Search Results (108)

The evaluation of optimization algorithms for electric vehicle routing problems depends strongly on the quality of the benchmark instances used during experimentation. However, many synthetic instances simplify the joint effects of geometry, topography, operation, and energy, which can distort algorithmic assessment. This article proposes a modular and reproducible pipeline for generating synthetic instances of the Electric Vehicle Steiner Traveling Salesman Problem (EV-STSP), calibrated from a real urban reference network based on publicly available Madrid data. The pipeline combines directed graph construction, geometric control, attribute enrichment, charging-infrastructure placement, structured export, and explicit traceability mechanisms. To assess the realism of the generated instances, a three-level validation protocol is introduced, covering marginal distributional similarity, physical coherence among dependent variables, and structural–operational consistency. A controlled ablation design is then used to quantify the contribution of individual modules to overall benchmark realism. Within the experimental domain explored here, the results show that benchmark realism is not supported uniformly by all modules; instead, it depends primarily on arc-length generation, topographic alignment, and energy modeling. The proposed framework therefore offers not only a reproducible way to generate EV-STSP benchmarks, but also an explicit methodology for verifying whether such benchmarks are suitable for comparative algorithmic experimentation. Full article

The efficient resolution of complete NP problems, such as the Traveling Salesman Problem (TSP), particularly for large instances, remains a major challenge in operations research and combinatorial optimization, especially for many businesses, particularly in sectors such as logistics, urban planning, and networks, where efforts are made daily to optimize routes and delivery times. Optimization methods inspired by collective behavior, such as Ant Colony Optimization (ACO), offer competitive results for solving these types of problems. The main problem is the size of the instances because, when it becomes large, many existing algorithms fail to converge to a good solution within a reasonable timeframe: the execution time is generally very long, and the solution obtained is generally far from being the optimal solution to the problem. In this article, we propose a new way of approaching the resolution of the TSP through new metaheuristics inspired by artificial intelligence techniques and ant colony theory. To evaluate the effectiveness of our methodology, particularly the Multi-colony Ant Colony Optimization version 2-SK (MACOV2SK) method, simulations were performed on several instances of the TSP, focusing on large-scale instances. The experimental results clearly demonstrate that the proposed approach significantly improves upon several other approaches in the literature in terms of execution time and solution quality, especially for large-scale problems. Full article

UAV aerial cinematography has become increasingly important in film production, surveying, and smart-city applications due to its efficiency and creative potential. However, existing UAV filming workflows still rely heavily on manual operation and professional piloting skills, resulting in complex mission design, limited planning autonomy, and inconsistent visual quality. To address these challenges, this paper proposes a unified aesthetics-aware trajectory planning framework for multi-region-of-interest (multi-ROI) UAV aerial cinematography that automatically generates safe, efficient, and visually coherent flight paths from user-specified ROIs. The proposed framework consists of three main components. First, for each ROI, candidate viewpoints are sampled using a spiral trajectory, and a learning-based aesthetic evaluation network is applied to select visually optimal viewpoints for local trajectory generation. Second, transition trajectories between ROIs are generated using a Goal-biased Bidirectional Rapidly exploring Random Tree Star (Goal-biased BiRRT*) planner and evaluated through a multi-objective cost function to determine the most suitable transition paths. Third, the global connection of multiple ROIs is formulated as a Set Traveling Salesman Problem (STSP) to obtain an efficient visiting sequence. By integrating learning-based aesthetic evaluation with hierarchical trajectory planning and coordinated multi-ROI route organization, the proposed framework jointly considers flight feasibility, planning efficiency, visual composition quality, and trajectory continuity within a unified planning pipeline. Experimental results demonstrate that the proposed method generates more visually appealing and coherent aerial trajectories than traditional manual or rule-based approaches, while significantly reducing operational complexity. The proposed system provides an effective solution for autonomous UAV aerial cinematography with improved global consistency, aesthetic performance, and practical planning capability in complex environments. Full article

