Search Results (181)

Deep reinforcement learning (DRL) with self-play has emerged as a promising paradigm for solving combinatorial optimization (CO) problems. The recently proposed Gumbel AlphaZero Plan-to-Play (GAZ PTP) framework adopts a competitive training setup between a learning agent and an opponent to tackle classical CO tasks such as the Traveling Salesman Problem (TSP). However, in complex and multi-constrained environments like the Electric Vehicle Routing Problem (EVRP), standard self-play often suffers from opponent mismatch: when the opponent is either too weak or too strong, the resulting learning signal becomes ineffective. To address this challenge, we introduce Two-Stage Self-Play GAZ PTP (TSS GAZ PTP), a novel DRL method designed to maintain adaptive and effective learning pressure throughout the training process. In the first stage, the learning agent, guided by Gumbel Monte Carlo Tree Search (MCTS), competes against a greedy opponent that follows the best historical policy. As training progresses, the framework transitions to a second stage in which both agents employ Gumbel MCTS, thereby establishing a dynamically balanced competitive environment that encourages continuous strategy refinement. The primary objective of this work is to develop a robust self-play mechanism capable of handling the high-dimensional constraints inherent in real-world routing problems. We first validate our approach on the TSP, a benchmark used in the original GAZ PTP study, and then extend it to the multi-constrained EVRP, which incorporates practical limitations including battery capacity, time windows, vehicle load limits, and charging infrastructure availability. The experimental results show that TSS GAZ PTP consistently outperforms existing DRL methods, with particularly notable improvements on large-scale instances. 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

As a high-value fruit crop grown worldwide, apples require efficient harvesting solutions to maintain a stable supply. Intelligent harvesting robots represent a promising approach to address labour shortages. This study introduced a Cartesian robot integrated with a continuous-picking end-effector, providing a cost-effective and mechanically simpler alternative to complex articulated arms. The system employed a hand–eye calibration model to enhance positioning accuracy. To overcome the inefficiencies resulting from disordered harvesting sequences and excessive motion trajectories, the harvesting process was treated as a travelling salesman problem (TSP). The conventional fixed-plane return trajectory of Cartesian robots was enhanced using a three-dimensional continuous picking path strategy based on a fixed retraction distance (H). The value of H was determined through mechanical characterization of the apple stem’s brittle fracture, which eliminated redundant horizontal displacements and improved operational efficiency. Furthermore, an improved grey wolf optimizer (IGWO) was proposed for multi-fruit path planning. Simulations demonstrated that the IGWO achieved shorter path lengths compared to conventional algorithms. Laboratory experiments validated that the system successfully achieved vision-based localization and fruit harvesting through optimal path planning, with a fruit picking success rate of 89%. The proposed methodology provides a practical framework for automated continuous harvesting systems. Full article

Property city is a newly emerging property service mode attracting widespread attention. Addressing the gap in quantitative analysis of the vehicle routing problem (VRP) of a property city based on quantitative analysis in existing studies, this study introduces the single-loop traveling salesman problem (TSP) and multi-loop VRP models for different service scenarios of a property city. An intelligent optimization framework combining the nearest insertion method and genetic algorithm was constructed to solve these problems. The example analysis results show that the intelligent algorithm is feasible, outperforming the nearest insertion method in designing reasonable operational schemes, while the total operational cost of the multi-loop scenario was lower than that of the single-loop scenario. This study enriches the theoretical system of property city and provides references for its service practice. Full article

The Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem with broad applications in logistics and smart agriculture. However, despite significant progress in Transformer-based deep reinforcement learning methods, two major challenges remain. First, standard linear embedding layers struggle to capture dynamic local geometric relationships between nodes. Second, the quadratic complexity of self-attention in the decoder hinders efficiency in large-scale TSP instances. To address these issues, this paper proposes a Dynamic Topology-Aware Linear Attention Network (DTALAN). The encoder employs a Channel-aware Topological Refinement Graph Convolution (CTRGC) module to model local geometric structures and a Global Attention Mechanism (GAM) for adaptive feature recalibration. The decoder introduces a temporal locality-aware attention mechanism that focuses only on recently visited nodes, reducing self-attention complexity from quadratic to linear while preserving solution quality. The policy network is trained using the REINFORCE algorithm with baseline and the Adam optimizer. Experiments on random instances and the TSPLIB benchmark show that DTALAN outperforms leading deep reinforcement learning methods in both optimality gap and inference efficiency. For TSP100, it achieves an optimality gap of 0.55%, producing near-optimal solutions. Ablation studies confirm that both the improved CTRGC and enhanced GAM modules are essential to these results. 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

