Using simulated annealing algorithm to optimize three-dimensional spatial structure in environmental art design

Abstract

Existing methods for optimizing three-dimensional spatial structures in environmental art design often rely on subjective experience and intuition, lacking scientific rigor and systematic quantitative analysis. This limitation frequently results in suboptimal solutions, particularly in multi-objective optimization scenarios where local optima are prevalent, thereby restricting innovation and practicality. To address these challenges, this paper proposes the use of the simulated annealing (SA) algorithm to optimize spatial structures. A multi-objective optimization model is constructed, integrating functionality, aesthetics, and space utilization, with mathematical modeling employed to quantify these objectives. To enhance solution quality, a hybrid strategy combining domain knowledge with Latin hypercube sampling ensures uniformity and representativeness of initial solutions. The SA algorithm is configured with carefully selected parameters, including initial temperature and cooling rate, while a comprehensive penalty function handles multi-dimensional constraints. The transition probability mechanism further improves global search capability, preventing premature convergence. Experimental results demonstrate the algorithm’s superior performance: an average generation speed of 3.28 seconds/scheme, optimization time of 21.85 minutes, functional realization rate of 90.83%, space utilization rate of 94.79%, and significantly higher aesthetic scores compared to other methods. This study bridges the gap between artistic creativity and computational optimization, offering a transformative approach to spatial design. By enabling innovative, efficient, and balanced solutions, it advances intelligent methodologies in environmental art design, fostering sustainable and aesthetically pleasing environments.