多人共站第一类混流装配线平衡问题的优化

针对使用传统模型和算法求解第一类多人共站混流装配线的平衡问题，兼顾工作站数、工人数和工作站负荷均衡，引入了新变量和不对称约束来构建新的数学模型. 提出了一种改进的鸡群算法，使用基于优先权值的编码方式在解码过程中优先选择能最早开始作业的工人来减少序列相关空闲时间，设定工位分配接受准则来分配工人数量以减少工位平均空闲时间；根据适应值大小将种群分为3个不同的群体来实现系统的有效搜索，其中，公鸡群个体基于其适应值差异在不同大小的邻域范围内搜索，母鸡群个体基于适应值相关的参数分别向所归属的公鸡或者其他公鸡/母鸡方向搜索，小鸡群个体则向其归属的母鸡方向搜索；最后将新模型和改进的鸡群算法用于求解标杆算例. 研究结果表明:在算例验证中，对比传统的模型，新模型多找出8个算例的最优解，且寻优速度更快；在算法平均收敛运算时间相似的情况下，本文所提算法求得的平均工人数、工位数以及平滑指标系数等评价指标分别提高了10.74%、16.05%和44.89%，验证了所提模型和算法的有效性和优越性. 

Optimization Research on Mixed-Model Multi-manned Assembly Line Balancing Problem of Type I

Owing to the incapability of the traditional approaches in solving the mixed-model multi-manned assembly line balancing problem of type I (MMALBP-I), a new mixed integer mathematical model is built to minimize the number of stations/workers and to balance the load between stations by introduce new variants and unequal constraints. What’s more, a modified chicken swarm optimization is also proposed. The algorithm adopts a priority-based coding and in decoding procedure, a worker which the assigned task can start earlier is being selected to reduce the sequence-dependent idle time, and the number of workers is decided by the designed station assignment rules to rude the mean station idle time. Moreover, in order to achieve more systematic and efficient search, the chicken swarm is divided into three groups according to the fitness values of the chickens themselves. The roosters generate new solution by a local search in different range of places based on the fitness value, the hens follow their group-mate roosters or other chickens to search a new solution based on the fitness value, the chicks move around their mother hens to update themselves. The proposed approaches are applied to solve the standard test instances. The results show that compared with the old model, the optimal results of eight more instances are found in the new mode in less time. The performance of the three evaluation indicators obtained using the proposed algorithm are improved by 10.74%, 16.05%, 44.89%, respectively, within the approximate time. Thus, above results verify the effectiveness and superiority of the proposed model and algorithm.