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.
