Search Results (107)

The vehicle routing problem is one of the most often studied optimization problems. In this study, an improved artificial bee colony (ABC) algorithm is proposed which is structured specifically to address the capacitated vehicle routing problem (CVRP), a significant challenge in combinatorial optimization. The proposed algorithm integrates several novel features to improve its performance on CVRP instances. These include a unique initialization strategy that spreads non-repeated customers during initialization, an innovative dual group strategy in the employed bee phase, and an improved scout bee phase with perturbation techniques. Additionally, the proposed algorithm effectively handles infeasible solutions using a novel penalty function formula. The Chebyshev Minkowski’s distance is utilized for route evaluation, enhancing spatial relationship representation over traditional Euclidean distances. Moreover, the classical CVRP model is extended by introducing new variables and constraints to capture changing demand at each customer location within a route. The algorithm’s efficiency was extensively evaluated using benchmark data sets comprising 73 instances from data sets A, B, and P sourced from the VRP instances library site. This rigorous testing enables comprehensive assessments and meaningful comparisons with other algorithms. Overall, the proposed ABC algorithm offers a promising solution for addressing CVRP challenges, providing advancements in solution quality, robustness, and adaptability. Finally, the optimal results are compared in terms of their statistical significance using Friedman and Wilcoxon rank tests with three well-known optimizer algorithms in the literature. Full article

Background: Planning power distribution networks is crucial in contemporary infrastructure development. Current distribution paradigms require not only cost minimization but also reliability and fault tolerance. However, designing meshed network topologies is a computationally demanding combinatorial optimization problem, especially for large instances. Methods: We reframe this problem as a multi-depot vehicle routing problem in which electrical substations act as depots and power lines represent routes. We develop a four-phase Large Neighborhood Search (LNS) that combines geographically-based destroy operators with a topology-specific MILP repair operator. Each repair subproblem is solved to optimality under the adopted topological, flow conservation, and line capacity constraints. Results: Experiments on realistic medium-voltage distribution network instances with up to 1150 nodes show that the proposed method handles cases that are beyond the reach of exact global optimization. Compared with a greedy constructive heuristic, the best LNS solution achieves an average cost reduction of 28.5%. Ablation and sensitivity analyses support the algorithmic design and show stable behavior under reasonable parameter variations. AC power flow analyses on the largest instance confirm electrical consistency under the tested single-branch outage scenarios, with a maximum voltage deviation of 5.1%. Conclusions: The proposed optimal-repair LNS provides a scalable approach for planning large fault-tolerant distribution networks under topology and line capacity constraints. Full article

Combinatorial optimization problems (COPs), including the Knapsack Problem (KP), the Traveling Salesman Problem (TSP), and regional variants such as the Close-Enough Traveling Salesman Problem (CETSP), constitute fundamental models for addressing complex decision-making tasks in modern computational systems. Their computational difficulty has motivated the development of a broad range of exact, heuristic, metaheuristic, learning-based, and hybrid optimization approaches. This work presents a structured survey and problem-structure-oriented comparative analysis of these methods, covering Genetic Algorithms (GAs), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Simulated Annealing (SA), Tabu Search (TS), Artificial Bee Colony (ABC), Graph Neural Networks (GNNs), and learning-enhanced hybrid approaches. Particular attention is given to how differences in problem structure, formulation characteristics, feasibility requirements, computational cost, and evaluation settings influence the suitability of different optimization paradigms. The practical relevance of these approaches is discussed through two case studies based on our prior work: Virtual Machine Placement (VMP) in cloud computing, examined through a simplified single-resource 0–1 KP abstraction, and UAV trajectory optimization for data collection in Wireless Sensor Networks (WSNs), examined through TSP-, CETSP-, and neighborhood-based routing models. The reviewed evidence indicates that metaheuristic approaches can provide flexible search mechanisms in computationally challenging settings, while learning-based models may support rapid inference, prediction, initialization, or search guidance when appropriate training data and generalization conditions are available. Hybrid learning–optimization frameworks may be beneficial when their components address complementary limitations of the underlying problem, although their effectiveness remains dependent on problem structure, training requirements, computational budget, feasibility handling, and implementation design. In cloud environments, knapsack-based VMP formulations provide useful abstractions for resource-allocation decisions, whereas in UAV-assisted WSNs, routing models such as the TSP and CETSP provide structured representations of trajectory and data-collection decisions. Overall, this survey highlights the complementary strengths and limitations of modern optimization paradigms and emphasizes that method selection should be guided by problem structure, operational requirements, feasibility considerations, and computational constraints. Full article

