ABSTRACT. Given a set of target points, each associated with a circular neighborhood of fixed radius, the Close Enough Traveling Salesman Problem (\ce) consists in finding a minimum-length tour, starting and ending at a depot, that intersects each neighborhood at least once. In this work, we address the Multiple Close-Enough Traveling Salesman Problem (\mc), a variant of \ce, which aims to find $m$ routes satisfying the following conditions: \textit{i)} each route starts and ends at the depot, and \textit{ii)} every neighborhood must be visited by at least one of the routes. The goal of the problem is to minimize the length of the longest of the $m$ routes.

The \mc\ finds applications in precision agriculture, where a fleet of drones can collect information from ground sensors by simply flying close enough to retrieve their data while minimizing the total collection time. In this paper, we propose a three-phase heuristic approach to tackle the problem. The first phase discretizes the neighborhoods to obtain an instance of the Multiple Generalized Traveling Salesman Problem, which is then heuristically solved during the second phase. The feasible solution obtained at the end of the second phase defines, for each route, the visiting sequence of its neighborhoods. In the third phase, a second-order cone programming model is applied to obtain the optimal solution of \mc\ according to these fixed visiting sequences. We tested the effectiveness of our approach using benchmark instances of the \ce\ available in the literature.

ABSTRACT. In this work, we study the single-depot min-max Multiple Traveling Salesman Problem with a heterogeneous-speed fleet, where each vehicle completes a closed tour and the objective is to minimize the makespan, i.e., the maximum travel time among vehicles. Unlike the homogeneous case, route quality depends on vehicle speed, which couples customer assignment and routing decisions. To address this setting, we extend the Construct, Merge, Solve & Adapt framework with Reinforcement Learning (RL-CMSA) proposed for the homogeneous variant, introducing a city--vehicle preference model and time-aware evaluation within construction and improvement phases, while the restricted exact subproblem jointly selects routes and assigns them to vehicles. We evaluate the method on random instances with up to 200 cities and on four TSPLIB benchmarks under three realistic speed ranges (70-80, 60-90, and 50-100 km/h). Results show that RL-CMSA outperforms a strong greedy baseline that optimally solves intra-cluster tours using Concorde. Performance degrades as instance size grows and the speed interval widens, indicating that stronger heterogeneity yields a harder search landscape. At the same time, wider speed ranges tend to reduce the makespan, suggesting that a few faster vehicles can shorten completion time even though it increases the problem’s difficulty.

ABSTRACT. The Traveling Salesman Problem with Profits (TSPP) is an NP-hard combi-natorial optimization problem that involves simultaneous selection and se-quencing decisions under limited resources. This study addresses a multi-objective TSPP for travel route planning, aiming to minimize total travel and visiting time of selected attractions while maximizing total rating score, which represents collected profits. To solve this problem, we develop an en-hanced Multi-Objective Ant Colony Optimization (MOACO) algorithm that incorporates key mechanisms, including bi-pheromone learning, elitist rein-forcement, and local search procedure to improve search efficiency and solu-tion quality. A real-world railway tourism routing case is used to evaluate the proposed approach. Computational results demonstrate that the proposed MOACO efficiently generates high-quality Pareto solutions within practical computation time, indicating strong effectiveness for complex multi-objective routing problems.

ABSTRACT. This paper introduces a parameter-less version of the Step Counting Hill Climbing (SCHC) algorithm, a simple, general-purpose, and memory-efficient optimisation technique. Unlike many algorithms that rely on memory to store previous solutions or their costs, SCHC operates as a one-point search methodology and requires tuning only a single parameter: the counter limit, which governs the acceptance of worsening moves. By adopting a doubling mechanism for the counter limit parameter, previously introduced in the literature for a similar algorithm, we eliminate the need for manual parameter tuning. Through experiments, we demonstrate that parameter-less SCHC (pSCHC) achieves solution quality comparable to SCHC with fixed counter limits. The proposed pSCHC is evaluated on seven instances of the Traveling Salesman Problem (TSP), and results validate its efficacy.

