improves upon the best results reported in the literature and achieves comparable or superior solution quality in significantly reduced computational time, outperforming existing metaheuristic methods in many instances.

ABSTRACT. The Single Row Facility Layout Problem (SRFLP) is a classical NP-hard combinatorial optimization problem with important applications in manufacturing and logistics systems. Given a set of facilities with predefined lengths and pairwise interaction weights, the goal is to arrange the facilities along a single line so as to minimize the total weighted center-to-center distance. In this talk, we present a novel matheuristic that embeds exact optimization within a simulated annealing framework to efficiently solve large-scale SRFLP instances. The core component of our approach is a window-based strategy that optimally reorders subsets of consecutive facilities using mixed-integer programming, while maintaining the relative order of facilities outside the selected window. This hybrid design enables high-quality intensification without sacrificing global exploration. To the best of our knowledge, this is the first matheuristic specifically tailored to the SRFLP. Computational experiments on widely used benchmark instance sets demonstrate the effectiveness of the proposed method. Our approach improves the best-known solutions for 13 out of 70 instances and matches the best-known solutions for the remaining 57 instances, outperforming existing state-of-the-art metaheuristics.

ABSTRACT. The 1-Survivable Ring Star Problem (1-S-RSP) models the design of ring-star networks that must remain operational after the failure of any single node. In addition to building the ring and assigning terminal nodes to hubs, as done in the classical Ring Star Problem (RSP), the 1-S-RSP requires the inclusion of backup edges that preserve the ring-star structure under failure scenarios. This coupling between routing, assignment, and survivability decisions makes the problem highly challenging from a computational standpoint.

This research presents a hybrid metaheuristic for the 1-S-RSP that combines an evolutionary framework with problem-specific local search procedures. The method uses a compact chromosome representation that stores only information about which nodes belong to the ring and act as hubs. This encoding reduces the search space explored by the algorithm, while dedicated procedures efficiently reconstruct complete feasible solutions from the encoded information. To improve solution quality while preserving feasibility, the algorithm incorporates specialized 2-opt and 3-opt backup methods that properly account for survivability requirements.

Computational experiments on benchmark instances show that the proposed method compares favourably with respect to the best feasible solutions reported in the literature, often matching or improving them while requiring computing times that are two to three orders of magnitude shorter. These results indicate that the algorithm is an effective and scalable alternative for solving large 1-S-RSP instances arising in survivable network design.

ABSTRACT. This work addresses the Ordered Median Tree Location Problem (OMT), a combinatorial optimization problem recently introduced that involves the p-median and minimum spanning tree problems. The OMT seeks to locate $p$ facilities and connect them via a tree structure to serve a set of customers, minimizing ordered weighted customer assignments and tree connection costs. To efficiently solve this problem, we propose a Greedy Randomized Adaptive Search Procedure (GRASP), incorporating a swap-based local search. Computational experiments demonstrate that the proposed metaheuristic significantly outperforms the state-of-the-art exact formulation, finding the best-known solution for all instances with low computational cost.

ABSTRACT. The Gradual Minimum Covering Location Problem (GM- CLP) consists in locating a set of undesirable facilities within a given area. These facilities cover the demand for a certain product but have a negative impact on the nearby population. Therefore, the goal is to open enough facilities to comply the restrictions while minimizing the population affected by the influence of these undesirables facilities. The first constraint requires that enough facilities must be located to cover the demand of the product generated by them. The second constraint ensures that any two located facilities are separated by at least a given distance dmin > 0, since closer proximity may be dangerous. This version of the problem considers different size levels of facilities, each one having different demand coverage and different influence radius. In this work, we propose a heuristic algorithm for the original nonlinear formulation of the problem, based on GRASP and VND search. The proposed approach is compared with the existing solution method. Numerical experiments show that the algorithm obtains slightly better solutions while reducing the time required to achieve high-quality solutions.