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions. Most BO methods rely on Gaussian process (GP) surrogates, which perform well in continuous domains but encounter difficulties when decision variables include categorical or mixed discrete–continuous components. In particular, GP-based approaches typically require ad hoc numerical encodings of categorical variables that may fail to capture the structure of discrete decision spaces. In this work, we propose MNL-BO (Multinomial Logit Bayesian Optimization), a preference-based Bayesian optimization framework that replaces the GP surrogate with a multinomial logit (MNL) model trained from pairwise preference comparisons. The resulting surrogate provides a natural and interpretable representation of categorical alternatives while allowing continuous, discrete, and categorical variables to be handled within a unified optimization framework. The predictive utility estimates and uncertainty indicators generated by the MNL model are employed to formulate acquisition functions that reconcile exploration with exploitation. The proposed methodology is evaluated on three progressively complex optimization challenges: a purely categorical benchmark, a combinatorial Traveling Salesman problem, and a constrained mixed-variable engineering design problem concerning material selection in pressure vessel optimization. Multi-run tests provide consistent advantages over random search and exhibit stable convergence behavior across diverse random initializations. In addition to heuristic baselines such as local search and classical metaheuristics, we also compare against tree-based Bayesian optimization baselines inspired by the Sequential Model-based Algorithm Configuration (SMAC) framework. The results indicate that the proposed MNL-BO method achieves competitive performance under comparable evaluation budgets while providing an interpretable probabilistic surrogate for categorical decision spaces. These findings suggest that preference-based surrogate modeling provides a practical and flexible alternative for Bayesian optimization in categorical and mixed-variable optimization problems. Full article

Background: Combinatorial optimization problems (COPs) are central to Logistics and Supply Chain decision making, yet their NP-hardness prevents exact optimal solutions in reasonable time. Methods: This work addresses that limitation by developing a novel ternary network flow linear programming (LP) model of the assignment problem (AP) polytope. The model is very large scale (with $\mathsf{\Theta }\left(m^9\right)$ variables and $\mathsf{\Theta }\left(m^8\right)$ constraints, where m is the number of assignments). Although not intended to compete with conventional two-dimensional formulations of the AP with respect to solution procedures, it enables hard COPs to be solved exactly as “strict” (integrality requirements-free) LPs through simple transformations of their cost functions. Illustrations are given for the quadratic assignment problem (QAP) and the traveling salesman problem (TSP). Results: Because the proposed LP model is polynomial-sized and there exist polynomial-time algorithms for solving LPs, it affirms “$P=NP$.” A separable substructure of the model shows promise for practical-scale instances due to its suitability for large-scale optimization techniques such as Dantzig–Wolfe Decomposition, Column Generation, and Lagrangian Relaxation. The formulation also has greater robustness relative to standard network flow models. Conclusions: Overall, the approach provides a systematic, modeling-barrier-free framework for representing NP-complete problems as polynomial-sized LPs, with clear theoretical interest and practical potential for medium to large-scale Logistics and other COP-intensive applications. Full article

This study proposes an end-to-end mathematical framework to automatically transform warehouse layout images into optimization-ready route matrices. The objective is to convert visual spatial information into a discrete, graph-based representation suitable for combinatorial route optimization. The problem is formulated as a mapping from continuous image space to a structured grid representation, integrating image segmentation, graph construction, and Traveling Salesman Problem (TSP)-based routing. Synthetic warehouse layouts were generated to create labeled training data, and a U-Net convolutional neural network was trained to perform multi-class segmentation of warehouse elements. The predicted grid representation was then converted into a graph structure, where feasible cells define vertices and adjacency defines edges. Shortest path distances were computed using Breadth-First Search, and the resulting distance matrix was used to solve a TSP instance. The segmentation model achieved approximately 98% training accuracy and 95–97% validation accuracy. The generated route matrices enabled successful construction of feasible and optimal round-trip routes in all tested scenarios. The proposed framework demonstrates that warehouse layouts can be automatically transformed into discrete mathematical representations suitable for logistics optimization, reducing manual preprocessing and enabling scalable integration into digital logistics systems. Full article

