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Effective Heuristic Algorithms Solving the Jobshop Scheduling Problem with Release Dates
Mathematics ( IF 2.4 ) Pub Date : 2020-07-25 , DOI: 10.3390/math8081221
Tao Ren , Yan Zhang , Shuenn-Ren Cheng , Chin-Chia Wu , Meng Zhang , Bo-yu Chang , Xin-yue Wang , Peng Zhao

Manufacturing industry reflects a country’s productivity level and occupies an important share in the national economy of developed countries in the world. Jobshop scheduling (JSS) model originates from modern manufacturing, in which a number of tasks are executed individually on a series of processors following their preset processing routes. This study addresses a JSS problem with the criterion of minimizing total quadratic completion time (TQCT), where each task is available at its own release date. Constructive heuristic and meta-heuristic algorithms are introduced to handle different scale instances as the problem is NP-hard. Given that the shortest-processing-time (SPT)-based heuristic and dense scheduling rule are effective for the TQCT criterion and the JSS problem, respectively, an innovative heuristic combining SPT and dense scheduling rule is put forward to provide feasible solutions for large-scale instances. A preemptive single-machine-based lower bound is designed to estimate the optimal schedule and reveal the performance of the heuristic. Differential evolution algorithm is a global search algorithm on the basis of population, which has the advantages of simple structure, strong robustness, fast convergence, and easy implementation. Therefore, a hybrid discrete differential evolution (HDDE) algorithm is presented to obtain near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions. The superiority of the HDDE algorithm is highlighted by contrast experiments with population-based meta-heuristics, i.e., ant colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). Average gaps 45.62, 63.38 and 188.46 between HDDE with ACO, PSO and GA, respectively, are demonstrated by the numerical results with benchmark data, which reveals the domination of the proposed HDDE algorithm.

中文翻译:

有效的启发式算法解决带发布日期的Jobshop调度问题

制造业反映了一个国家的生产力水平,在世界发达国家的国民经济中占有重要份额。Jobshop Schedule(JSS)模型起源于现代制造,其中许多任务按照其预设的处理路径在一系列处理器上单独执行。这项研究以最小化总二次完成时间(TQCT)的标准解决了JSS问题,其中每个任务都可以在其自己的发布日期使用。引入构造性启发式算法和元启发式算法来处理不同规模的实例,因为问题是NP难题。鉴于基于最短处理时间(SPT)的启发式和密集调度规则分别对TQCT准则和JSS问题有效,提出了一种结合SPT和密集调度规则的创新启发式算法,为大规模实例提供了可行的解决方案。一种基于单机的抢占式下限,用于估计最佳计划并揭示启发式算法的性能。差分进化算法是一种基于种群的全局搜索算法,具有结构简单,鲁棒性强,收敛速度快,易于实现的优点。因此,提出了一种混合离散微分进化算法(HDDE),以获得中等规模实例的最佳解,其中多点插入和局部搜索方案可提高最终解的质量。通过基于群体的元启发式实验(即蚁群优化(ACO),粒子群优化(PSO)和遗传算法(GA)。HDDE与ACO,PSO和GA之间的平均差距分别为45.62、63.38和188.46,这是通过具有基准数据的数值结果证明的,这表明了所提出的HDDE算法的优势。
更新日期:2020-07-25
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