ABSTRACT. The 2-Optimality Motif Finding (2OMF) problem is a com- binatorial optimization problem seeking the most representative string s in a set of input strings S: the consensus of S is a string s that minimizes the sum of the squared Hamming distances to all strings in S. We develop a Simulated Annealing approach with dynamic cooling. We benchmark this algorithm against a state-of-the-art hybrid Genetic Algorithm and against an exact solver using a Mixed-Integer Quadratic Programming formulation. We introduce two procedures to generate problem instances of two different types, uniform and balanced. The experimental analysis shows that while uniform instances are easily solvable by all methods, balanced instances pose a challenge. Our Simulated Annealing (SA) algo- rithm produces the best results on the large majority of instances com- pared to the exact solver and the Genetic Algorithm on the balanced instances. Statistical tests confirm the significance of these performance differences, establishing our SA approach as a superior method for diffi- cult classes of the 2OMF problem

ABSTRACT. In combinatorial optimization, the Fourier Transform (FT) on the symmetric group has been used to analyze and optimize permutation-based problems. However, the difficulties that arise when working within Fourier space have limited its potential in practical scenarios. To address this issue, rather than using the FT to decompose the objective function, an alternative possibility is to use the FT as a tool to break down the instance defining the problem at hand. This strategy captures the information from each Fourier coefficient as a separate instance of the same problem, resulting in a potentially more usable setting in the context of optimization. So far, the FT-based instance decomposition has been limited to a small sample of problems characterized by low-order Fourier coefficients. In this work, we generalize this notion to a much broader class of problems, known as k-adic Assignment Problems (k-APs). We present a general framework for the decomposition of k-AP instances and discuss its practical applications. As a possible use case, we propose an instance generation method that exploits the FT-based instance decomposition to create artificial instances with tunable difficulty levels.

ABSTRACT. This research explores a realistic variant of the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP), a well-known optimization problem in project planning where each activity can be executed in one of several modes under limited resources. Each execution mode represents an alternative combination of resource requirements and activity duration. We extend the classical setting by introducing time-dependent resource costs and capacities, meaning that the availability and cost of a given resource depend not only on the resource itself, but also on the specific time periods during which it is employed—a situation that often arises in real-world scenarios. Furthermore, we adopt a multi-objective framework, with the objectives of minimizing the makespan and the total cost of resource usage. A mathematical formulation is presented for this problem, and an attempt is made to solve it using an exact method to find the Pareto front (PF), i.e., the set of non-dominated solutions where no objective can be improved without deteriorating another. Nonetheless, the inability of exact techniques to handle large-sized instances of this hard problem motivates the development of a metaheuristic to approximate the PF. We design an innovative multi-objective genetic algorithm that effectively integrates the new problem elements to build high-quality solutions. A comprehensive computational study is conducted on a benchmark set of instances for this novel bi-criteria, multi-mode problem. The results demonstrate the effectiveness of the proposed metaheuristic.

ABSTRACT. This paper investigates an extended version of the multi-skill resource-constrained project scheduling problem that incorporates multiple efficiency rates for resources, as well as fixed and skill-dependent variable costs. This formulation captures key features commonly observed in real-world project management environments. The problem consists of determining both the start times of activities and the assignment of (resource, skill) pairs in order to minimize the project makespan while accounting for cost considerations. Since higher-skilled resources typically incur higher costs, time and cost naturally constitute conflicting objectives, leading to a multi-objective optimization framework. Exact solution approaches become computationally infeasible even for small- and medium-sized instances of this problem. To address this limitation, we propose a multi-objective metaheuristic based on an innovative solution encoding and problem-specific crossover and mutation operators that effectively exploit domain knowledge to generate high-quality solutions. Preliminary computational experiments show that the proposed method provides promising results in terms of computational time and solution quality for the instances considered, and constitutes a viable alternative for tackling larger problem instances.