As manufacturing progresses, the demand for precision inspection of complex parts has intensified. To guarantee functionality and sensory performance, high-efficiency 3D shape measurement is required. In this paper, a collaborative robot-based approach for efficient and high-precision 3D shape inspection of complex parts is proposed. The system employs a collaborative robot to drive the scanner along optimized trajectories. First, the configuration of the inspection system is presented, and the ideal measurement mode for the sensor is analyzed. Subsequently, adaptive viewpoints are generated through parametric discretization based on surface geometric features. For inter-region scanning path planning, the problem is modeled as the Shortest Path Problem (SPP) within the framework of the Traveling Salesman Problem (TSP) and solved by constructing a Successive Approximation Algorithm (SAA). Furthermore, a Modified Denavit-Hartenberg (MDH) method is applied to establish the precise kinematic model of the collaborative robot. Inverse kinematics solutions are derived to convert planned viewpoints into target joint configurations, thereby achieving precise end-effector pose control. Simulation and experimental results on an engine cover and a cylinder head demonstrate that the proposed approach enables comprehensive 3D shape inspection of complex parts in a single setup and achieves higher efficiency and accuracy compared to existing methods. This work offers a viable solution for integrating robotic actuation and active sensing in the automated inspection of complex geometries. Full article

Triangular mesh surface representation is widely adopted in geometric design and reverse engineering applications. However, in high-precision Computer Numerical Control (CNC) machining, significant limitations persist in automated Computer-Aided Manufacturing (CAM) tool path generation for such representations. Conventional CAM workflows heavily rely on manual engineering interventions, such as creating drive surfaces or tuning extensive parameters—a dependency that becomes particularly acute for generic free-form models. To address this critical challenge, this paper proposes a novel end-to-end single-step end-milling tool path generation methodology for triangular mesh surfaces in high-precision five-axis CNC machining. The framework includes clustering analysis for optimal workpiece orientation, normal vector distribution analysis to identify shallow and steep regions, Graphics Processing Unit (GPU)-accelerated collision detection for feasible tool orientation domains, and iso-planar tool path generation with Traveling Salesman Problem (TSP) optimization for efficient tool lifting and movement. Experimental validation confirms the framework ensures machining quality and algorithmic robustness. Full article

Multiple Unmanned Aerial Vehicle (UAV) collaborative coverage path planning is widely applied in fields such as regional surveillance. However, optimizing the trade-off between deployment costs and task execution efficiency remains challenging. To balance resource costs and execution efficiency with an uncertain number of UAVs, this paper analyzes the characteristics of irregular mission areas and formulates a bi-level optimization model for multi-UAV collaborative CPP. The model aims to minimize both the number of UAVs and the total path length. First, in the upper level, an improved Best Fit Decreasing algorithm based on binary search is designed. Straight-line scanning paths are generated by determining the minimum span direction of the irregular regions. Task allocation follows a longest-path-first, minimum-residual-range rule to rapidly determine the minimum number of UAVs required for complete coverage. Considering UAV’s turning radius constraints, Dubins curves are employed to plan transition paths between scanning regions, ensuring path feasibility. Second, the lower level transforms the problem into a Multiple Traveling Salesman Problem that considers path continuity, range constraints, and non-overlapping path allocation. This problem is solved using an Improved Biased Random Key Genetic Algorithm. The algorithm employs a variable-length master–slave chromosome encoding structure to adapt to the task allocation of each UAV. By integrating biased crossover operators with 2-opt interval mutation operators, the algorithm accelerates convergence and improves solution quality. Finally, comparative experiments on mission regions of varying scales demonstrate that, compared with single-level optimization and other intelligent algorithms, the proposed method reduces the required number of UAVs and shortens the total path length, while ensuring complete coverage of irregular regions. This method provides an efficient and practical solution for multi-UAV collaborative CPP in complex environments. Full article

