This paper addresses the Tourist Trip Design Problem (TTDP) in an urban context, focusing on weekend itineraries in Montreal, Canada. The problem is modeled as a multi-objective combinatorial optimization task that incorporates real-world constraints such as attraction opening hours, transportation modes, budget, and user preferences. A Multi-objective Variable Neighborhood Search (MOVNS) metaheuristic is applied, combining seven neighborhood operators with an adaptive shake strategy to explore diverse regions of the Pareto front. As a reference method, we consider the Non-dominated Sorting Genetic Algorithm II (NSGA-II) under the same computational budget. Both algorithms are evaluated on realistic instances built from GTFS, OpenStreetMap, and online tourist platforms. Experimental results show that MOVNS achieves higher Hypervolume and lower Inverted Generational Distance than NSGA-II, while maintaining competitive Spread and additive epsilon-indicator values. Taken together, these indicators suggest that MOVNS provides a broader and more informative approximation of the Pareto front for the same time budget. A qualitative analysis also shows that the algorithm can generate customized itineraries for different traveler profiles (economic vs. premium). Overall, the results indicate that MOVNS is suitable for real-world tour planning scenarios and can serve as a core component of intelligent recommendation systems in urban tourism.
We propose an Adaptive Variable Neighbourhood Search (AVNS) metaheuristic for dynamic optimisation of tourist itineraries at destination for use in an interactive online tourist route recommender. The recommendation must use up-to-date information and be able to adapt the recommendation according to changes in the circumstances of the touristic activities or to specific requirements of the tourist user. Instead of using an algorithm to get the new recommendation from scratch after the changes, we propose to apply AVNS from the previous proposal. The adaptive mechanism takes into account previous performance to tune the parameters to the change that occurred. We test the proposal using real data from the tourist island of Tenerife in the Canary Islands. The results show that our proposal provides better results in less computational time.
The rise of the internet and social networks has posed new challenges in studying people’s behavior on these platforms. People tend to trust or align with a small group of users, leading to the development of viral marketing techniques to effectively propagate information about products or services. This has led to the definition of problems related to social influence maximization/minimization and dominance sets. The Minimum Positive Influence Dominating Sets (MPIDS) problem involves finding a minimum cardinality dominance set to influence an entire social network. For a vertex to be influenced, at least half of its neighbors must be in the dominance set. Considering that MPIDS is an 𝒩𝒫 -hard problem, where exact approximations are impractical due to the size of social networks, this work proposes using Basic Variable Neighborhood Search (BVNS). Given an initial solution generated by a constructive method, this metaheuristic consists of two phases: a shaking and an improvement phase. In the shaking phase, the solution is modified by removing and reconstructing it using a randomized greedy approach. The improvement phase involves an innovative local search strategy based on generating holes, which removes the δ -neighborhood of a vertex to facilitate a greedy solution reconstruction.
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
This paper studies the two-stage no-wait hybrid flow shop scheduling problem with a single server at the first stage, involving two parallel machines in stage one and a single machine in stage two. The presence of no-wait and server constraints makes the problem highly challenging. A mixed-integer programming (MIP) model is proposed to solve small instances optimally. For larger cases, we develop two constructive heuristics and metaheuristic approaches, including SA and several variants of GVNS. Computational experiments show that while the MIP is limited to small sizes, GVNS significantly outperforms the heuristics and SA, delivering high-quality solutions in short computation times. The best GVNS variant achieves the lowest average gaps relative to the lower bound, demonstrating the efficiency and robustness of the proposed methods.
This work focuses on implementing a metaheuristic algorithm for solving the Periodic Capacitated Vehicle Routing Problem with Time Windows and Driver Consistency (PCVRPTW-DC), a problem that hybridizes the Consistent Vehicle Routing Problem and the Vehicle Routing Problem with Time Windows. Additionaly, the final goal of the work is the development of a customized solution for weekly logistic route planning in a distribution company. Initially, the planning was manually generated by company experts and, later, by using a commercial solver (Hexaly). Due to new flexibility and technological independence requirements, it was decided to replace this tool with an in house system. Experimental results show that this new system provides competitive and even superior solutions compared with the previous approaches, establishing the groundwork for a more adaptable and efficient solution.