ABSTRACT. We propose RepHVTRand-TASV, a date-aware extension of disruption-and-repair large neighborhood search for shift scheduling. Existing methods often rely solely on horizontal (per-staff) violations, limiting solution diversity and scalability. Our method addresses this by integrating five key components: (1) alternating horizontal and vertical violation-based staff selection to minimize violations related to individual staff and daily schedules; (2) a tabu list to suppress repeatedly non-improving staff subsets; (3) a late-phase randomized selection to escape local optima when solution improvement stagnates; (4) three initialization strategies adopted to enhance stability and prevent excessive perturbation of the solution; and (5) time-based termination to replace exhaustive enumeration. We evaluate six variants on 20 public nurse rostering benchmarks (up to 60 staff, 2–12-week horizons), comparing against both a baseline and the ejection chain method. The proposed method consistently yields higher feasible solution rates and objective improvements of up to 62% (10-min runs) and 69% (60-min runs) over the baseline. Ablation studies confirm the effectiveness of each component, with vertical penalties and hybrid initialization being especially critical for larger instances. Importantly, RepHVTRand-TASV is applicable to all shift scheduling problems involving staff and dates, regardless of constraint types, making it a robust and general-purpose scheduling engine.

ABSTRACT. This case study tackles a real-world problem of a transportation company that is modeled as a scheduling optimization problem. The main goal of the considered problem is to schedule the maximum number of jobs that must be performed by vehicles over a specific planning horizon in order to minimize the total operational costs. Here, each customer request corresponds to a job composed of multiple operations, such as loading, unloading, and mandatory jobs, each associated with a specific location and time window. Once a job is allocated to a vehicle, all its operations must be executed by that same vehicle within their designated time constraints. Due to the imposed limitations, not every job can feasibly be scheduled. To address this challenge, two distinct methodologies are proposed. The first, a Holistic approach, solves the entire problem formulation using a black-box optimizer, serving as a comprehensive benchmark. The second, a Divide-and-Conquer approach, combines a heuristic greedy algorithm with a binary linear programming, decomposing the problem into sequential subproblems. Both approaches are implemented using the solver Hexaly. A comparative analysis is conducted under different scenarios and problem settings to highlight the advantages and drawbacks of each approach. The results show that the Divide-and-Conquer approach significantly improves computational efficiency, reducing time by up to 99% and vehicle usage by around 15–20% compared to the Holistic method. On the other hand, the Holistic method better ensures that mandatory jobs are completed, although at the cost of more resources.

ABSTRACT. The Radiotherapy Scheduling Problem (RTSP) involves determining an optimal schedule for patients undergoing radiation treatments, a task that has a massive impact on clinical outcomes given the central role of radiotherapy in cancer care. The daily batch approach--which consists of scheduling all the newly arrived patients together at the end of each day--modelled with Integer Linear Programming, is currently one of the most effective methods for the RTSP. However, this kind of formulation requires substantial computational resources in terms of time and memory. Here, we address these limitations by developing two novel greedy heuristics (named RTSP First Fit and RTSP Best Fit) and use them as constructive heuristics for a Simulated Annealing (SA) approach to optimize the scheduling. The proposed methods--the heuristics alone and their combination with SA--are evaluated on a publicly available dataset against an integer linear program formulation solved with two different state-of-the-art exact solvers. Evaluation metrics include six scheduling objectives capturing patient waiting times, preference satisfaction, and changes in linear accelerator assignment (aggregated in four different weight configurations), solving time, and memory consumption. The results show that the novel heuristics achieve solutions close to those of exact methods, while dramatically reducing runtime and memory usage; furthermore, when combined with SA, they further improve the solution quality while maintaining low runtime and memory usage.

ABSTRACT. The Three-Stage Remanufacturing System Scheduling Problem (3T-RSSP) is a NP-hard optimization problem related to the Circular Economy. While exact methods exist, they struggle to scale, often failing to find feasible solutions for large instances. In this work, we propose an efficient GRASP metaheuristic that incorporates a multistage sequential constructive phase, a multi-strategy local search, and an efficient evaluation mechanism for the objective function. Experimental results on 51 benchmark instances show that our proposal outperforms state-of-the-art methods. In small and medium-scale instances, GRASP achieves the best average makespan with an average execution time over an order of magnitude shorter than the best exact model. In larger scenarios, our algorithm proves its robustness by finding high-quality solutions where exact models fail within the time limit.

ABSTRACT. This paper investigates whether Large Language Models (LLMs) can reliably support the solution of combinatorial optimization problems. Using the Traveling Salesman Problem (TSP) and two artificial variants as case studies, we evaluate the ability of several state-of-the-art LLMs to generate correct exact and heuristic algorithms, adapt to non-standard problem formulations, and correctly characterize the nature of the proposed solution methods. The results show strong performance on classical formulations, but significant limitations when the logical structure of the problem becomes more complex.

