Transfer function-guided mixed-variable optimization for joint mining decisions and resource allocation in mobile edge computing-integrated blockchain networks

Recently, mobile edge computing (MEC) technology has been integrated with wireless blockchain networks to improve the computational capabilities of Internet of Things devices during the mining process. Jointly, optimizing miner selection (discrete) and resource allocation (continuous) in MEC-integrated blockchain networks is a challenging mixed-variable, NP-hard problem. Although several algorithms have been presented in the literature to solve it, they still suffer from low-quality results due to either slow convergence speed, local optima stagnation, or both, especially for small or medium problem sizes. To address this, we propose a transfer-function-guided encoding (TFE) framework that introduces a principled link between continuous metaheuristic search and discrete miner-operator control. Specifically, each individual maintains one discrete control variable determining insertion, deletion, or replacement of a miner and two continuous controls representing transmission power and computing resource allocation. Continuous metaheuristic outputs are converted to discrete decisions through families of S-shaped and V-shaped transfer functions, providing tunable exploration–exploitation balance and probabilistic control over operator selection. This mechanism is integrated with several state-of-the-art algorithms. Extensive experiments on MEC-blockchain networks with m ∈ [ 50 , 1000 ] miners demonstrate that TFE consistently accelerates convergence and improves system profit for small–medium scales, with HNOA-TFE achieving the best overall performance. The numerical results show that the hybrid nutcracker optimization algorithm with the TFE mechanism is effective across most problem instances. Also, the comparative study with recent MEC/blockchain resource-allocation and vehicular-edge benchmarks shows the robustness and scalability of the proposed method.