Deep reinforcement learning (DRL)-based algorithms for solving the Traveling Salesman Problem (TSP) have demonstrated competitive potential compared to traditional heuristic algorithms on small-scale TSP instances. However, as the problem size increases, the NP-hard nature of the TSP leads to exponential growth in the combinatorial search space, state–action space explosion, and sharply increased sample complexity, which together cause significant performance degradation for most existing DRL-based models when directly applied to large-scale instances. This research proposes a two-stage reinforcement learning framework, termed GCRL-TSP (Graph Convolutional Reinforcement Learning for the TSP), which consists of a heatmap generation stage based on a graph convolutional neural network, and a heatmap-assisted Proximal Policy Optimization (PPO) training stage, where the generated heatmaps are used as auxiliary guidance for policy optimization. First, we design a divide-and-conquer heatmap generation strategy: a graph convolutional network infers m-node sub-heatmaps, which are then merged into a global edge-probability heatmap. Second, we integrate the heatmap into PPO by augmenting the state representation and restricting the action space toward high-probability edges, improving training efficiency. On standard instances with 200/500/1000 nodes, GCRL-TSP achieves a Gap% of 4.81/4.36/13.20 (relative to Concorde) with runtimes of 36 s/1.12 min/4.65 min. Experimental results show that GCRL-TSP achieves more than twice the solving speed compared to other TSP solving algorithms, while obtaining solution quality comparable to other algorithms on TSPs ranging from 200 to 1000 nodes. Full article

The construction cost of offshore wind farms (OWFs) is heavily influenced by vessel scheduling and meteorological uncertainties. To address these challenges, this paper proposes a constraint-driven hierarchical optimization framework for the coordinated scheduling of installation vessels (IVs) and transport vessels (TVs). First, a Mixed-Integer Linear Programming (MILP) model is established to describe the operational constraints, which is then decomposed into two interrelated sub-problems: vessel path planning and scheduling optimization. For path planning, the problem is modeled as a Multiple Traveling Salesman Problem (MTSP) to ensure balanced fleet workloads. This stage is solved via a tailored three-stage heuristic combining balanced sweep clustering and penalized local search. For scheduling optimization, a hybrid Earliest Deadline First (EDF)-Simulated Annealing (SA) strategy is employed, where EDF generates a strictly feasible baseline to warm-start the SA optimization. Furthermore, a stochastic optimization approach integrates historical meteorological data to ensure schedule robustness against weather uncertainty. The validity of the framework is supported by two real-world OWF cases, which demonstrate total cost reductions of 15.44% and 13.20%, respectively, under stochastic weather conditions. These results demonstrate its effectiveness in solving high-constraint offshore engineering problems. Full article

Autonomous exploration is essential for various mapping tasks, including data collection, environmental monitoring, and search and rescue operations. Unmanned aerial vehicles (UAVs), owing to their low cost and high maneuverability, have become key enablers of such applications, particularly in complex or hazardous environments. However, existing approaches often suffer from issues such as redundant exploration and unstable flight behavior. In this study, we propose a hierarchical exploration approach specifically designed for limited-field-of-view UAVs in geospatial mapping applications. The approach addresses these challenges through hybrid viewpoint generation, an innovative boundary exploration sequence, and a two-stage global path planning strategy. To balance exploration efficiency and computational cost, we adopt a hybrid approach that combines collision-free spherical sampling with adaptive viewpoint generation based on stochastic differential equations. This approach generates high-quality candidate viewpoints while minimizing computational overhead. Furthermore, we introduce a novel heuristic evaluation function to prioritize frontiers within small regions, thereby facilitating optimal path planning. Based on this formulation, the global coverage path is modeled as a traveling salesman problem (TSP). The two-stage global planning framework consists of an initial stage that applies a history-aware trajectory enhancement strategy with smoothing corrections, followed by a second stage employing a sliding-window TSP algorithm to construct the global path. This design mitigates motion inconsistencies caused by frequent heuristic updates and enhances flight stability and trajectory smoothness. To evaluate the performance of the proposed framework, we compare it with state-of-the-art approaches in both simulated and real-world environments. Experimental results demonstrate that our approach shortens flight paths and reduces exploration time, thereby improving overall exploration efficiency. Full article