ABSTRACT. Metaheuristics are widely used in combinatorial optimization to address large-scale problems but often require considerable expertise and engineering effort. In this paper, we investigate whether recent large language models (LLMs) can translate state-of-the-art algorithmic descriptions into performant code with minimal human intervention. We introduce a generalizable prompting framework: Context, Communication, and Iteration (CCI), and apply it to replicate a Variable Neighborhood Search for the balanced minimum sum-of-squares clustering problem using Gemini 2.5 Pro and Claude Sonnet 4. According to our computational experiments, Gemini achieved solutions with a mean difference of 0.032% from the reference implementation (median: 0.009%), being statistically non-inferior within a 0.01% margin. Notably, Gemini corrected a missing mathematical term in the neighborhood evaluation formula described in the source paper, whereas Claude did not. Our findings suggest that LLM-assisted engineering is a viable pathway to facilitate algorithm replication, making high-performance methods more accessible to researchers and allowing them to tackle larger and more complex problems.

ABSTRACT. Automatic algorithm configuration tools such as irace efficiently tune parameter values but leave algorithmic code unchanged. This paper introduces a first version of irace-evo, an extension of irace that integrates code evolution through large language models (LLMs) to jointly explore parameter and code spaces. The proposed framework enables multi-language support (e.g., C++, Python), reduces token consumption via progressive context management, and employs the Always-From-Original principle to ensure robust and controlled code evolution. We evaluate irace-evo on the Construct, Merge, Solve \& Adapt (CMSA) metaheuristic for the Variable-Sized Bin Packing Problem (VSBPP). Experimental results show that irace-evo can discover new algorithm variants that outperform the state-of-the-art CMSA implementation while maintaining low computational and monetary costs. Notably, irace-evo generates competitive algorithmic improvements using lightweight models (e.g., Claude Haiku 3.5) with a total usage cost under \euro 2. These results demonstrate that coupling automatic configuration with LLM-driven code evolution provides a powerful, cost-efficient avenue for advancing heuristic design and metaheuristic optimization.

ABSTRACT. Large Language Models (LLMs) have recently attracted rising attention beyond natural language processing, including their integration with Evolutionary Algorithms (EAs) for optimization tasks. This study investigates the use of LLMs to tune the parameters of Metaheuristic Algorithms (MAs) through a structured framework, LLM-EPCO, designed to evaluate their configuration capabilities under standardized experimental conditions. The proposed approach guides the iterative adjustment of key parameters, such as scaling factor, crossover rate, population size, and iteration budget, and compares the resulting configurations against established automatic configurators, namely Optuna and SMAC3. The results show that the LLM-based configurations improve the base algorithms' original parameter settings and achieve competitive performance relative to the reference frameworks.

ABSTRACT. Can an LLM learn how an optimizer behaves--and use that knowledge to control it? We extend Code World Models (CWMs), LLM-synthesized Python programs that predict environment dynamics, from deterministic games to stochastic combinatorial optimization. Given suboptimal trajectories of (1+1)-RLSk, the LLM synthesizes a simulator of the optimizer's dynamics; greedy planning over this simulator then selects the mutation strength k at each step. On \lo{} and \onemax{}, CWM-greedy performs within 6\% of the theoretically optimal policy -- without ever seeing optimal-policy trajectories. On \jump{k}, where a deceptive valley causes all adaptive baselines to fail (0\% success rate), CWM-greedy achieves 100\% success rate -- without any collection policy using oracle knowledge of the gap parameter. On the NK-Landscape, where no closed-form model exists, CWM-greedy outperforms all baselines across fifteen independently generated instances (36.94 vs.\ 36.32; p<0.001) when the prompt includes empirical transition statistics. The CWM also outperforms DQN in sample efficiency (200 offline trajectories vs.\ 500 online episodes), success rate (100\% vs.\ 58\%), and generalization (k=3: 78\% vs.\ 0\%). Robustness experiments confirm stable synthesis across 5 independent runs.

