Optimizing Territorial Functional Layouts for Carbon–Economic Coordination Using a Cellular-Automata-Based Multi-Objective Spatially Explicit Model

Territorial spatial function layout optimization can alleviate the conflict between low-carbon development and economic growth by regulating the quantitative composition and spatial allocation of production, living, and ecological functions. However, existing spatial optimization models remain limited in their ability to simultaneously address quantitative uncertainty, spatial functional conflicts, and the coordination among spatial layouts, quantitative structures, and optimization objectives. This study develops a cellular automata (CA)-based Territorial Spatial Function Layout Optimization (TSFLO) model. The model integrates multi-objective fuzzy linear programming to optimize the target-year quantitative structure, a non-homogeneous Markov process to characterize functional transitions, and a game-theoretic approach to coordinate spatial conflicts. Furthermore, the model inversely derives the optimal quantitative structure of the base year through the Markov state transition equation, adjusts the base-year layout according to coordinated suitability to construct the CA initial state, and compares the TSFLO model with the PLUS model using Qionglai City, China, as a case study. Relative to the 2020 baseline layout, the proportions of areas without functional transitions under the TSFLO scenario were 81.40% and 73.60% in 2025 and 2030, respectively, which were 3.39 and 0.28 percentage points higher than those of the PLUS model. The maximum absolute relative errors between the TSFLO-optimized results and the target quantitative structure were 0.07% and 0.05%, respectively, representing reductions of 99.28% and 98.52% compared with the PLUS model. The minimum matching degrees between the seven territorial spatial functions and their corresponding high-coordinated-suitability areas were 71.86% and 69.51% in 2025 and 2030, respectively. From 2020 to 2030, the decoupling index of ecological regulation service functions was −2.8642, compared with −1.9128 for PLUS, indicating that the TSFLO scenario improved the decoupling intensity by 49.7%. The results demonstrate that TSFLO can integrate quantity optimization, spatial conflict coordination, and initial state construction within a unified CA framework, thereby improving quantitative allocation accuracy and spatial suitability matching. This provides methodological support for coordinating low-carbon development and economic growth through territorial spatial function layout optimization.