ABSTRACT. The K-page crossing number minimization problem (KPMP) aims to reduce the number of crossings between edges of a graph when it is embedded on a structure referred to as a book, composed of a spine, where vertices are placed, and pages, where edges are assigned. In this work, we propose a bi-objective variant of the KPMP that, in addition to minimizing crossings between edges assigned to the same page, simultaneously minimizes the total edge length along the spine. We propose three different multi-objective evolutionary algorithms using a mixed-integer encoding that combines a permutation (vertex order) with an integer vector (edge-to-page assignment). The three algorithms are tuned independently via automatic configuration and evaluated over 70 benchmark instances on books with K ∈ {2, 4, 6} pages. Results show that SMS-EMOA achieves the best overall performance for K ≥ 4, while NSGA-II dominates for K = 2.

ABSTRACT. Optimizing the customer-order picking process in robotic mobile fulfillment systems depends on two closely related decisions: How to schedule the processing of orders on a workbench of limited size and how to sequence the racks that are lifted and transported by automated guided vehicles (robots) to the picking-station to supply the requested items for order-processing? Minimizing the number of these so-called rack-visits at the picking-station is well suited to reduce robot utilization and the makespan of customer-order processing. We present a heuristic solution approach for the order-scheduling and rack- sequencing problem at a single picking-station using column generation to partition the set of customer-orders into batches, while minimizing the number of rack-assignments to batches, which in turn minimizes the rack-visits. The generated batches possess a property that allows to derive an order-processing schedule straightforwardly. Then, we refine the heuristic solution by rearranging the processing of batches and their assigned racks. A comprehensive and comparative computational study demonstrates superior performance of our approach on the vast majority of instances compared to several heuristics from literature, both in terms of solution quality with up to 15% fewer rack-visits and runtime. The average worst-case optimality gap in comparison with valid lower bounds is 10.72% and the solutions are close to optimal if around ten orders can be processed simultaneously on the workbench. It is also shown that the proposed heuristic provides very competitive results for the order-scheduling and rack-sequencing problem at multiple picking-stations.

ABSTRACT. This work addresses a class of mixed-integer linear programming (MILP) problems that integrate assignment decisions with a routing subproblem, a combination that frequently arises in real-world operational planning con-texts. While formulating the global optimization model provides a clear representation of the problem, this model rapidly becomes computationally intractable as instance size increases. To address this challenge, we propose a sequential optimization framework that decomposes the global problem into two interconnected stages. The first stage focuses on the determination of the assignment decisions or other high-level decisions, whereas the sec-ond stage is devoted to the solution of the routing problem, conditioned on the outcomes of the first stage. The two problems are linked by a set of time-dependent constraints that encode the mutual dependencies between as-signment choices and routing feasibility. These coupling constraints are governed by continuous parameters that reflect the use of time spent on routing. Simulated annealing is considered to optimize these coupling pa-rameters, with the sequential subproblems being iteratively solved. It can be formally demonstrated that there exist parameter values for which the sequential decomposition provides the optimal solution for the global MILP model. Computational experiments were conducted considering the home care planning problem. The results indicate that the sequential approach sub-stantially reduces computational effort while preserving high solution quality, outperforming direct solution of the integrated model for realisti-cally sized instances. This study makes both methodological and practical contributions. It proposes a structured decomposition approach for hybrid assignment–routing problems and demonstrates its use in a healthcare planning setting. The framework supports efficient resource allocation and routing decisions in cases where solving the fully integrated problem is computationally difficult.