The capacitated vehicle routing problem (CVRP) is a representative NP-hard combinatorial optimization problem with broad applications in logistics and transportation. This paper proposes a hybrid metaheuristic, termed SPSOM-CVRP, which integrates an improved set-based particle swarm optimization (SPSO) with a self-organizing map (SOM). In SPSOM-CVRP, the improved SPSO is responsible for constructing feasible CVRP solutions, whereas the SOM performs route-level refinement to improve solution quality. To strengthen exploration, when the personal best of a particle remains unchanged for a predefined number of generations, two new learning exemplars are randomly reassigned to the particle. To enhance exploitation while avoiding excessive computational cost, SOM-based route optimization is activated only when the global best solution stagnates and is applied to selected elite solutions. In this manner, particle-level and population-level stagnation information is jointly employed to coordinate exploration and exploitation. Experimental studies on three benchmark datasets demonstrate that SPSOM-CVRP achieves competitive solution quality with relatively low computational cost. In addition, the proposed method obtains several promising route configurations, including solutions with shorter travel distances than previously reported results under modified route numbers. It should be noted that the proposed algorithmic configuration is empirically motivated; its effectiveness is demonstrated on the selected CVRP benchmark suites and the specific route-number settings under test, rather than being claimed as a universally optimal solution for all possible CVRP instances or all combinatorial optimization problems. Full article

Recent studies have proposed post-processing strategies that iteratively reconstruct a partial segment of current solutions using Neural Combinatorial Optimization (NCO) solvers, thereby improving their performance on large-scale Vehicle Routing Problem (VRP) instances. However, the reconstruction subproblem is essentially a Shortest Hamiltonian Path Problem (SHPP) instance, which differs fundamentally from the original VRP variant on which the solver is trained. Consequently, the NCO solver may suffer from performance degradation during reconstruction due to limited generalization across problem variants. Moreover, relying solely on the solver may be insufficient to effectively identify and correct complex intersections or suboptimal topological structures. To address these limitations, we propose a post-processing strategy termed Hybrid Reconstruction Framework (HRC). Specifically, HRC first fine-tunes the NCO solver on SHPP instances and then exploits the enhanced solver to perform large-neighborhood random reconstruction. Subsequently, HRC conducts small-neighborhood reconstruction using 2-opt and kNN-DGR. The experimental results on both synthetic and real-world Traveling Salesman Problem and Capacitated Vehicle Routing Problem instances demonstrate that HRC substantially improves the performance of two representative NCO solvers on large-scale instances and achieves better overall performance than the state-of-the-art reconstruction strategy. Finally, ablation studies further validate the effectiveness of all proposed designs. Full article

Radioactive source cleanup in nuclear environments is an important task for facility decommissioning and autonomous radiation management. In multi-target cleanup scenarios, each source removal action alters the subsequent radiation risk distribution. This action-dependent evolution invalidates the static planning assumptions commonly adopted in conventional routing and path planning methods. To address this challenge, this work formulates multi-target radioactive hotspot cleanup as a preference-conditioned sequential combinatorial optimization problem. We propose a neural sequential optimization framework that integrates hotspot map encoding and radiation field image encoding through cross-modal interaction. The proposed framework generates preference-conditioned risk-aware cleanup policies, enabling effective coordination between target selection and safe navigation under different risk–efficiency trade-offs. The nuclear hot-cell simulation environment is constructed using the Robot Operating System (ROS) and the Gazebo physics simulation engine. Compared with classical heuristic methods, evolutionary optimization methods, and reinforcement learning-based baselines, the proposed method achieves lower cumulative radiation exposure across different problem scales while maintaining competitive task efficiency. The results demonstrate that the proposed framework provides an effective task-level sequencing strategy for radiation-aware robotic cleanup in action-dependent risk fields. Full article

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two classical combinatorial optimization problems. In recent years, their drone-assisted variants, the Traveling Salesman Problem with Drones (TSP-D) and the Vehicle Routing Problem with Drones (VRP-D) have attracted growing attention. Generally, these problems are solved using exact algorithms or metaheuristic algorithms. However, as the problem complexity increases and the scale of instances grows, these approaches often become less efficient. In this paper, we propose a reinforcement learning method with a shared attention encoder and a hierarchical dual-decoder architecture, where truck–drone coordination is achieved by first decoding the truck’s next node and then conditionally decoding the drone action. To further explore the solution space of large-scale instances, the proposed method adopts a multi-rollout learning strategy. We conducted experiments on large-scale TSP-D and VRP-D instances, and the results show that this model outperforms traditional metaheuristic algorithms in terms of both solution quality and computational efficiency. Full article