Extensive research on path planning and automated navigation has been carried out for weeding robots in fields such as corn, soybean, wheat, and sugar beet, but until now, no literature reports relative studies in turfs that are not cultivated using row-crop methods. This paper proposes a practical solution that comprises path planning and path tracking to minimize the weeding robot’s travel distance in turfs for the first time. An inter-sub-region scheduling algorithm is developed using the Traveling Salesman Problem (TSP) model, followed by a boundary-shifting-based coverage path planning algorithm to achieve full coverage within each weed subregion. For path tracking, a Real-Time Kinematic Global Positioning System (RTK-GPS) fusion positioning method is developed and combined with a dynamic pure pursuit algorithm featuring a variable preview distance to enable precise path following. After path planning based on real-world site data, the weeding robot traverses all weed subregions via the shortest possible path. Field experiments showed that the robot traveled along the shortest path at speeds of 0.6, 0.8, and 1.0 m/s; the root mean square errors of autonomous navigation deviation were 0.35, 0.81, and 1.41 cm, respectively. The proposed autonomous navigation solution significantly reduces the robot’s travel distance while maintaining acceptable tracking accuracy. Full article

In the rapidly evolving landscape of logistics and last-mile delivery, optimizing efficiency and minimizing costs are paramount. This paper introduces a novel heuristic approach designed to enhance the efficiency of a truck-and-drone delivery system. Our method addresses the complex challenge of coordinating the movements of a truck, which serves as a mobile depot, and an unmanned aerial vehicle (UAV or drone), which performs rapid, short-distance deliveries. Our system proposes a two-step heuristic. For truck routes, we utilized the Concorde Solver to determine the optimal path, based on real-world road distances between locations in Bacău County, Romania. This data was meticulously collected and processed as a Traveling Salesman Problem (TSP) instance with precise geographical information. Concurrently, a drone is deployed for specific deliveries, with routes calculated using the Haversine formula to determine accurate distances based on geographical coordinates. A crucial aspect of our model is the integration of the drone’s limited autonomy, ensuring that each mission adheres to its operational capacity. Computational experiments conducted on a real-world dataset including 93 localities from Bacău County, Romania, demonstrate the effectiveness of the proposed two-stage heuristic. Compared to the optimal truck-only route, the hybrid truck-and-drone system achieved up to 15.59% cost reduction and 38.69% delivery time savings, depending on the drone’s speed and autonomy parameters. These results confirm that the proposed approach can substantially enhance delivery efficiency in realistic distribution scenarios. 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 aging of the Portuguese population is a multifaceted challenge that requires a coordinated and comprehensive response from society. In this context, social service institutions play a fundamental role in providing aid and support to the elderly, ensuring that they can enjoy a dignified and fulfilling life even in the face of the challenges of aging. This research proposes a Balanced Multiple Traveling Salesman Problem based on the Ant Colony Optimization algorithm (ACO-BmTSP) to solve a distribution of meals problem in the municipality of Mogadouro, Portugal. The Multiple Traveling Salesman Problem (mTSP) is an NP-complete problem where m salesmen perform a shortest tour between different cities, visiting each only once. The primary purpose is to minimize the sum of all distance traveled by all salesmen keeping the tours balanced. This paper shows the results of computing obtained for three, four, and five agents with this new approach and their comparison with other approaches like the standard Particle Swarm Optimization and Ant Colony Optimization algorithms. As can be seen, the ACO-BmTSP, in addition to obtaining much more equitable paths, also achieves better results in lower total costs. In conclusion, some benchmark problems were used to evaluate the efficiency of ACO-BmTSP, and the results clearly indicate that this algorithm represents a strong alternative to be considered when the problem size involves fewer than one hundred locations. Full article

Multi-drone operations face significant efficiency challenges when launch pad locations are predetermined without optimization, leading to suboptimal route configurations and increased travel distances. This research addresses launch pad positioning as a continuous planar location-routing problem (PLRP), developing a genetic algorithm framework integrated with multiple Traveling Salesman Problem (mTSP) solvers to optimize launch pad coordinates within operational areas. The methodology was evaluated through extensive experimentation involving over 17 million test executions across varying problem complexities and compared against brute-force optimization, Particle Swarm Optimization (PSO), and simulated annealing (SA) approaches. The results demonstrate that the genetic algorithm achieves 97–100% solution accuracy relative to exhaustive search methods while reducing computational requirements by four orders of magnitude, requiring an average of 527 iterations compared to 30,000 for PSO and 1000 for SA. Smart initialization strategies and adaptive termination criteria provide additional performance enhancements, reducing computational effort by 94% while maintaining 98.8% solution quality. Statistical validation confirms systematic improvements across all tested scenarios. This research establishes a validated methodological framework for continuous launch pad optimization in UAV operations, providing practical insights for real-world applications where both solution quality and computational efficiency are critical operational factors while acknowledging the simplified energy model limitations that warrant future research into more complex operational dynamics. Full article