ABSTRACT. Inter-terminal truck routing is a critical operational challenge in container ports, requiring efficient coordination of container movements between multiple terminals. While deep reinforcement learning has shown promise for this problem, standard implementations rely on greedy action selection based on one-step Q-value estimates, which can lead to myopic decisions and suboptimal routing performance. This paper proposes a lookahead-enhanced Deep Q-Network (DQN) framework integrating rollout-based planning into the action selection process. Drawing on principles from the rollout and the pilot method, the proposed approach evaluates candidate actions by simulating future trajectories and selecting the action with the highest estimated return. Importantly, the lookahead mechanism is applied only at deployment time, requiring no modification to the training procedure. Computational experiments demonstrate that a single-step lookahead can considerably reduce total operating costs and empty-truck trips compared to the baseline DQN with practical computational overhead. These results confirm that lookahead-enhanced DQN provides an effective mechanism to extend learned policies without retraining, bridging the gap between data-driven learning and classical operations research methods.

ABSTRACT. The increasing availability of heterogeneous, large-scale urban data has fostered the development of digital twins supporting real-time decision processes in smart cities. In this context, personalized and constraint-aware route planning plays a central role. Many practical navigation problems can be modeled as a Weight-Constrained Shortest Path Problem (WCSPP), where the objective is to minimize travel cost while respecting a bound on a secondary resource, such as slope, sun exposure, pollution level, or accessibility constraints or viceversa (i.e minimizing a function of the slope while respecting a bound on the maximum length of the path).

While several exact algorithms have been proposed for the WCSPP, their computational burden may become prohibitive in large-scale instances or under strict time requirements, as typically demanded by interactive digital twin applications. To address this challenge, we propose a novel heuristic framework, designed to provide high-quality feasible solutions within very short computational times.

The method integrates two complementary components. The first is an iterative graph-reduction mechanism that prunes nodes unlikely able to improve solutions. The second component is an adaptive parametric search procedure that considers a convex combination of cost and resource consumption, dynamically adjusting the trade-off parameter via a binary search strategy. The two mechanisms are embedded into a unified approach, enhancing robustness and solution quality.

Extensive computational experiments on benchmark instances from the DIMACS challenge demonstrate that the proposed heuristic consistently finds solutions within 1\% gap in a fraction of the time required by state-of-the-art exact methods.

The proposed approach provides an effective trade-off between optimality and computational efficiency, making it particularly suitable for real-time and large-scale applications such as urban digital twins, personalized pedestrian navigation, and resource-aware mobility services.

ABSTRACT. In this work, we study the integrated order picking and vehicle routing problem (IOPVRP) in a picker-to-part warehouse with a fixed vehicle fleet, focusing on maximizing the number of served customers within a planning horizon of a workday. This issue arises mainly in e-commerce contexts, in which customers place orders via online platforms and the purchased goods are subsequently delivered to their residential or workplace addresses. We study a scenario in which items must be picked from the warehouse in batches and transported by vehicles that are allowed to make multiple trips. We develop a novel hybrid solution framework that leverages the characteristics of the integrated problem to efficiently generate high-quality feasible solutions. Our approach explicitly considers split picking in the warehouse, allowing items for a single order to be distributed across multiple batches, increasing solution complexity but creating more opportunities to serve additional customers. Computational experiments on realistic, large instances demonstrate that split picking substantially improves performance compared to non-split strategies, highlighting its potential operational value in high-volume e-commerce logistics.

ABSTRACT. This paper describes the extension of the FILO2x algorithm, a parallel metaheuristic for the Capacitated Vehicle Routing Problem, de- signed to perform extremely long runs as required by the CVRPLib Best Known Solution Challenge. The approach was used by Team Galileo to participate to the challenge. The team overall ranked 6th and obtained several best known solutions (BKSs), three of which resisted until the end of the challenge.

ABSTRACT. Artificial Intelligence is booming, and the wild transformative power of the current technoscience lies in the strong coupling between Optimization and Machine Learning. Optimization drives Machine Learning, and Machine Learning improves Optimization by exploiting data produced while searching for better and better solutions, a spiral of continuously improving AI. Currently, this happens mostly by manually improving one with the help of the other, with a long-term vision of more and more self-improvement through automated (data-driven) creativity and innovation with human goals and control. In this tutorial I will mostly explain the main methods to use ML for Optimization (ML4Opt), both online and offline, from the past history to the future challenges.

