Sparse large-scale many-objective optimization problems (SLMOPs), with high-dimensional decision spaces and sparse optimal solutions, pose great challenges to traditional evolutionary algorithms. Existing methods often suffer from: (1) over-reliance on sparsity mining in the binary layer, neglecting nonlinear optimization in the real-valued layer; (2) weak interaction between layers, leading to unclear evolutionary directions; (3) difficulty in capturing complex variable relationships, increasing the risk of local optima. To address these issues, this paper proposes a Multi-Space Hybrid Algorithm (MSHA), which integrates a dual-encoding structure with a multi-space framework. The key components of MSHA are: (1) a neural evolution mechanism, where an MLP learns mappings from inferior to superior individuals to guide real-valued optimization; (2) frequent itemset mask optimization, which updates binary masks using co-occurrence patterns from elite solutions; (3) a multi-space collaborative framework, maintaining diversity in the original space while enhancing search efficiency in the reduced space. Experimental results show that MSHA outperforms existing algorithms in IGD and HV on SMOP benchmarks. In problems with 1000–5000 decision variables and 2–3 objectives, it achieves better convergence and diversity, demonstrating its effectiveness for high-dimensional sparse optimization.