The job-shop scheduling problem is one of the well-known hardest combinatorial optimization problems. The problem has captured the interest of a significant number of researchers, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. In this paper, a hybrid social-spider optimization algorithm with differential mutation operator is presented to solve the job-shop scheduling problem. To improve the exploration capabilities of the social spider optimization algorithm (SSO), we incorporate the DM operator (a mutation operator taken from the deferential evolutionary (DE) algorithm) into the framework of the female cooperative operator. The experimental results show that the proposed method effectiveness in solving job-shop scheduling compared to other optimization algorithms in the literature.

中文翻译：

---

求解作业车间调度问题的具有变异变异算子的混合社会蜘蛛优化算法

车间调度问题是众所周知的最困难的组合优化问题之一。该问题吸引了众多研究人员的兴趣，但是尚未找到有效的求解算法来在多项式时间内将其求解为最优。本文提出了一种基于差分变异算子的混合社会蜘蛛优化算法来解决作业车间调度问题。为了提高社交蜘蛛优化算法（SSO）的探索能力，我们将DM运算符（从差分进化（DE）算法获得的变异运算符）合并到女性合作运算符的框架中。实验结果表明，与文献中的其他优化算法相比，所提出的方法在解决车间作业调度中的有效性。