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In this article, the modeling of a distribution network problem of agricultural products with high perishability under uncertainty is discussed. The designed model has three levels of suppliers, distribution centers, and retailers, in which suppliers can directly or indirectly meet retailers’ demand. Due to agricultural product distribution network unpredictability, robust possibilistic optimization (RPO) has been applied. This model is innovative and takes uncertainty into account. The findings show that uncertainty increases network demand. Supply, distribution, maintenance, and order expenses have grown. By examining the rate of perishability of agricultural products, it has been revealed that, with the growth of this rate, the costs have increased according to the ordering and spoilage of the products. The genetic algorithm (GA), whale optimization algorithm (WOA), and arithmetic optimization algorithm (AOA) have also been applied to analyze the model. The calculations on 10 sample problems in larger sizes show that the AOA has the best performance in achieving near-optimal solutions. Conversely, the WOA has the lowest computing time compared to other meta-heuristic algorithms. Additionally, the statistical test results show no significant difference between the average calculation time and the objective function among the applied algorithms.