ABSTRACT. Designing effective greedy heuristics for combinatorial optimization typically relies on manually crafted scoring functions requiring domain expertise and careful tuning. We propose an LLM-guided genetic programming framework that automatically evolves symbolic scoring functions represented as closed-form analytical expressions over a predefined grammar and a set of problem-specific features. All variation operators are generated by a large language model acting as a semantic variation engine, producing structurally meaningful mutations and crossovers within a formally constrained symbolic space. A grammar validation operator ensures structural and numerical robustness, and an optional seeding mechanism allows prior expert knowledge to be injected into the initial population. The framework ultimately returns a deterministic, interpretable heuristic deployable without runtime dependency on the LLM, making it particularly suited to high-stakes decision-support contexts requiring auditability and transparency. Evaluated on 64 benchmark instances of the Set Packing Problem, the best evolved expression achieves a 30.9% reduction in average optimality gap over a standard baseline within approximately 20 minutes of computation, demonstrating the viability of hybrid symbolic and statistical approaches for automated and explainable heuristic design.

ABSTRACT. This presentation explores the powerful role of mathematical optimization and algorithmic and metaheuristic tools in transforming social and healthcare services. The use of optimization techniques can lead to significant cost savings, improved utilization of resources, higher satisfaction among personnel and service users, and—most importantly—ensure that limited resources are directed to those who need them most. Ultimately, this fosters a more equitable and sustainable society. The talk will showcase real-world implementations developed in partnership with organizations like the Barcelona City Council, Suara, and Banc del Moviment. Key applications discussed will include: - Streamlining logistics and scheduling for in-home social and healthcare services. - Improving the delivery systems for assistive technologies. - Enhancing mobility solutions and shared door-to-door transit for individuals with disabilities.

Finally, the session will explore the specific mathematical models and metaheuristic algorithms behind these solutions, highlighting the unique complexities of applying optimization to human-centered social care compared to traditional sectors like retail and manufacturing.

ABSTRACT. The inventory routing problem (IRP) focuses on jointly optimizing inventory and distribution operations from a supplier to retailers over multiple days. Compared to other problems from the vehicle routing family, the interrelations between inventory and routing decisions render IRP optimization more challenging and call for advanced solution techniques. A few studies have focused on developing large neighborhood search approaches for this class of problems, but this remains a research area with vast possibilities due to the challenges related to the integration of inventory and routing decisions. In this study, we advance this research area by developing a new large neighborhood search operator tailored for the IRP. Specifically, the operator optimally removes and reinserts all visits to a specific retailer while minimizing routing and inventory costs. We propose an efficient tailored dynamic programming algorithm that exploits preprocessing and acceleration strategies. The operator is used to build an effective local search routine, and included in a state-of-the-art routing algorithm, i.e., Hybrid Genetic Search. Through extensive computational experiments, we demonstrate that the resulting heuristic algorithm leads to solutions of unmatched quality up to this date, especially on large-scale benchmark instances.

ABSTRACT. The Meal Delivery Routing Problem (MDRP) requires as- signing couriers to orders and computing delivery routes under stochastic demand, tight customer time windows, and heterogeneous courier fleets. We propose a Biased Random-Key Genetic Algorithm with Rolling Hori- zon (BRKGA-RH) for the MDRP and evaluate two fitness variants — BRKGA-Coverage (maximizing orders delivered) and BRKGA-Travel (minimizing travel time) — against a Business Model and a Business Model Lookahead that defers low-volume stores via demand forecasting. All four methods operate under a rolling-horizon architecture. Experi- ments use real-world instances from a Latin American food-delivery plat- form. On small and medium instances, both BRKGA variants achieve the highest average coverage rate, outperforming the Business Model Lookahead and the Business Model by roughly eight and fifteen per- centage points, respectively. On large instances the ranking reverses: the Business Model Lookahead attains the best coverage, surpassing BRKGA-Coverage by nearly four percentage points, as the bounded gen- eration budget limits metaheuristic search on high-volume days. Both BRKGA variants are computationally faster than the Business Model Lookahead. BRKGA-Travel delivers equivalent coverage while running approximately a quarter faster than BRKGA-Coverage, making it the preferred choice for small-to-medium deployments; the Business Model Lookahead is recommended for large instances. A hybrid strategy that switches between methods based on daily order volume captures the best of both approaches.

