面向产品族设计的一类双层规划模型及其遗传算法研究

发布时间：2018-10-20 14:59

【摘要】：产品族设计是一个复杂的过程，它不仅是顾客域、功能域、物理域和工艺域依次相互作用，还受到供应链设计、产品销售和售后服务等的影响。从系统论的角度来看，产品族设计的各阶段之间以及产品族设计与其相关系统之间存在着许多主从关系。双层规划模型是体现经济和管理问题中的主从关系的一类数学模型，它属于NP-难问题，虽然对其算法的研究很多，但这些研究往往只是针对有特殊性状的双层规划。遗传算法是一种比较流行的智能算法，它具有简单通用性、鲁棒性、全局收敛性、适用并行处理等特点，在数学优化领域方面的应用尤其广泛。本文通过介绍产品族设计的一般过程和影响因素，提出了产品族设计中存在的一些主从关联优化问题，在已有面向产品族设计的双层规划的研究中提炼出一类具有典型特征的双层规划模型，并设计了一种遗传算法求解方法。最后，本文给详细介绍了产品族设计中的一类主从关联优化问题，并将模型和求解算法应用到具体的实例中。本文的主要工作和创新点如下： 1.基于产品族设计的一般过程，本文提出了产品族设计中的几类主从优化问题，并提炼出一类面向产品族设计的值型双层规划模型。 2.基于遗传算法，本文设计了求解所给模型的方法，并给出了算法的依据、收敛性和数值算例验证。该方法依据双层规划解的概念，采用嵌套的遗传算法，外层遗传算法求解上层问题，，内层遗传算法求解在上层变量给定下的下层问题，并将最优值反应到外层遗传算法以便其进行迭代运算。这种算法既能保证所求的解在双层规划的约束域内，也能保证其为近似最优解。 3.基于已有产品族模块配置和供应链设计的关联研究，本文将设计的模型和算法应用到二者的主从关联优化中。
[Abstract]:Product family design is a complex process. It is not only the interaction of customer domain, functional domain, physical domain and process domain, but also the influence of supply chain design, product sales and after-sales service. From the point of view of system theory, there are many principal and subordinate relationships among the stages of product family design and between product family design and its related systems. The bilevel programming model is a kind of mathematical model which embodies the relationship between principal and subordinate in economic and management problems. It belongs to the NP- problem. Although there are a lot of researches on its algorithm, these researches are usually only aimed at bilevel programming with special characters. Genetic algorithm (GA) is a popular intelligent algorithm, which has the characteristics of simple generality, robustness, global convergence and parallelism, especially in the field of mathematical optimization. By introducing the general process and influencing factors of product family design, this paper puts forward some principal and subordinate association optimization problems in product family design. A class of bilevel programming models with typical characteristics has been abstracted from the previous studies of bilevel programming for product family design, and a genetic algorithm (GA) method has been designed. Finally, this paper gives a detailed introduction of a class of master-slave association optimization problems in product family design, and applies the model and solution algorithm to a concrete example. The main work and innovation of this paper are as follows: 1. Based on the general process of product family design, this paper presents several kinds of master-slave optimization problems in product family design, and extracts a class of value bilevel programming models for product family design. 2. Based on genetic algorithm, this paper designs a method to solve the given model, and gives the basis of the algorithm, convergence and numerical examples. According to the concept of bilevel programming solution, the method uses nested genetic algorithm, outer genetic algorithm to solve the upper layer problem, and inner layer genetic algorithm to solve the lower layer problem given in the upper variable. The optimal value is reflected to the outer genetic algorithm for iterative operation. This algorithm can not only guarantee the solution in the constrained domain of the bilevel programming, but also guarantee that the solution is approximately optimal. 3. Based on the existing product family module configuration and supply chain design, this paper applies the designed model and algorithm to the master-slave association optimization.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB472;TP18

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