Real-world information diffusion frequently spans multiple heterogeneous platforms and relational layers, making multilayer influence maximization (MLIM) a critical and challenging problem. Existing methods for multilayer networks often rely on local structural signals for surrogate evaluation, failing to accurately characterize multi-hop diffusion and inter-layer coupling effects. In discrete combinatorial search, meta-heuristic random exploration often disrupts the structural inheritance and reuse of effective node configurations, compromising search stability and quality. To address these challenges, this paper proposes a Probabilistic-Based Multilayer Slime Mold Algorithm (PB-MSMA). It employs the slime mold algorithm as its search framework to perform discrete combinatorial optimization within a controlled candidate space. It utilizes the Preference-based Expected Diffusion Value (P-EDV) as a surrogate fitness metric during the search phase. This design reduces the need for repeated Monte Carlo simulations for iterative candidate evaluation while improving the characterization of inter-layer and higher-order diffusion effects. Furthermore, a probabilistic pipeline mechanism is introduced to encode recurring effective node configurations from historical searches as statistical priors, guiding the search process to enhance structural inheritance and stability. After the seed sets are obtained, the final influence spread of all compared methods is evaluated using 10,000 Monte Carlo simulations under the MLIC model. Experiments on six real-world multilayer network datasets and nine seed budgets show that PB-MSMA achieves a dataset-level improvement range of 3.68–14.50% over representative baselines, including CELF, DPSOMIM, Degree, DIRCI, and PRGC, with an average improvement of 10.32%. These results indicate that PB-MSMA provides an efficient seed-selection strategy for multilayer diffusion scenarios where repeated simulation-based evaluation is costly.
Chen et al. (Sat,) studied this question.