针对以最大完工时间为目标的柔性作业车间调度问题，在鲸鱼群算法（WSA，Whale swarm algorithm）基础上，提出一种改进的鲸鱼群算法。首先，设计了一种基于工序加工顺序的个体位置表达方式及相应距离计算方法，使鲸鱼群算法能够直接应用于求解离散型问题。其次，在寻找"较好及较近"鲸鱼过程中引入协同搜索机制，提高"较好及较近"鲸鱼的质量和数量，扩大鲸鱼个体的搜索范围。同时，引入基于关键路径的变邻域搜索算法，搜索当前最优鲸鱼个体的邻域解，提高种群局部搜索能力。最后采用BRdata基准算例进行测试，验证了算法的可行性和有效性。
An improved whale swarm algorithm is proposed for solving flexible job shop schedule problem(FJSP) with the objective to minimize makespan based on whale swarm algorithm(WSA). First of all, the position representation and distance calculation method of individuals were well-designed based on processing sequence so that the WSA could solve discrete problem such as FJSP directly. Secondly, cooperating search was introduced to develop "better and near" whale swarm with quality and quantity, expanding the moving region of individuals. Finally, variable neighborhood search(VNS) based on critical path was embedded to enhance the local exploitation ability. Numerical experiments and comparisons were conducted against the best performing algorithms reported in the literature. The results validate the effectiveness and efficiency of proposed algorithm.