ABSTRACT. The Inventory Routing Problem (IRP) is a central optimization problem in supply chain management that integrates vehicle routing, delivery scheduling, and inventory control decisions over a finite planning horizon. Frequently arising in vendor-managed inventory systems, the IRP requires jointly determining when to serve customers, how much to deliver, and how to route a fleet of vehicles, while minimizing total transportation and inventory holding costs. Despite decades of research, many benchmark instances remain challenging, as highlighted by the recent 12th DIMACS Implementation Challenge.

This work presents a Hybrid Genetic Search framework tailored specifically for the IRP. Our approach integrates two complementary paradigms: the Hybrid Genetic Search (HGS), a state-of-the-art memetic algorithm originally developed for vehicle routing problems, and the Network Simplex IRP (NSIRP), an approach that efficiently computes optimal inventory levels via a minimum-cost flow formulation. The key idea is to exploit HGS for global exploration of routing and scheduling decisions while embedding a fast exact inventory decoder to optimally determine inventory levels for any fixed routing structure.

To enable this integration, we introduce several methodological contributions. First, we propose a unified solution representation composed of delivery, routing, and giant-tour chromosomes, allowing effective recombination while preserving feasibility. Second, we develop a novel Periodic-Tour-Non-Uniform (PTNU) crossover operator designed to respect the temporal and structural characteristics of IRP solutions. This operator partitions customers into disjoint subsets and constructs offspring giant tours by selectively inheriting period-specific genetic material from both parents. Inventory quantities are then computed using a giant-tour-based flow decoder, followed by route reconstruction through a Split procedure. Third, we refine the solution by recalculating deliveries with a fast optimal inventory computation based on network flows. This significantly improves the quality of initial solutions. Fourth, we enhance the local search by combining a fast Capacitated Vehicle Routing Problem (CVRP) improvement phase with a full IRP local search that incorporates efficient inventory recomputation. Additional acceleration mechanisms include heuristic upper bounds to avoid unnecessary exact inventory evaluations, candidate arc lookup strategies in the network simplex, and routing arc update tracking. Together, these components substantially reduce computational overhead while preserving solution quality.

The resulting algorithm, denoted HGSIRP, was extensively evaluated on 1,098 benchmark instances from the classical IRP literature, covering both single- and multi-vehicle scenarios and varying problem sizes. Computational experiments were conducted using standardized time adjustments to ensure fair comparisons with 22 state-of-the-art methods. Across all benchmark categories, HGSIRP consistently outperformed existing approaches. The method produced 137 new best-known solutions on classical instances and 180 new best-known solutions on a recent larger instance set. Under the evaluation rules of the 12th DIMACS Implementation Challenge, our algorithm would rank first overall.

ABSTRACT. In this paper, we introduce the Selective Multi-Commodity Pickup and Delivery Traveling Salesman Problem. Each customer may supply and/or demand multiple commodities. A single capacitated vehicle selects which customers to visit and in which order, and decides how much of each commodity to pick up and deliver under a route-duration limit, with the objective of maximizing total satisfied demand. We propose an adaptive large neighbourhood search (ALNS) algorithm and evaluate it on benchmark instances adapted from a related problem.

ABSTRACT. This paper introduces a hybrid genetic algorithm (GA) for solving a special case of pickup and delivery problem with time windows (PDPTW). The proposed approach is tested against Li & Lim’s benchmark PDPTW instances and yielded optimal solutions for 29 out of 45 independent runs whereas basic GA achieved optimality in 25 out 45 runs. A real case study from an animal by-products processing industry is also presented where the proposed model solved with hybrid GA obtained around 27% more reductions in quality deterioration cost with no increase in travel distance and emission compared to the standard PDPTW solved with basic GA.

