The NP-hard no-wait flow shop scheduling problems with makespan and total flowtime minimization are considered. Objective increment properties of the problems are analyzed. A non-dominated classification method is introduced to class population individuals into Pareto fronts to improve searching efficiency. Besides investigating the crowding distance and the elitist solution strategy, two effective bi-criteria local search procedures based on objective increments are presented to improve searching effectiveness. Based on the properties and methods, a hybrid evolutionary algorithm is proposed for the considered problems and compared with the best existing algorithms. Experimental results show that the proposed algorithm is effective with high efficiency.
针对截止期限约束下有向无环图DAG(directed acyclic graph)表示的工作流费用优化问题,提出两个新的费用优化算法:时间约束的前向串归约算法FSRD(forward serial reduction within deadline)和时间约束的后向串归约算法BSRD(backward serial reduction within deadline).算法利用DAG图中串行活动特征给出串归约概念;基于分层算法对串归约组的时间窗口重定义,并提出动态规划的求解策略实现组内费用的最优化.两种归约算法综合考虑DAG图中活动的串并特征,改变分层算法中仅对单一活动的费用优化策略,实现了串归约组的时间收集和最优利用.模拟实验结果表明:BSRD和FSRD能够显著改进相应分层算法的平均性能,且BSRD优于FSRD.
In order to solve the no-wait flowshop scheduling problem to minimize the maximum lateness,three job-block-based neighborhoods are proposed,among which the block exchange neighborhood have a size of O（n4）while the block swap and the simplified block exchange neighborhoods have a size of O（n3）.With larger sizes than the existing neighborhoods,the proposed neighborhoods can enhance the solution quality of local search algorithms.Speedup properties for the neighborhoods are developed,which can evaluate a neighbor in constant time and explore the neighborhoods in time proportional to their proposed sizes. Unlike the dominance-rule-based speedup method,the proposed speedups are applicable to any machine number.Three neighborhoods and the union of block swap and the simplified block exchange neighborhoods are compared in the tabu search.Computational results on benchmark instances show that three tabu search algorithms with O（n3）neighborhoods outperform the existing algorithms and the tabu search algorithm with the union has the best performance among all the tested algorithms.
To solve the NP-complete no-wait flowshop problems, objective increment properties are analyzed and proved for fundamental operations of heuristics. With these properties, whether a new generated schedule is better or worse than the original one is only evaluated by objective increments, instead of completely calculating objective values as the traditional algorithms do, so that the computational time can be considerably reduced. An objective increment-based hybrid genetic algorithm （IGA） is proposed by integrating the genetic algorithm （GA） with an improved various neighborhood search （VNS）as a local search. An initial solution generation heuristic（ISG） is constructed to generate one individual of the initial population. An expectation value-based selection mechanism and a crossover operator are introduced to the mating process. The IGA is compared with the traditional GA and two best-so-far algorithms for the considered problem on 110 benchmark instances. An experimental results show that the IGA outperforms the others in effectiveness although with a little more time consumption.
No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tasks is analyzed, and objective increment properties are established for the fundamental operators of the heuristics. The quality of the new schedules generated during a heuristic is judged only by objective increments and not by the traditional method, which computes and compares the objective of a whole schedule. Based on objective increments, the time complexity of the heuristic can be decreased by one order. A seed phase is presented to generate an initial solution according to the transformed objective. Construction and improvement phases are introduced by experimental analysis. The FCH （fast composite heuristic） is proposed and compared with the most effective algorithms currently available for the considered problem. Experimental results show that the effectiveness of the FCH is similar to that of the best methods but requires far less computation time. The FCH can also be efficient in real time scheduling and rescheduling for no-wait flow shops.
LI XiaoPing1,2 & WU Cheng3 1 School of Computer Science & Engineering, Southeast University, Nanjing 210096, China
