In this paper, we have proposed a stochastic Knapsack Problem (KP) based mathematical model for small-scale vegetable sellers in India and solved it by an advanced Genetic Algorithm. The knapsack problem considered here is a bounded one, where vegetables are the objects. In this model, we have assumed that different available vegetables (objects) have different weights (that are available), purchase costs, and profits. The maximum weight of vegetables that can be transported by a seller is limited by the carrying capacity of the vegetable carrier and the business capital of the seller is also limited. The aim of the proposed mathematical model is to maximize the total profit of the loaded/traded items, with a set of predefined constraints on the part of the vegetable seller or retailer. This problem has been solved in a Type-2 fuzzy environment and the Critical Value (CV) reduction method is utilized to defuzzify the objective value. We have projected an improved genetic algorithm based approach, where we have incorporated two features, namely refinement and immigration. We have initially considered benchmark instances and subsequently some redefined cases for experimentation. Moreover, we have solved some randomly generated proposed KP instances in Type-2 fuzzy environment.

在本文中，我们为印度的小规模蔬菜销售商提出了一个基于随机背包问题 (KP) 的数学模型，并通过先进的遗传算法对其进行了求解。这里考虑的背包问题是有界的，其中蔬菜是对象。在这个模型中，我们假设不同的可用蔬菜（对象）具有不同的权重（可用的）、购买成本和利润。卖家可以运输的蔬菜最大重量受蔬菜运输车的承载能力限制，卖家的经营资金也有限。所提出的数学模型的目的是最大化装载/交易项目的总利润，对蔬菜销售商或零售商有一组预定义的约束。该问题已在 Type-2 模糊环境中得到解决，并利用临界值 (CV) 缩减方法对目标值进行去模糊化。我们设计了一种改进的基于遗传算法的方法，其中我们结合了两个特征，即细化和迁移。我们最初考虑了基准实例，随后考虑了一些重新定义的案例进行实验。此外，我们已经在 Type-2 模糊环境中解决了一些随机生成的建议 KP 实例。