Information announcement is the process of propagating and synchronizing the information of Computing Resource Nodes (CRNs) within the system of the Computing Networks. Accurate and timely acquisition of information is crucial to ensuring the efficiency and quality of subsequent task scheduling. However, existing announcement mechanisms primarily focus on reducing communication overhead, often neglecting the direct impact of information freshness on scheduling accuracy and service quality. To address this issue, this paper proposes a hierarchical and clustering-based announcement mechanism for the wide-area Computing Networks. The mechanism first categorizes the Computing Network Nodes (CNNs) into different layers based on the type of CRNs they interconnect to, and a top-down cross-layer announcement strategy is introduced during this process; within each layer, CNNs are further divided into several domains according to the round-trip time (RTT) to each other; and in each domain, inspired by the “Six Degrees of Separation” concept from social propagation, a RTT-aware fast clustering algorithm canopy is employed to partition CNNs into multiple overlap clusters. Intra-cluster announcements are modeled as a Traveling Salesman Problem (TSP) and optimized to accelerate updates, while inter-cluster propagation leverages overlapping nodes for global dissemination. Experimental results demonstrate that, by exploiting shortest path optimization within clusters and overlapping-node-based inter-cluster transmission, the mechanism is significantly superior to the comparison scheme in key indicators such as convergence time, Age of Information (AoI), and communication data volume per hop. The mechanism exhibits strong scalability and adaptability in large-scale network environments, providing robust support for efficient and rapid information synchronization in the Computing Networks. 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

Maximizing the lifetimes of Wireless Sensor Networks (WSNs) is a prominent area of research. The energy hole problem is a major cause of network shutdown, where nodes within the Sink coverage deplete their energy faster due to the high energy cost of forwarding data from distant nodes to the Sink. Several research works have proposed solutions to address this issue, including the use of a mobile Sink to balance energy consumption throughout the network. However, most Sink mobility models overlook the energy consumption caused by overhearing, which is a critical factor in WSNs. In this paper, we introduce Linear Programming (LP) and Cuckoo Search (CS) metaheuristic optimization-based solutions to maximize the lifetime of WSNs by determining the optimal Sink sojourn points and associated durations. The proposed approaches consider the energy consumption levels of both reception and transmission, in addition to accounting for overhearing as an additional source of energy consumption. This allows for a comparison between the LP and CS solutions in terms of their effectiveness. To further enhance our solution, we apply the Travel Salesman Problem (TSP) to find the shortest path between the Sink sojourn points. By incorporating the TSP, we can optimize the routing path for the mobile Sink, thereby minimizing energy consumption and maximizing network lifetime. Test results demonstrate that the LP solution provides more accurate Sink sojourn times and locations, while the CS solution is faster, particularly for large WSNs. Moreover, our findings indicate that overlooking overhearing leads to a 48% decrease in WSN lifetime, making it essential to consider this factor if one is to achieve realistic results. Full article

This paper proposes the Open Competency Optimization (OCO) approach, based on adaptive combinatorial operators, to solve the Dynamic Green Traveling Salesman Problem (DG-TSP), which extends the classical TSP by incorporating dynamic travel conditions, realistic road gradients, and energy consumption considerations. The objective is to minimize fuel consumption and emissions by reducing the total tour length under varying conditions. Unlike conventional metaheuristics based on real-coded representations, our method directly operates on combinatorial structures, ensuring efficient adaptation without costly transformations. Embedded within a dynamic metaheuristic framework, our operators continuously refine the routing decisions in response to environmental and demand changes. Experimental assessments conducted in practical contexts reveal that our algorithm attains a tour length of 21,059, which is indicative of a 36.16% reduction in fuel consumption relative to Ant Colony Optimization (ACO) (32,994), a 4.06% decrease when compared to Grey Wolf Optimizer (GWO) (21,949), a 2.95% reduction in relation to Particle Swarm Optimization (PSO) (21,701), and a 0.90% decline when juxtaposed with Genetic Algorithm (GA) (21,251). In terms of overall offline performance, our approach achieves the best score (21,290.9), significantly outperforming ACO (36,957.6), GWO (122,881.04), GA (59,296.5), and PSO (36,744.29), confirming both solution quality and stability over time. These findings underscore the resilience and scalability of the proposed approach for sustainable logistics, presenting a pragmatic resolution to enhance transportation operations within dynamic and ecologically sensitive environments. Full article