基于免疫算法的并行机间歇过程模糊生产调度

研究了一类具有顺序无关模糊产品切换时间和成本以及模糊单位加工时间和成本的并行机间歇过程调度问题，目的是确定每种产品在每个设备上处理的批次数目、批量以及批次顺序，优化目标为最小化总完成时间和最小化总生产成本。根据任意设备上同种产品的所有批次均顺序处理的性质，建立了问题的模糊运输模型。利用加权和方法将多目标函数转化为单目标函数，并使用基于积分值的方法对模糊数进行排序。提出了基于排列边集编码的免疫算法，通过求解不同规模的问题实例证明，免疫算法不仅能获得比遗传算法和免疫遗传算法更好的解，而且比免疫遗传算法更高效，同时具有良好的动态性能。

Fuzzy scheduling with parallel machines batch process based on immune algorithm

A kind of parallel machines batch process scheduling problem with fuzzy sequence independent changeover time and cost as well as fuzzy unit processing time and cost was studied. Objective of the study was to determine number of batch, batch volume and processing sequence of all batches for each product on each machine. Optimization objectives were to minimize total production time and total production cost. A fuzzy transportation model was constructed to deal with the scheduling problem based on the properties that all batches of the same product on the same machine must be processed sequentially in the optimal solution of problem. Multi-objective function was converted into single objective function using weighted-sum approach. Fuzzy numbers were ranked based on integral value. An immune algorithm with sorted edge set encoding was proposed to resolve the fuzzy transportation problem. The computation results demonstrated that the immune algorithm could obtain better solution than genetic algorithm and immune genetic algorithm, and was more efficient than immune genetic algorithm. Moreover, the immune algorithm exhibited good dynamic performance.