The Job Shop Scheduling Problem is a classic combinatorial optimization problem and one of the most well-studied scheduling problems. Several methodologies, both exact and metaheuristic, have already been proposed for the solution of this computationally difficult problem. This work presents for the first time a solution approach based on Variable Neighborhood Programming for the Job Shop Scheduling Problem. Variable Neighborhood Programming is a recent methodology which constitutes a combination of Genetic Programming and Variable Neighborhood Search. In addition, some encouraging comparative computational results are also shown against the state-of-the-art Gurobi optimization solver using medium- and large-scale benchmark instances. The findings of this work have a plethora of modern applications in Manufacturing-as-a-Service online platforms. All experimental evaluations were performed on the Google Cloud Platform.
Semi-supervised clustering is a learning approach that primarily relies on unlabeled data but incorporates some prior information to improve the clustering results. Among various clustering objectives, the minimum sum-of-squares clustering (MSSC) is widely used to partition data by minimizing intra-cluster variances. In our work, we propose a Variable Neighborhood Search (VNS) heuristic for semi-supervised MSSC, where prior information is given in the form of pairwise must-link and cannot-link constraints. Our approach reformulates the optimization problem by representing must-link constraints through the construction of super-points, which implicitly satisfy these constraints, while cannot-link constraints are incorporated as penalties in the objective function. Computational experiments indicate that, in the majority of tested cases, our proposed VNS heuristic outperforms the solutions obtained by the state-of-the-art heuristic algorithm found in the literature within the same computational time.
Software testing activities are critical for the development of high-quality software systems. In this context, high-quality models that accurately represent the system under test are an essential tool. To improve their quality, the inference of these models has been addressed as a multi-objective optimization problem in the literature. In this work, we propose a method based on the Multi-Objective Variable Neighborhood Descent (MO-VND) scheme to solve the problem of inferring behavioral models of software systems built on user-reported bugs. To configure the MO-VND we introduce five different neighborhood structures. The performance of the method is evaluated on a benchmark of real-world instances. The results show that the order in which the neighborhoods are explored greatly affects the performance of the MO-VND method. We compare the proposed method with three well-known algorithms that have already been studied in the literature for this problem: NSGA-II, NSGA-III, and MOEA/D. The results show that, although the proposed MO-VND method is capable of finding high-quality models, there is still room for improvement. In particular, the method might benefit from strategies for an efficient evaluation of neighbor solutions or the identification of promising solutions within the proposed neighborhoods.
We address a variant of the Capacitated Facility Location Problem in which each customer can be assigned to multiple facilities, subject to customer incompatibility constraint where, specifically, no two incompatible customers may be served by the same facility. In this paper, we extend the model by introducing a maximum budget service constraint, requiring that each customer must be assigned only to facilities within a predefined maximum unitary cost. This variant has practical applications where proximity and compatibility are critical, such as emergency logistics, last-miler delivery, and distribution of social services. Given the 𝒩𝒫 -hard nature of the problem, we propose a metaheuristic based on General Variable Neighborhood Search (GVNS), which integrates adaptive neighborhood structures and efficient local search procedures. Extensive computational experiments confirm the robustness and efficiency of the proposed method, particularly in scenarios with tight budget service restrictions.
This paper addresses the Integrated Production Routing Problem (IPRP), which requires the joint coordination of lot-sizing and vehicle routing decisions over a finite planning horizon. The problem accounts for several real-world features, including multiple products with different items, weights and sizes, sequence-dependent setup times and costs, limited production capacity, and safety stock requirements. For distribution operations, a heterogeneous fleet must serve customers with multiple time windows and strict deadlines, with routes possibly spanning several periods. The objective is to determine an integrated production and routing plan that minimizes setup changeover, inventory holding, and transportation costs. For this purpose, a Skewed Hybrid Variable Neighborhood Search (SHVNS) algorithm is proposed, relying on neighborhood structures specifically designed to modify routing decisions, while production planning is obtained from a mixed-integer programming model. Extensive computational experiments on benchmark instances demonstrate the effectiveness of the method in solving large-scale instances.