ABSTRACT. This work addresses the Shared Customer Collaboration Vehicle Routing Problem (SCC-VRP), an NP-hard problem in which competing carriers can transfer shared customers between each other to reduce total distribution costs. We propose Guided Strategic Oscillation with Reinforcement Learning (GSO-RL), a metaheuristic that combines adaptive memory programming and strategic oscillation, using a Multi-Armed Bandit mechanism to select between intensification and diversification strategies based on regional search history. The algorithm maintains a set of guiding solutions that partition the search space into concentric subregions, each of which is managed by an independent learning agent. Computational experiments on benchmark and new large-scale instances show that GSO-RL outperforms the state of the art across all tested configurations, achieving the best-known solution in 100% of the evaluated instances while requiring significantly less computational time.

ABSTRACT. This paper introduces a reinforcement learning framework for adaptive control of Particle Swarm Optimization, where agents learn to adjust algorithm parameters, trigger restarts, and coordinate subswarm behaviors through interaction with the optimization process. The unified environment supports both discrete and continuous control, enabling flexible experimentation across multiple adaptation mechanisms. Tests on selected CEC’13 benchmarks show that learned policies consistently outperform canonical PSO, with continuous agents achieving modest improvements and hybrid restart–hyperparameter controllers delivering the largest and most robust gains.

ABSTRACT. We present PB-MODE-T, a surrogate-assisted multi-objective Differential Evolution framework for Neural Architecture Search tai- lored to digital pathology. PB-MODE-T uses a compact path-based cell search space and a continuous 10-dimensional encoding to represent DAG-based cells and macro-architectures, enabling efficient exploration of lightweight models suitable for whole-slide image (WSI) patch clas- sification. Its core novelty is a triplet-based surrogate: a triplet net- work is trained on anchor–positive–negative triplets constructed from fully evaluated architectures to learn dominance-preserving embeddings. A tree-based predictor uses concatenated triplet embeddings to per- form pairwise ranking classification, reframing surrogate modeling as a ranking problem that is more robust when labeled evaluations are scarce. The evolutionary loop alternates between fully evaluated genera- tions and surrogate-assisted candidate generation, reducing training cost while maintaining Pareto diversity. Evaluated on the BCNB WSI patch classification task, PB-MODE-T discovers highly efficient architectures (medium solution ≈0.22M parameters, ≈0.91 MB) that achieve superior accuracy–efficiency trade-offs (test accuracy 0.723, F1 0.543) compared to handcrafted CNNs, lightweight nets, transformers, and NAS base- lines. PB-MODE-T demonstrates that dominance-aware triplet embed- dings effectively guide Pareto-centric NAS towards practically deploy- able, high-performing models for medical imaging.

ABSTRACT. Artificial Neural Networks (ANNs) are widely used in various application domains, particularly for classification tasks. Among them, the Multilayer Perceptron (MLP) remains a reference model, whose performance strongly depends on three interrelated aspects: feature selection, network architecture, and training. This paper proposes a unified multi-objective optimization framework that simultaneously addresses these three aspects. The problem is formulated as a tri-objective optimization task aiming to minimize the training error, the network complexity, and the number of selected features. An adapted version of the Non-Dominated Sorting Genetic Algorithm III (NSGA-III) is employed to solve this problem. Experimental results obtained on four well-known benchmark datasets show that the proposed approach achieves high classification accuracy while significantly reducing the number of selected features, hidden neurons, and network connections. Comparisons with existing multi-objective methods demonstrate the effectiveness of the proposed framework in producing compact and accurate MLP models.

ABSTRACT. Simulated Annealing is among the most used metaheuristics, yet many of its design parameters are still chosen based on rules of thumb or inherited conventions. In this work, we aim to shed light on its underlying mechanics by investigating the role of the temperature length strategy, which determines how many neighboring solutions are evaluated at each temperature level and thus regulates the trade-off between exploration and intensification. We study three strategies on two benchmark problems. Preliminary results indicate that, unsurprisingly, performance is problem-dependent. Overall, simpler strategies are favored when evaluated through rank-based analyses, whereas sophisticated strategies are superior when considering objective value differences.

ABSTRACT. Metaheuristic algorithms are fundamental techniques in modern combinatorial optimization: they deliver high-quality solutions to NP-hard problems within practical time budgets, and their relevance is growing alongside the scale and complexity of data-driven decision problems. Yet a fundamental and often underappreciated question governs their practical effectiveness: \emph{when should a metaheuristic stop?} Devoting computational resources beyond the point at which meaningful improvement is statistically unlikely is wasteful; stopping too early sacrifices solution quality. Answering this question well is therefore critical to unlocking the full potential of any metaheuristic, across any application domain.