Electric trucks operating as mobile depots for delivery drones are promising for last-mile logistics, yet fleet electrification makes depot charging a critical issue governed by distribution-grid limits. Existing truck–drone routing formulations omit the electrical network, treating energy as exogenous, while grid-aware routing models overlook the combinatorial structure of mobile-depot drone synchronization. This paper introduces an energy-aware bi-level framework for the truck–drone routing problem that closes this gap. A distribution-grid leader solves slot-wise alternating current (AC) optimal power flow (OPF) under time-varying base loads and line deratings, returning a grid-feasible energy headroom and shadow prices. A logistics follower then co-optimizes truck routes, drone sorties, and ramp-constrained charging against this effective price, within a multi-objective cost structure. A damped fixed-point iteration couples the two levels, communicating grid scarcity through a single price signal without the logistics layer solving power-flow equations. On a Tokyo-inspired 100-customer instance with a stressed IEEE 33-bus feeder, the framework confines charging to slots with genuine headroom, reaching at most 81% loading and returning the fleet fully charged, whereas a grid-blind baseline reaches 109% loading. This comparison validates shadow pricing as an effective coordination mechanism. Full article

Combinatorial Route Optimization (CRO) problems, such as the Vehicle Routing Problem (VRP) or the Travelling Salesman Problem (TSP), are commonly seen in scheduling, logistics, and transportation. While current machine learning (ML) methods can overcome certain limitations of traditional approaches, including exact and heuristic algorithms, they typically require substantial computational resources, large training datasets, and carefully designed models, thereby limiting their scalability and practical deployment. In this paper, we develop a method to address such concerns in a data-efficient and near-training-free manner using foundation models. We select TSP, one of the most well-known combinatorial optimization problems, to solve in our experiments and employ the Tabular Prior-Data Fitted Network (TabPFN), one of the newly designed foundation models. Specifically, we develop a node-based formulation that converts TSP into a sequence of localized prediction tasks and constructs a complete route through in-context learning provided by TabPFN. The proposed method enables TabPFN, a model developed for regression and classification, to be applied to CRO problems with only one TSP sample for fine-tuning. We evaluate the proposed method across varying TSP instance sizes and demonstrate that our approach generalizes effectively without retraining, maintains competitive solution quality, and exhibits promising scalability. These findings suggest that CRO problems can be approached through foundation models, enabling scalability as well as generating rapidly deployable solutions with near-training-free adaptation. Full article

The optimal expansion of unbalanced three-phase distribution networks in non-interconnected zones requires the simultaneous resolution of two highly complex planning decisions: the selection of feeder routes and the sizing of conductors. This problem, formulated as a non-convex mixed-integer nonlinear program (MINLP), poses significant computational challenges due to the combinatorial explosion of radial topologies, discrete conductor choices, and the nonlinearity of three-phase power-flow equations. While metaheuristics offer flexible exploration, they lack optimality guarantees and repeatability, whereas exact MINLP solvers provide rigorous solutions but become computationally intractable for systems of realistic size. To overcome these limitations, this paper introduces a novel hybrid exact–metaheuristic framework that synergistically combines the global exploration capabilities of the Equilibrium Optimizer (EO) with the rigorous evaluation power of an exact MINLP model. In this cascade architecture, EO efficiently navigates the discrete space of radial topologies, while the exact MINLP stage, solved using BONMIN with an interior-point branch-and-bound scheme, optimizes conductor selection and evaluates the full annualized cost, rigorously enforcing voltage, ampacity, and physical constraints. The proposed methodology was validated on 10-, 30-, 50-, and 110-node test systems derived from real Colombian non-interconnected zones (Nuquí, Leticia, San Andrés, and a large-scale urban case). Comparative analysis against pure metaheuristics (SSA, GWO, VSA) and standalone MINLP demonstrates that EO-MINLP consistently yields the lowest total annualized costs, achieving savings of up to 0.42%, 0.71%, and 1.36% over the best pure metaheuristic for the 10-, 30-, and 50-node systems, respectively. Crucially, the hybrid strategy dramatically enhances scalability, reducing the standalone MINLP computational time by 15.79%, 78.68%, and 88.95% for these cases, while preserving solution quality and improving repeatability (standard deviation reduced from over 1.2% to as low as 0.11%). For the challenging 110-node system, where the standalone MINLP proved computationally infeasible, the proposed method successfully delivered a feasible, high-quality solution with a standard deviation of just 0.43%, confirming its practical applicability to large-scale planning. These results demonstrate that the EO-MINLP framework provides a robust, scalable, and economically superior tool for the cost-effective design of unbalanced distribution networks, effectively bridging the gap between the flexibility of stochastic search and the rigor of mathematical programming. Full article