Python’s Package Index hosts over 640,000 packages without standardized categorization, making library discovery difficult. This work formulates library recommendation as multi-objective combinatorial optimization balancing linked usage from project dependencies, semantic similarity from package descriptions, and recommendation set size. We implement Multi-Objective General Variable Neighborhood Search with domain-specific neighborhood structures for addition, removal, and swap operations. The framework processes 10,000 PyPI packages and co-occurrence patterns from 24,000 GitHub repositories. Experimental evaluation with 30 independent runs per algorithm across two context libraries shows MO-GVNS achieves significantly higher hypervolume than NSGA-II (37.4
The Cyclic Min-Max Sitting Arrangement (CMMSA) is a graph layout optimization problem where the vertices of an input signed graph must be assigned to those of a cyclic host graph in a one-to-one correspondence. The input graph contains weighted edges, +1 or -1 , representing positive and negative relationships between the vertices. For each vertex, a penalty occurs when an adjacent vertex connected by a negative-labeled edge is positioned closer in the cycle than any other adjacent vertex connected by a positive-labeled edge. The goal is to minimize the maximum number of such penalties occurring at any single vertex. This paper presents a comprehensive study based on the Variable Neighborhood Search (VNS) methodology for solving the CMMSA. Building upon successful applications of VNS in related problems, we analyze multiple algorithmic variants and strategies. Specifically, our investigation focuses on Variable Formulation Search (VFS), which defines multiple formulations for the problem, allowing it to further explore the solution space. We propose a total of four alternative formulations specially suited for this problem. The use of VFS within the VNS methodology outperforms the use of a default VNS schema, obtaining a better solution in 19 out of 20 instances considered in the study. The findings not only highlight the efficacy of the proposed approach but also provide a foundation for future research on the CMMSA and related graph layout optimization problems.
The Uncapacitated Facility Location Problem (UFLP) is widely recognized as a relevant problem in logistics, resource distribution, and telecommunications network planning. Given a set of potential facility locations and a set of customers, the goal is to determine which facilities to open to serve all customers while minimizing both opening and assignment costs. Since this problem is classified as 𝒩𝒫 -hard, obtaining exact solutions at large scales could not be possible, thereby motivating the use of approximation techniques and metaheuristics. Although early studies used exact formulations derived from the UFLP model, recent research has emphasized the efficacy of approximate and metaheuristic algorithms, which achieve high-quality solutions with substantially reduced computational effort. This work introduces a Variable Neighborhood Search approach to tackle this problem. With the aim of guiding the search toward higher-quality solutions, machine learning techniques have been incorporated to this process. Experimental results on well-known benchmark datasets demonstrate that our method reaches solutions very close to the optimal values, with significantly shorter execution times, outperforming state-of-the-art algorithms validated by the pairwise non-parametric Wilcoxon statistical test.
In this work, we deal with a dynamic problem arising from outpatient healthcare facility systems. Patients in need of service arrive during the day at the facility. Their requests are expected to be satisfied within a given target time, otherwise, tardiness is incurred. The facility has multiple identical servers that operate simultaneously and are in charge of providing the patients with the requested services. Each server can provide only a finite subset of services, and each subset is called a configuration. The objective is to assign to each server a configuration selected from a set of predefined configurations, aiming at minimizing total tardiness. Assignments are not fixed statically, but they can be dynamically changed over time to better cope with the requested services. As the problem nature is dynamic, we propose a re-optimization algorithm that periodically optimizes the assignments with a Reduced Variable Neighborhood Search (RVNS). The RVNS works on neighborhood structures based on changing the assignments of one or more servers. The RVNS has been extensively tested on realistic instances. The results prove its efficiency in reaching low-tardiness solutions under low computing time.
