ADPSO-ERLS is a discrete swarm algorithm that treats this allocation as an explicit, tunable design variable, and ranks first under the Friedman test, and all twenty-five multiplicity-controlled Wilcoxon comparisons favor it with large, near-complete distributional separation.
Abstract
The Traveling Salesman Problem is a canonical setting for studying how a population-based method should allocate a fixed search budget between exploration and progressively stronger local intensification. We propose ADPSO-ERLS, a discrete swarm algorithm that treats this allocation as an explicit, tunable design variable. It couples memory-guided swap mutation, heterogeneous initialization, selective candidate-restricted 2-opt during evolution, and an incumbent-only final refinement combining candidate-restricted and optional full 2-opt with double-bridge perturbations. The method is PSO-inspired, using personal and global memories yet dispensing with velocity, inertia, and acceleration coefficients. All six algorithms are implemented in Rust, run on identical hardware, and stopped at a strict, recorded limit of 100,000 candidate-solution assessments, so that programming language, hardware, and evaluation budget are held common across methods; wall-clock time is reported separately because equal assessment counts need not correspond to equal arithmetic work. Over 50 runs on five symmetric TSPLIB instances under the integer \texttt{EUC\_2D} convention, ADPSO-ERLS attains the lowest best and mean cost on every instance, with best-tour Gap of $1.93$--$4.17\%$ and relative error of $3.04$--$5.50\%$. It ranks first under the Friedman test, and all twenty-five multiplicity-controlled Wilcoxon comparisons favor it with large, near-complete distributional separation. A paired ablation with common seeds links initialization, in-run local search, and final refinement to quality gains, while candidate restriction chiefly cuts runtime, by up to a factor of roughly $38$. Further experiments up to $16{,}862$ cities keep best-tour Gaps below $6.7\%$, solving the largest case in under eleven minutes.
Global optimization problems often involve nonlinear, multimodal, non-separable, and constrained search landscapes that challenge population-based metaheuristics under limited function-evaluation budgets. This paper proposes the camel foraging optimization algorithm (CFEOA), a mechanism-driven metaheuristic that combines endurance-regulated state control with bounded Grünwald–Letnikov fractional-order displacement memory. In CFEOA, endurance acts as an agent-specific variable regulating the transition between exploration and local refinement, while the bounded fractional-memory term introduces directional persistence from recent accepted displacements. The camel-foraging analogy is used only as an organizing metaphor; the search process is defined through explicit mathematical operators, boundary repair, acceptance rules, and function-evaluation accounting. CFEOA is evaluated using 30 independent runs, fixed random seeds, equal function-evaluation budgets, disabled early stopping in the main benchmark comparisons, full parameter disclosure, and public code availability. The main validation uses the CEC 2022 suite with classical swarm baselines and adaptive DE-family comparators, including NL-SHADE-LBC as an additional recent SOTA reference. Across 18 function–dimension blocks, NL-SHADE-LBC achieves the most favorable aggregate rank, whereas CFEOA retains statistically significant advantages over PSO, GWO, and WOA and shows no significant difference from DE, JADE, SHADE, L-SHADE, and TLBO after Holm correction. Component-wise ablation, parameter sensitivity, convergence, diversity, CPU-time, scalability, and constrained engineering analyses indicate that CFEOA provides a transparent, reproducible, and reliability-oriented search framework with landscape-dependent strengths rather than universal SOTA dominance. The results position CFEOA as a controlled-search alternative for selected complex and constrained optimization settings where repeatability, feasibility, and auditable mechanism design are important.
The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization problem where traditional intelligent algorithms often suffer from slow convergence and premature convergence to local optima. This paper proposes a novel hybrid optimization framework (HGA-PSO-ACO) that integrates the global exploration capability of the Genetic Algorithm (GA), the rapid convergence characteristics of Particle Swarm Optimization (PSO), and the positive feedback mechanism of Ant Colony Optimization (ACO) through a three-stage adaptive coordination model. The key design challenge is to determine when each component should dominate the search and how information should be transferred across stages without causing premature homogenization of the population. To address this issue, the algorithm employs fitness variance (FVD) for real-time population state monitoring and implements dynamic algorithm switching strategies. Experimental validation on a 40-city TSP benchmark demonstrates that the hybrid algorithm achieves a 40% faster convergence speed, a 2.1% lower relative error, and a 58.3% reduction in run-to-run standard deviation compared to individual algorithms, indicating improved solution stability together with favorable parameter sensitivity control.