ABSTRACT. The Periodic Vehicle Routing Problem (PVRP) extends the classical Capacitated Vehicle Routing Problem by integrating multi-day scheduling and specific service patterns. This study focuses on a challenging variant: the PVRP with Driver Consistency (PVRP-DC). In this model, the same vehicle and driver must service a specific customer for every visit throughout the planning horizon. This constraint is critical in industries such as healthcare, beverage distribution, and retail, where stable service relationships are operationally beneficial. We propose several heuristics based on Variable Neighborhood Search coupled with a Path Relinking post-processing to obtain high-quality solutions. Computational results indicate that our approach performs well compared with a recently published heuristic and known optimal solutions as well.

ABSTRACT. The Knapsack Problem with Forfeit Sets (KPFS) extends the classical $0$--$1$ knapsack problem by allowing violations of predefined forfeit-set constraints at an associated cost, together with a global upper bound on the total number of violations. This modeling flexibility significantly increases the computational difficulty of the problem and motivates the development of advanced solution approaches. In this paper, we propose an implementation of the reinforcement learning variant of Construct, Merge, Solve, and Adapt (RL-CMSA). Items are treated as solution components, and solutions are generated by iteratively constructing feasible item subsets, followed by exact optimization on dynamically maintained sub-instances. This CMSA variant incorporates learning by associating quality values to solution components, which are updated online using feedback from the solutions produced by the exact solver. To maintain search diversity, it employs a convergence detection mechanism that triggers a restart of the learning process. Computational experiments on the most common KPFS benchmark instances show that the proposed method consistently achieves state-of-the-art results.

ABSTRACT. Oral cancer represents a significant global health burden, where early and accurate diagnosis is essential to improve survival rates and treatment outcomes. Conventional diagnostic approaches are often manual, time-consuming, and susceptible to variability, which can delay detection and clinical intervention. To overcome these limitations, this study proposes an enhanced deep learning framework for automated oral cancer classification that integrates DenseNet-201 for deep feature extraction and a Multilayer Perceptron (MLP) for final decision-making. To further improve performance, a novel Quantum-Enhanced Chaotic Differential Evolution (QCDE) algorithm is introduced for hyperparameter optimization, where chaotic mapping enhances population diversity and quantum-inspired strategies strengthen the exploration-exploitation balance, thereby accelerating convergence and reducing overfitting. The effectiveness of QCDE is validated using the CEC2022 benchmark test suite to demonstrate its optimization capability and robustness. By combining QCDE-driven optimization, deep feature representation, and advanced image processing techniques, the proposed framework provides a reliable, efficient, and accurate solution for early oral cancer detection. Experimental results demonstrate that QCDE-MLP achieves 96.43 % accuracy, surpassing competing metaheuristic-optimized classifiers.

ABSTRACT. This paper presents SP-CLA, a multi-population biased random-key genetic algorithm for the three-dimensional strip packing problem. Given a set of rectangular boxes and a container with fixed width and height but variable length, the objective is to pack all boxes while minimizing the required container length. The proposed algorithm integrates a BRKGA evolutionary framework with a search procedure for minimizing strip length. The decoder interprets chromosomes as packing sequences and constructs feasible arrangements using a wall-building strategy with maximal-space representation. Computational experiments in SP-BR benchmark instances demonstrate that SP-CLA achieves a mean volume utilization of 94.10%, outperforming all existing methods in all ten test classes.

ABSTRACT. This paper studies the Two-Dimensional Variable-Sized Cutting Stock Problem (2DVSCSP), a variant of the classical cutting stock problem in which the dimensions of the stock material are not predetermined but must be decided as part of the optimization process. In this setting, a set of rectangular items with known dimensions and demand must be cut from larger rectangular panels. Unlike the traditional cutting stock problem, where the size of the panels is fixed in advance, the manufacturer can determine both the width and the length of the stock panels to be produced. The objective is to determine the panel sizes and the cutting patterns that minimize the total material used to satisfy the demand.

