Automated design of chemical formulations is a cornerstone of materials science, yet it requires navigating a high-dimensional combinatorial space involving discrete compositional choices and continuous geometric constraints. Existing Large Language Model (LLM) agents face significant challenges in this setting, including context window limitations during long-horizon reasoning and path-dependent exploration that may lead to mode collapse. To address these issues, we introduce AI4S-SDS, a closed-loop neuro-symbolic framework that integrates multi-agent collaboration with a tailored Monte Carlo Tree Search (MCTS) engine. We propose a Sparse State Storage mechanism with Dynamic Path Reconstruction, which decouples reasoning history from context length and enables arbitrarily deep exploration under fixed token budgets. To reduce local convergence and improve coverage, we implement a Global--Local Search Strategy: a memory-driven planning module adaptively reconfigures the search root based on historical feedback, while a Sibling-Aware Expansion mechanism promotes orthogonal exploration at the node level. Furthermore, we bridge symbolic reasoning and physical feasibility through a Differentiable Physics Engine, employing a hybrid normalized loss with sparsity-inducing regularization to optimize continuous mixing ratios under thermodynamic constraints. Empirical results show that AI4S-SDS achieves full validity under the adopted HSP-based physical constraints and substantially improves exploration diversity compared to baseline agents. In preliminary lithography experiments, the framework identifies a novel photoresist developer formulation that demonstrates competitive or superior performance relative to a commercial benchmark, highlighting the potential of diversity-driven neuro-symbolic search for scientific discovery.