Locating all roots of nonlinear equation of systems (NESs) in a single computational procedure remains a fundamental challenge in computational mathematics. The Dynamic Neighborhood Particle Swarm Optimization algorithm based on Euclidean Distance (EDPSO) is proposed to address this issue. First, a dynamic neighborhood strategy based on Euclidean distance is proposed, to facilitate particles within the population with forming appropriate neighborhoods. Secondly, the Levy flight strategy is integrated into the particle velocity-update mechanism to balance the global search capability and local search capability of particles. Furthermore, integrating a discrete crossover strategy into the PSO algorithm enhances its capability in solving high-dimensional nonlinear equations. Finally, to validate the effectiveness and feasibility of the proposed algorithms, the EDPSO algorithm, along with its comparative counterparts, is applied to solve 20 NESs problems and the forward kinematics equations of a 3-RPS parallel mechanism. Experimental results demonstrate that for the 20 NESs, the EDPSO algorithm achieved the highest success rate (SR = 0.992) and root rate (RR = 0.999) among all compared methods, followed by LSTP, NSDE, KSDE, NCDE, HNDE, and DR-JADE. In solving the forward kinematics of the 3-RPS parallel mechanism, the EDPSO algorithm achieved the highest SR of = 0.9975 and RR = 0.9800, followed by LSTP, KSDE, DR-JADE, NCDE, NSDE, and HNDE, based on these metrics.

AI-assisted thyroid nodule evaluation shows promise in improving thyroid nodule detection, which can be missed by ultrasound(US)-guided hand-held transducer due to the complexity of nodules segmentation. this paper proposed the paper proposes an efficient 4-level framework for ultrasound images segmentation, consisting of Dus-KFCM, Patch Learning, One Class Cross Learning, and parallel computing layer. The developed ML-OCX network considers the contributions of patches to predict the final image-level label by using a GS agent. The authors also created a novel ultrasonography dataset with 4 types of thyroid ultrasound scanning images. Extensive experiments demonstrate the effectiveness of the ML-OCX model, which outperforms other learning methods. The paper also presents an effective multi-modality learning framework to enhance segmentation performance by utilizing prior knowledge of one modality and finding a set of reliable positive and negative examples. The parallel algorithm achieves ~50% improvement in computation efficiency compared to the original serial algorithm. The model is trained on FL-TN, TI-RADS, and DDTI datasets and achieves an accuracy of 97.574%, Fmeasure of 86.150%, and precise judgement of GS-thyroid nodules location from ultrasound assessment, demonstrating its generalization ability. This can help endocrinologist more easily find missed atypia and decrease the follicular lesion miss rate. It may be applicable in daily clinical practice to reduce the burden on physicians. The technology also allows high-risk precancerous lumps to be detected, which has the clinical and biological significance analysis on thyroid nodules echotherapy finding. More prospective studies are needed to make AI-aided thyroid ultrasound diagnosis universal in thyroid nodule clinic.

To address the bottlenecks faced by traditional ground transportation in hilly terrain due to topographical constraints, this study proposes a multi-strategy Enhanced Multi-Objective Phototropic Growth Algorithm (EMOPGA) to tackle the challenges of multi-Unmanned Aerial Vehicles (UAV) cooperative transport for material delivery tasks. This approach aims to overcome the limitations of standard Phototropic Growth Algorithm (PGA), such as susceptibility to local optima and suboptimal initial population quality. It constructs an optimization framework by integrating chaotic mapping for initialization, Lévy flight mutation operators, and an environmental selection mechanism based on Pareto dominance and elite retention strategies. Simulation experiments across nine scenarios demonstrate that EMOPGA achieves a 112.11% improvement in the Average Hypervolume (HV) metric and a 43.11% reduction in the Spacing (SP) metric compared to MOPGA. In comparative experiments against 11 representative algorithms in the complex scenario, EMOPGA achieved an average HV of 9.31 × 10 ¹³ and an average SP of 0.0322. Specifically, EMOPGA achieves a 29.1% HV improvement over MOPGA (the best HV baseline) and a 75.0% SP reduction relative to MOEA/D (the best SP baseline). EMOPGA provides an efficient optimization paradigm for multi-UAV path planning in complex terrain, combining high convergence, strong uniformity, and robust performance. It demonstrates significant potential for practical applications in logistics and emergency response.