Bio-inspired projected gradient method for leader selection in minimum cost problem

Abstract

Inspired by the independent and efficient synaptic connections in biological neural networks, this paper introduces the Diagonal Projected Gradient Method (DPGM), a bio-inspired approach to optimize leader selection in networks. Existing methods, such as the Trace-constraint-based Projected Gradient Method (TPGM) and the Orthonormal-constraint-based Projected Gradient Method (OPGM), impose constraints on the input matrix but suffer from redundancy and overlap in input connections, leading to distorted importance indices and suboptimal leader selection. DPGM employs a diagonal input matrix, ensuring that each input affects exactly one node, akin to how synapses independently influence specific neurons. By optimizing the input vector rather than a full matrix, this method simplifies the optimization process and mirrors the efficiency of biological systems, allowing the importance index to reflect the independent influence of each node accurately. We provide a convergence analysis of the proposed method and demonstrate through simulations on real-world networks that DPGM outperforms TPGM and OPGM in leader selection, resulting in improved control efficiency.