基于罚函数的设施定位布置问题模型与算法

Model and Algorithm for Fixed-positioning Layout Based on Penalty Function

针对系统内部设施布置决策,以定位布置问题为研究对象,提出了一种求解该问题的改进分布估计算法(IEDA)。通过分析定位布置问题的基本特征,建立了带容量约束的基本非线性整数规划模型;引入了基于罚函数的约束处理方法建立了定位布置问题的改进数学模型,进而使用带惩罚项的目标函数引导IEDA的搜索方向;在IEDA中融入了一种概率矩阵变异机制和基于互换型邻域结构的局部搜索策略,用于平衡算法的全局和局部搜索能力;并通过仿真实验比较和对某建筑工地实例求解验证了模型的合理性与算法的有效性。

Considering the decision of interior facility layout in the production systems and aiming at facility layout problem,an improved estimation of distribution algorithm（IEDA）is given to solve this problem. Firstly,based on its essential characteristics,a nonlinear integer programming model with capacity constraints is established to formulate associated basic properties. Secondly,a modified mathematical model combining with the penalty function based constraint handling method is constructed,which indicates that if the capacity constraint of any position is not satisfied,the related penalty term will be set to a high punishment,otherwise set to zero. And thereafter,the objective function with penalty terms is used to guide the search direction of our proposed IEDA. Thirdly,a mutation mechanism for probability matrix and an interchange-based local search with first move strategy are embedded into IEDA to balance the global and local search ability. Finally,the results of simulation experiments and case study from a construction site demonstrate the rationality of the model and the effectiveness of the presented IEDA.