Xuhang Chen, Zhengrui Zhang, Ze-Hong Chen et al.· 2026 3rd World Conference on...· 0 citations
In evolutionary algorithms (EAs), static operator configurations often depend on human expertise and may lead to search stagnation. Existing adaptive methods either overlook real-time optimization states or require substantial computational overhead. Recent LLM-based methods support adaptive decision-making; however, applying an LLM to a single population requires the model to resolve conflicting exploration and exploitation objectives, which may reduce the reliability of operator selection. To address this limitation, this paper proposes DEAL, a Dual-Pool Evolutionary Algorithm with LLM-Driven Adaptive Operator Selection. DEAL separates the population into an exploitation pool and an exploration pool, enabling the LLM to pursue different search objectives: refining promising solutions in the exploitation pool and exploring alternative candidate structures in the exploration pool. DEAL further incorporates an offline experience collection module and a structured prompt template that jointly provide operator information, population status, and relevant historical evidence. Benchmark experiments on EUC-2D TSP instances show that DEAL reduces the average optimality gap on most tested categories compared with conventional baselines, suggesting the effectiveness of dual-pool LLM-driven operator scheduling.
Teming Qi, Yishun Liu, Chunhua Yang et al.· 2026 IEEE 27th China Confere...· 0 citations
Metaheuristics require sustained global search without sacrificing local refinement, yet many variable-structure methods change operators through one-way iteration schedules. We introduce the Weather State Ants Optimizer (WSAO), in which a discrete-time Markov chain recurrently selects one of three population updates. Sunny, cloudy, and rainy states correspond to global exploration, movement toward nests, and local refinement, respectively. An archive-based mechanism also maintains several spatially separated nests as concurrent search centers. Thirty independent runs compared WSAO with 11 algorithms on 29 CEC2017 and 12 CEC2022 functions. WSAO achieved the lowest Friedman mean rank on both suites, at 2.48 and 2.33. Across five constrained design cases, it joined the leading group by mean objective value on four cases and ranked second on pressure-vessel design. Targeted CEC2022 controls showed that no alternative transition matrix dominated the baseline. Eliminating the trial perturbation worsened every selected function, whereas the contribution of multiple nests depended on the landscape structure. The combined evidence supports recurrent state-controlled search as a competitive framework for continuous numerical and constrained optimization.
Comprehensive experiments on numerical benchmarks and neuroevolution robotic control tasks demonstrate that AutoPSO consistently discovers novel PSO variants that significantly outperform strong baselines and confirm that AutoPSO achieves increasing performance gains with larger swarm sizes.
Xin-Meng Yu, Jia-Xin Gao, Jianguo Zhang et al.· IEEE Transactions on Evoluti...· 0 citations
In maritime search and rescue (SAR) operations, the estimated location of survivors spreads over time, causing the search area to expand continuously. Deploying limited search and rescue units (SRUs) efficiently is critical, but as the search area grows, the number of possible deployment combinations increases exponentially, making exhaustive search impractical. This study proposes a two-stage metaheuristic-based optimization framework that balances computational efficiency and solution quality. In the first stage, the search area is discretized into a grid using simulated particle diffusion results, and grid cell importance is estimated based on particle distribution to assign limited SRUs to high-priority cells first. In the second stage, SRU deployment within each selected cell is reformulated as a permutation-based matching problem to refine resource allocation. The proposed framework was evaluated across 72 scenarios using genetic algorithm, simulated annealing, particle swarm optimization, and differential evolution. Results show that genetic algorithm consistently outperformed other algorithms under resource-constrained conditions while maintaining high solution diversity, providing multiple high-quality alternatives for practical SAR decision-making.
Tae-Hoon Kim, H. Jeong, Choong-ki Kim et al.· GECCO Companion· 0 citations
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