Optimizing the tomato growth environment in a greenhouse using improved NSGA-II

The tomato can be one of the most representative crops under protected cultivation. There is a high sensitivity of its growth rate and plant health status to the environmental conditions. It is often required to regulate the environmental factors in greenhouses due to the complex and resource-intensive tomato production. The crop growth rate can be enhanced by means of multi-objective optimizationHowever, traditional single-objective or static multi-objective optimization methods struggle to simultaneously ensure crop health and growth rate, which may lead to unsatisfactory regulation effects of the growth environment and even system instability. This study aims to propose a stability-aware multi-objective optimization, the Chaos-Lyapunov-enhanced Non-dominated Sorting Genetic Algorithm II (CL-NSGA-II). The robust decision-support tool was also provided to generate the high-performance, dynamically stable, and operationally viable environmental control setpoints. Two frameworks were introduced into the standard NSGA-II architecture. Firstly, the chaotic initialization with the logistic map and mutation operator was embedded to enhance the population diversity over the search space, effectively preventing the premature convergence to the local optima other than the global ones. Adaptive adjustment with dynamic chaotic perturbation is adopted to further strengthen the global search ability. Secondly, the dynamic penalization mechanism with the Lyapunov exponent was integrated into the selection. Only solutions with negative Lyapunov exponents (λ < 0) are retained as stable candidates. Finally, the largest Lyapunov exponent was calculated for the simulated environmental trajectory of each candidate solution; The solutions predicted that the positive exponents (indicating chaotic or unstable long-term behavior) were penalized and progressively eliminated from the population.In addition, an attractor clustering analysis and an elite-guided strategy are proposed, and a dynamic termination criterion is constructed based on population distribution entropy and attractor coverage to judge the convergence state of the algorithm.An optimal model was established using a high-fidelity dataset. The environmental variables of the high-precision sensors were then logged into a fully instrumented and controlled greenhouse compartment at one-minute intervals over a full cycle of the tomato growth. Therefore, the formal multi-objective problem was defined to maximize the growth rate and the composite plant health index. A series of experiments was conducted on the benchmark CL-NSGA-II. The NSGA-II algorithm and the variants were enhanced only with chaos, in order to isolate the contribution of the stability constraint. The performance was evaluated over three key metrics: convergence speed to the reference Pareto front, diversity and spread of the final solution set, and dynamic stability of the control strategies. The experimental results show that the CL-NSGA-II significantly outperformed the NSGA-II. Specifically, the solution set coverage increased by 19.7%, the convergence speed was improved by 15%, and the dynamic stability was substantially enhanced, where the Lyapunov exponent was reduced to −0.054. The stability was also verified after optimization. Chaotic global search was fused with the Lyapunov stability constraints. The dynamic operational stability also served as a non-negotiable and quantitative criterion during optimization. The tomato growth rate and plant health were effectively coordinated for a more efficient and sustainable greenhouse. A reliable technical tool was provided for the precision environmental control in modern agriculture. At the same time, the long-term stable operation of the environmental system can also offer strong support for the intelligent control strategies and parameter optimization of the tomato growing environments in protected agriculture.