This paper presents a variable neighborhood search based heuristic to minimise the number of resources for the single-processor scheduling problem with time restrictions which is known to be NP-complete problem. In particular, we study the performance of the Basic Variable Neighborhood Search algorithm (BVNS) under the use of different initial solutions. The obtained results were compared with an exact method published in the literature. Computational results show that the proposed algorithm is efficient and effective as it can obtain optimal solutions in 95.55% of the cases in a reasonable amount of time.
There are several hard combinatorial optimization problems that, in the context of communication networks, must be solved in short computing times since they are solving real-time critical tasks. This work is focused on the monitor placement problem, whose objective is to locate specific devices, called monitors, in certain nodes of a network with the aim of performing a complete network surveillance. As a consequence of the constant evolution of networks, the problem must be solved in real time if possible. If a solution cannot be found in the allowed computing time, then a penalty is assumed for each link of the network which remains uncovered. A Variable Neighborhood Search algorithm is proposed for solving this problem, comparing it with a hybrid evolutionary algorithm over a set of instances derived from real-life networks to evaluate its efficiency and efficacy.
Signed graphs are a particular type of graph, in which the vertices are connected through edges labeled with a positive or negative weight. Given a signed graph, the Minimum Sitting Arrangement (MinSA) problem aims to minimize the total number of errors produced when the graph (named the input graph) is embedded into another graph (named the host graph). An error in this context appears every time that a vertex with two adjacent (one positive and one negative) is embedded in such a way that the adjacent vertex connected with a negative edge is closer than the adjacent vertex connected with a positive edge. The MinSA can be used to model a variety of real-world problems, such as links in online social networks, the location of facilities, or the relationships between a group of people. Previous studies of this problem have been mainly focused on host graphs, whose structure is a path. However, in this research, we compare two variants of the MinSA that differ in the graph used as the host graph (i.e., a path or a cycle). Particularly, we adapted a previous state-of-the-art algorithm for the problem based on Basic Variable Neighborhood Search. The solutions obtained are compared with the solutions provided by a novel Branch & Bound algorithm for small instances. We also analyze the differences found by using non-parametric statistical tests.
The Bi-Objective Multi-Row Facility Layout Problem is a problem belonging to the family of Facility Layout Problems. This problem is challenging for exact and metaheuristics approaches. We use the Pareto front approach instead of the weight approach by means of a non-dominated solution set which we update in order to keep only the non-dominated solutions. To tackle this problem, we propose a Basic VNS algorithm based on a constructive method that generates random solutions, a mono-objective local search that relies on an interchange move, and a shake method that applies insert moves. In this regard, we also explain how to adapt the mono-objective schema of the BVNS for a multi-objective one. Then, we compare our results with the state of the art and propose future work.
Nowadays, social networks are one of the most important sources of information available on the Internet, since new users and relationships between them emerge every day in this type of networks. For this reason, it is important to have procedures and mechanisms to obtain, process and analyze the information extracted from them and transform it into useful data. This situation has given rise to new hard combinatorial optimization problems related to social networks, such as influence analysis, sentimental analysis or polarization. All these topics are grouped under the research field of Social Networks Analysis (SNA). In this paper, we focus on one of these topics: the Community Detection Problem (CDP). Specifically, we will deal with a variant of the CDP known as the Overlapping Community Detection Problem (OCDP), in which the same user can be assigned to more than one community simultaneously, which cannot occur in the classical Community Detection Problem. The problem is approached from a heuristic point of view, applying a Greedy Randomized Adaptive Search Procedure (GRASP) combined with a Basic Variable Neighborhood Search (BVNS) algorithm. The proposal is compared with the best method found in the literature, a Density Peaks based algorithm. Synthetic instances are used to evaluate the performance of the proposal. To analyze the quality of the obtained solutions, an evaluation metric that has been adapted from the well-known modularity metric has been used: the overlapping modularity.
