Multi-label feature selection (MFS) is critical in high-dimensional data analysis and multi-label learning, yet existing federated MFS methods often suffer from low solution quality, weak convergence, and limited privacy protection. To overcome these limitations, we propose Fed-MGACO, a novel federated framework that integrates manifold sparse constraints (MSC) and game-theoretic evolutionary ant colony optimization (GTEACO). In this framework, each client executes a two-stage MSC-GTEACO algorithm: in the first stage, MSC performs manifold preservation with sparse constraints to derive an initial feature weight matrix; in the second stage, GTEACO refines the solution through a heterogeneous ant colony, guided by game-theoretic pheromone updates, to capture cross-label dependencies and local distribution variations. Federated training employs a feature-weight–driven adaptive aggregation and distribution strategy, where clients share only their optimized feature-weight matrices with the server–while retaining raw data locally to preserve privacy–for secure aggregation. The aggregated results are then redistributed to clients to guide subsequent local refinements until convergence. Extensive evaluations on the CEC2022 benchmark functions and multiple real-world multi-label datasets show that Fed-MGACO delivers superior global optimization capability and faster convergence than baseline methods, while also yielding consistent improvements across key evaluation metrics, thereby demonstrating the effectiveness and robustness of the proposed method.

This study proposes an enhanced Black-kite Algorithm (BKA), termed SMNBKA-ICMIC, to improve optimization performance. The algorithm introduces four key improvements: ICMIC-based initialization to enhance population diversity, integration of the Simulated Binary Crossover (SBX) operator to strengthen exploration, a refined position-update formula of migration to mitigate premature convergence, and a novel natural replacement mechanism to balance global and local search. The SMNBKA-ICMIC demonstrates exceptional performance in benchmark functions from CEC 2017, 2020, and 2022, securing the top rank from best value in these tests. Additionally, the algorithm demonstrates superior performance across a diverse set of representative benchmarks. It achieves the top of best value in 9 out of 10 complex engineering optimization problems—chosen for their relevance to real-world design and control challenges—and exhibits remarkable effectiveness in the canonical multi-knapsack problem, a standard test for combinatorial optimization. These results validate SMNBKA-ICMIC as a state-of-the-art metaheuristic, ensuring robust convergence and practical utility for complex numerical optimization.