Research on Crop Planting Strategies Based on NSGA-2 and Bi-level Robust Optimization

Making full use of limited farmland resources, selecting suitable crops, optimizing planting schemes, and developing modern agriculture have great practical significance for rural economic development. In this paper, we focus on answering a key question: given the uncertainties in expected sales, yield per mu, planting costs, sales prices, and potential planting risks of various crops, what is the optimal crop planting plan for the village from 2024 to 2030? We adopt the breakeven point and safety margin ratio from economic theory, combined with the 2023 crop yields, to define the expected sales volumes. Additionally, we use the entropy weight method-evaluation model to score crops on different plots and construct an objective function to maximize planting scores. At the same time, we also establish an objective function to maximize rural planting profits. This paper employs a two-layer robust optimization model based on the outer-layer NSGA-2 non-dominated sorting genetic algorithm and the inner-layer simulated annealing algorithm to solve the multi-objective programming problem in an uncertain environment. Among the Pareto-optimal solutions, we find the optimal solution using the evaluation model. The outer-layer NSGA-2 seeks to maximize profits, while the inner-layer simulated annealing algorithm seeks to minimize profits, thus maximizing the minimum profit and obtaining an optimal robust solution capable of addressing the maximum risk. This solution yields a profit of 33.0674 million yuan and a planting score of 450.67 in the worst uncertainty scenario. The research results show that the optimal robust solution obtained by this method has high profits and can effectively address market uncertainty risks.