Collaborative task allocation for multiple unmanned ground vehicles (UGVs) is a constrained combinatorial optimization problem in which symmetric vehicle resources must be coordinated with asymmetric task requirements. In delivery and inspection scenarios, homogeneous vehicles operate under identical rules, whereas task points differ in spatial distribution, demand, service time, and time window requirements. These asymmetries make compact, temporally feasible, and workload-balanced routing difficult. SACWDO-PSO is developed as a discrete particle swarm optimization framework that integrates Clarke–Wright savings initialization, adaptive parameter control, and simulated annealing local search. The savings strategy improves initial swarm quality, adaptive control adjusts exploration and exploitation during the search, and simulated annealing refines local route structures. The method is evaluated on Solomon VRPTW benchmark data under a soft time window penalty objective and insimulation scenarios developed using Unreal Engine 4.27 integrated with Microsoft AirSim 1.8.1. SACWDO-PSO obtains lower objective values and fewer time window violations than the compared swarm-intelligence baselines on most benchmark instances, while Wilcoxon signed-rank tests indicate statistically significant improvements over PSO, DPSO, and GA. 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

With the continuous expansion of unmanned aerial vehicle (UAV) applications, generating near-optimal paths and achieving effective obstacle avoidance in complex environments remain highly challenging tasks. To address the problems of multi-objective path planning and obstacle detection for UAV flight missions in orchard environments, this paper proposes a novel hybrid algorithmic framework named NeuroJPS-A. The main scientific contribution is the synergistic integration of neural combinatorial optimization, 3D-JPS, and adaptive APF, enabling task-aware obstacle avoidance and closed-loop trajectory adjustment. This method introduces neural combinatorial optimization from the TSP into the 3D-JPS algorithm, optimizing the search mechanism of the traditional JPS and further shortening the UAV’s globally planned path length. In addition, this study integrates the proposed algorithm with the APF to solve the local dynamic obstacle avoidance problem. Quantitative results show that NeuroJPS-A reduces path length by 10% and the number of turns by 47.8% in 2D, and achieves a 24.9% shorter path and 22% of A*’s computation time in 3D. To verify the performance of the proposed method, comprehensive simulation experiments were conducted. The experimental results demonstrate that the NeuroJPS-A algorithm enables UAVs to quickly and effectively generate optimal planned routes, ensuring safe navigation in complex orchard environments and preventing collisions during flight missions. Full article

Combinatorial optimization is a key component in critical decision problems such as routing, scheduling, network design, and graph optimization. Although combinatorial optimization methods, including exact algorithms, approximation methods, constraint programming, mixed integer programming, and metaheuristics, are widely available, they often face obstacles, such as limited scalability and adaptability in various applications. In this study, a systematic critical review of machine learning for combinatorial optimization is provided to characterize the usage and evaluation of learning-based approaches. A detailed analysis is used to infer and determine findings and limitations. The paper emphasizes how machine learning for computational optimization has changed over time, moving from end-to-end neural solvers to hybrid systems. Learning components are essential for directing, speeding up, or enhancing traditional solver backbones such as constraint programming and metaheuristics in hybrid systems. The review also critically examines current limits that impact performance in general, including scalability, deployment readiness, generalization, and benchmark consistency. Even though using large language models for problem formulation and heuristic synthesis has potential, more work needs to be done to ensure reliable validation. As a conclusion, this article examines recent studies’ findings, emphasizes the growing trend toward hybrid learning-driven optimization frameworks, and underlines important methodological limits and unresolved issues. Full article

Post-disaster Search and Rescue (SAR) missions demand rapid coordination of Heterogeneous Unmanned Aerial Vehicle (UAV) fleets under stringent payload and flight range limitations. Traditional heuristic solvers struggle to solve the Large-Scale Heterogeneous Team Orienteering Problem (LSH-TOP) within operational time limits due to the coupled complexity of task allocation and route planning. A Hierarchical Deep Reinforcement Learning framework decomposes this high-dimensional combinatorial problem into tractable sub-problems. An upper-level policy, guided by Monte Carlo Tree Search (MCTS), partitions the global target set to balance fleet workload distribution, whereas a lower-level Transformer-based model constructs near-optimal trajectories for individual agents. A Curriculum-Integrated Alternating Cooperative Training (C-ACT) protocol resolves the convergence difficulties associated with sparse feasible solutions in constrained environments. This protocol incorporates a dynamic constraint annealing strategy and a virtual agent buffer to progressively shape the solution space from relaxed to strictly constrained formulations. Experiments conducted on real-world geographic data demonstrate the proposed approach consistently outperforms all baselines across scales of 80 to 300 targets, improving over the strongest competitor by 0.63–8.51% and over conventional heuristics by up to 53.27% in objective value. Results indicate a task completion rate of 27.5% at the 300-target scale (versus 25.1% for the strongest baseline MCTS + OR) and balanced workload distribution, validating framework adaptability to complex emergency response scenarios. Full article