This study presents a systematic comparison of five crossover operators used in genetic algorithms (GA) for the Traveling Salesman Problem (TSP). Partially Mapped Crossover (PMX), Order Crossover (OX), Cycle Crossover (CX), Edge Recombination (ERX), and Alternating Edges (AEX) are evaluated within an identical GA framework using tournament selection, inversion mutation, generational replacement, and elitism. Experiments were conducted on seven datasets, including three TSPLIB benchmarks, a clustered synthetic instance, a uniformly random instance, and two real-world Croatian city sets of 50 and 100 cities. Thirty independent GA runs per operator were analyzed using the Friedman test followed by Holm-corrected Wilcoxon pairwise comparisons. The Friedman test shows highly significant global performance differences. After applying Holm correction, the top four operators (PMX, OX, CX, and ERX) are statistically comparable on most datasets, as the correction eliminates most pairwise differences among them. All pairwise comparisons involving AEX remain significant across every dataset, confirming its consistently inferior performance. OX achieves the best average ranks across all datasets consistently, while PMX, CX, and ERX exhibit comparable mid-range performance. To illustrate practical relevance, optimized routes for Croatian instances were used to estimate fuel consumption and CO₂ emissions for petrol, diesel, and electric vehicles. The results demonstrate meaningful sustainability benefits achievable through optimized routing. Full article

The quality of the initial population is a critical factor in the convergence speed and overall performance of an optimization algorithm. A well-structured initial population can significantly enhance the exploration capabilities of the algorithm, allowing it to more efficiently traverse the solution space and converge more quickly and reliably towards optimal or near-optimal solutions. In this paper, we present the Circle Group Heuristic (CGH), a spatially structured initialization method, for generating high-quality initial populations to enhance the convergence speed of the Discrete Bacterial Memetic Evolutionary Algorithm (DBMEA) in solving the Traveling Salesman Problem (TSP) and related combinatorial optimization problems. This work extends the CGH beyond the TSP to a broader class of routing problems. The results show that the integration of CGH into DBMEA demonstrated consistent performance improvements on the TSP, the Traveling Repairman Problem (TRP), and the Traveling Salesman Problem with Time Window (TSPTW) instances of varying sizes. In particular, CGH provided high-quality starting points that accelerated convergence and reduced computational cost. In all tested scenarios, DBMEA enhanced with CGH and consistently preserved the best-known solution quality while reducing execution time. Full article

Vehicle routing improvement has become a vital topic in modern transport digitalization projects. Presently, there are no fully adapted techniques to offer optimal solutions for finding the best routes that include all visiting locations, considering mandatory transportation constraints. This project explores the application of modern machine learning techniques in solving transportation problems, with a specific focus on Q-learning. We utilize Q-learning to address the traveling salesman and vehicle routing problems. The ability of Q-learning to find optimal solutions in dynamic environments helped overcome the vulnerabilities of traditionally used algorithms. Moreover, this project provides an advanced comparative analysis in terms of accuracy and speed between Q-learning and currently used algorithms in the same scope, using a set of generated routing datasets. Q-learning presented superior performance, generating solutions that were closest to the global optima, exhibiting impressive computational efficiency and fast action even with large-scale problem instances, suggesting that it can serve as a powerful tool for optimizing transportation systems. Full article