The work is motivated by a real application in a company producing honeycomb cardboard panels. In this production process, panels are manufactured in-house from paper rolls and a honeycomb mesh structure and are subsequently cut into smaller pieces. Because the panels are produced internally, the company has the flexibility to choose their dimensions before the cutting stage. However, operational constraints limit the number of different widths and stock sizes that can be used in each production run, and the cutting machines only allow guillotine cuts organized in two stages. These characteristics make the problem more complex than the classical two-dimensional cutting stock problem, since both the stock dimensions and the cutting patterns must be determined simultaneously.

To address this problem, the authors propose a genetic optimization model based on the Biased Random Key Genetic Algorithm (BRKGA). A candidate solution is represented as a chromosome composed of random keys that encode the grouping of item types, their assignment to stock sizes, and the selection of stock dimensions. During decoding, the algorithm first determines an ordering of item types and groups them into subsets. These subsets are then assigned to stock sizes, and the dimensions of each stock panel are determined while ensuring feasibility with respect to the item dimensions and the available widths. Finally, the cutting patterns are constructed by deciding whether items within each subset should be combined into the same pattern or separated into individual patterns, selecting the alternative that minimizes total material usage.

An important feature of the proposed framework is its flexibility. The chromosome structure can be adapted to different variants of the problem, including cases where stock dimensions are discrete, continuous, or mixed, as well as multi-stock settings in which panel sizes are predefined. The methodology can also accommodate limits on the number of stock sizes or the number of item types allowed in each cutting pattern, reflecting practical production constraints.

The approach is evaluated through extensive computational experiments on a dataset of industrial instances previously used in the literature. The results show that the genetic model produces solutions very close to those obtained by mixed-integer programming models and often improves them when optimality cannot be proven by the exact approach. Moreover, the algorithm obtains high-quality solutions in very short computational times, typically within a few seconds, and can handle more complex configurations involving multiple widths, several stock sizes, and cutting patterns with more item types than those manageable by exact models.

Overall, the study demonstrates that the BRKGA-based methodology is an efficient and robust tool for solving the two-dimensional variable-sized cutting stock problem. The results also indicate that increasing flexibility in the selection of stock sizes and widths can significantly reduce material waste, although this may increase operational complexity. Future research directions include extending the model to consider multiple simultaneous orders, integrating multi-period production planning, and incorporating sequencing decisions to better align cutting plans with delivery requirements.

ABSTRACT. The Distributor’s Pallet Loading Problem extends bin packing by arranging 3D boxes onto layers of pallets and by enforcing stability, load-bearing, and stackability constraints between layers. This work proposes a constructive heuristic and a refined matheuristic that both work in two phases: layer building and pallet creation. Computational results show that the matheuristic outperforms existing approaches, while the constructive heuristic remains competitive despite its simplicity.

ABSTRACT. Hexaly Optimizer is a new kind of global optimization solver. Its modeling interface is nonlinear and set-oriented. In a sense, Hexaly APIs unify and extend modeling concepts from mixed-linear programming, nonlinear programming, constraint programming, and black-box optimization. Under the hood, Hexaly combines various exact and heuristic optimization methods, such as branch-and-bound, automatic Dantzig-Wolfe reformulation, column and row generation, propagation methods, local search, direct search, and surrogate modeling techniques.

Regarding performance benchmarks, Hexaly distinguishes itself against the leading solvers in the market, like Gurobi, IBM Cplex, and Google OR Tools, by delivering fast and scalable solutions to Routing, Scheduling, Packing, Clustering, and Location problems.

This talk will introduce our set-based modeling formalism and show its scalability for large instances. We will then explore how the solver can use this formalism to automatically use state-of-the-art resolution techniques from the exact and heuristic fields.