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内容提要

今天我们继续阅读英文期刊文献《Modeling and optimizing a multi‑period closed‑loop supply chain for pricing, warranty period, and quality management》，中文翻译可理解为《关于产品定价、保修期和质量管理的多周期闭环供应链模型与优化》，上期我们将学习了约束条件，以及最终的整体模型表述，本期我们将学习文章种解决方案中的解题思路。

Today we continue our reading of the English journal article Modeling and optimizing a multi-period closed-loop supply chain for pricing, warranty period, and quality management. In the last issue we will learn the constraints, and the final overall model formulation, and in this issue we will learn several algorithms to be used in the article.

本期内容将从思维导图、精读内容和知识补充三部分展开。

In this issue, we will start with three parts: mind map, intensive reading content and knowledge supplement.

思维导图精读内容

在模型构建完成之后，作者开始对模型求解。作者根据已有研究的求解方法，提出了元启发式算法来处理，并在文章中提出了三种元启发式算法，这三种均 是处理棘手优化问题的有效算法，分别为：遗传算法（GA）、粒子群优化（PSO） 算法和入侵性杂草优化（IWO）。作者对这三种算法依次进行了详细的描述。

After the model is constructed, the authors start solving the model. The authors propose a metaheuristic algorithm to deal with the problem based on the solution methods that have been studied, and three metaheuristic algorithms are proposed in the paper, all three of which are effective algorithms to deal with tricky optimization problems: genetic algorithm (GA), particle swarm optimization (PSO) algorithm, and invasive weed optimization (IWO). The authors describe these three algorithms in detail in turn.

首先，文章指出为了提高三种拟议算法的效率，采用了以下的编码策略：

1. 随机生成二进制变量以初始化问题的群体。

2.在确定变量It的时候，需要满足以下条件。

First, the paper points out that the following coding strategies are used in order to improve the efficiency of the three proposed algorithms.

1. randomly generated binary variables to initialize the population of the problem.

2. the following conditions need to be satisfied when determining the variable It.

3.新产品和二手产品的需求按照下面的公式进行求取，这样也符合约束条件(13)-(14) 。

3. The demand for new and used products is derived according to the following formula, which also meets the constraints (13)-(14).

4.对生产数量、期初库存水平和期末库存初始化。第一阶段的生产量是需要在二手产品和企业最大产能之间，这种方法可以防止财政赤字，符合约束条件（15）。在计算了第一期的总产量后，客户的需求应该得到满足。在计算完第一期的总产量后，除去满足消费者的需求外，额外数量则作为企业的库存。最后，按照公式计算生产产品耗费的时间。

4. initialization of production quantities, opening inventory levels and closing inventories. The production quantity of the first period is required between the used product and the maximum capacity of the company, this method prevents financial deficit and meets the constraint (15). After calculating the total production in the first period, the customer's demand should be satisfied. After calculating the total production in the first period, the additional quantity, excluding the satisfaction of the consumer's demand, is used as the firm's inventory. Finally, the time consumed to produce the product is calculated according to the formula

5. 最后，文章公式（22）和（23）计算出收购成本，随后计算出收购数量。

5. Finally, the article equations (22) and (23) calculate the acquisition cost and subsequently the acquisition quantity.

基于以上的编码策略，文章提出了三种优化算法，并依次对这三种算法进行了解释，以及结合文章的模型进行算法过程的简要介绍，进行结果的计算。

Based on the above coding strategies, the article proposes three optimization algorithms, which are explained in turn, as well as a brief description of the algorithmic process in combination with the model of the article for the calculation of the results.

知识补充

遗传算法是通过模拟生物自然选择和进化过程而提出的一种搜索最优解的计算方法。

遗传算法首先要确定初始群体，判断群体中的个体是否满足条件，满足即可结束程序，得到我们想要的结果；如果不满足就需要进行下一步，计算出群体个体的适应值，然后按照概率选择遗传算子；然后从中选择一个个体复制到新群体中，随后将两个个体交叉插入新群体，紧接着选择一个个体进行变异后插入新群体，这样就能得到新群体。得到的新群体在重复新步骤，直至新群体个体满足条件，结束程序。

Genetic algorithm is a computational method to search for the optimal solution by simulating the process of natural selection and evolution of organisms.

The genetic algorithm first determines the initial population, determines whether the individuals in the population meet the conditions, and if they do, the procedure can be ended to get the result we want; if not, we need to proceed to the next step, calculate the fitness value of the individuals in the population, and then select the genetic operator according to the probability; then select an individual from it to copy into the new population, and subsequently cross two individuals into the new population, immediately after selecting an individual The new population is obtained by mutating and inserting it into the new population. The new population is repeated until the new individuals meet the conditions and the procedure is completed.

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参考资料：谷歌翻译、百度百科；

参考文献：

[1] Keshavarz-Ghorbani F , Khamseh A A . Modeling and optimizing a multi-period closed-loop supply chain for pricing, warranty period, and quality management[J]. Journal of Ambient Intelligence and Humanized Computing, 2021(6).

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