Background Optimizing stand spatial structure is essential for enhancing the multifunctional benefits of plantations, yet how to integrate multiple neighborhood-based indicators into a feasible thinning plan across developmental stages remains methodologically challenging. Methods We developed a simulated annealing (SA) optimization model for larch ( Larix principis-rupprechtii ) plantations at four ages (20, 29, 37, and 46 years) in Saihanba, northern China. Five spatial indices (uniform angle index W , dominance U , crowdedness C , canopy openness K , and intersection angle competition UCI ) were combined into a composite function Q under harvest intensity and diameter-class constraints. Results The SA-driven thinning raised Q by 1023.8–4660.1% across stages, with optimal thinning intensities of 33.8–46.4%. After optimization, the mean stand metrics were all in the random distribution range of 0.475, 0.517. The values of K ¯ increased, while C ¯ , U ¯ , and UCI ¯ decreased. Among these metrics, the value C ¯ showed the largest variation (45.1–55.2%), indicating that was the main constraint affecting the spatial structure of larch plantations at different developmental stages. Conclusion The SA-based approach effectively resolves multi-objective spatial optimization for larch plantations at different ages, with thinning priority given to relieving crown overlap. Long-term growth responses still need field validation, but the method offers a practical, spatially explicit decision tool for larch plantations.
Zhao et al. (Thu,) studied this question.