Classical stopping rules are either resource-based--capping iterations ($N$-rule) or wall-clock time ($T$-rule)--or stagnation-based, halting when the incumbent has not improved for $w$ consecutive iterations ($W$-rule). These rules are intuitive but blind to the underlying structure of the search: they cannot distinguish between a stagnating algorithm that has genuinely exhausted the promising region and one that is simply experiencing a temporary plateau. More sophisticated probabilistic approaches, estimate the probability density of observed objective values and terminate when the probability of further improvement falls below a threshold. These represent a significant conceptual advance, but they rely on \emph{parametric} distributional assumptions--typically normality or a Gamma family--which may be poorly suited to multimodal or irregular fitness landscapes, and they are often tailored to specific algorithm classes such as GRASP.

We present KDE-STOP, a nonparametric stopping rule applicable to any metaheuristic. Rather than fitting a parametric distribution, KDE-STOP uses \emph{Kernel Density Estimation} (KDE) to build a distribution-free estimate of the probability density of objective values encountered during the search. Every $it$ iterations, the estimate is refreshed on the basis of the most recently observed values. At each subsequent iteration, the rule evaluates the probability $p$ of improving the current incumbent $\bar{z}$ by at least a fraction $\pi$. If $p$ falls below a user-set threshold $\tau$, the algorithm terminates. Because KDE-STOP operates solely on objective function values, it is \emph{algorithm-agnostic}: integration requires no modification of the underlying metaheuristic beyond logging solution costs.

KDE-STOP was validated on four combinatorial optimization problems spanning distinct OR domains, each solved by a different target metaheuristic, and benchmarked against several competing stopping rules. Performance was assessed via a bi-objective score jointly rewarding solution quality and computational savings. The results show that KDE-STOP achieved the best average score on three out of four problems, and consistently ranked first across the majority of benchmark instances.

ABSTRACT. Many combinatorial decision problems exhibit a two-level decision structure, where high-level strategic choices influence lower-level operational decisions. Examples include Facility Location, Location Routing, and Outsourcing problems, where second-level decisions determine costs that depend on first-level choices. A key challenge in solving such problems efficiently is accurately and rapidly estimating second-level costs to guide first-level decision-making, since these costs typically require repeatedly solving a stochastic and dynamic combinatorial optimization problem. In this paper, we propose leveraging Reinforcement Learning (RL) to obtain fast and accurate approximations of second-level costs, which can then be integrated into traditional (meta)-heuristic frameworks for exploring first-level decisions. The resulting approach aims to preserve the flexibility of heuristic search at the first level while replacing expensive second-level evaluations with a learned surrogate that can be queried at scale to rapidly evaluate and compare candidate first-level decisions. More specifically, we demonstrate this approach on a daily distribution planning problem, named VRP-DO, where a fixed fleet must serve a set of customers whose demands are stochastic. Each day, the set of customers and their demand distributions are revealed. The decision-maker can outsource a subset of customers at a given cost while committing to serve the remaining ones. The objective is to determine the outsourcing decision and an efficient routing policy for the committed customers to minimize the overall expected cost, accounting for both outsourcing payments and the operational routing costs induced by stochastic demands. The VRP-DO follows a natural two-level structure: the first-level decision assigns customers to in-house or outsourced service, while the second-level decision determines a routing policy and its expected cost conditional on the committed set. We solve this problem using a heuristic algorithm that follows this decomposition. An Iterated Local Search (ILS) explores different outsourcing and commitment partitions, while a Deep Q-Network-based cost approximation (DQNCO) provides fast estimates of the expected second-level routing cost for candidate partitions. To address the distribution shift between real daily instances and the candidate partitions generated by ILS, we train DQNCO on synthetic daily scenarios with randomized customer subsets and demand distributions, aiming to generalize cost estimation across the search regions encountered during optimization. We validate the effectiveness of the proposed approach by comparing its performance against three alternative methods that rely on more traditional second-level evaluation and approximation strategies.