The paper investigats modeling and optimizing problems of parallel machine scheduling with resource - constrained and multi - step working procedure , acting bell - type annealing of shanghai baosteel yichang sheet lt . co . as practical background , designs and develops scheduling production system which is optimized according to practical demand of annealing workshop 本文以上海宝钢益昌薄板有限公司罩式炉退火过程为背景，研究了资源受限多步工序并行机器调度问题的建模和优化问题，结合退火炉车间生产调度的实际需要，进行了退火炉优化排产系统的设计和开发。
In chapter 3 we construct two approximation algorithms which applying bin packing algorithms for scheduling problems , one is ff ( first fit ) algorithm used in parallel machine scheduling problem pm / / dj = d / n which has a lower bound of asymptotic worst - case performance ratio , another problem is scheduling independent parallel tasks in parallel identical machine systems to minimize the makespan , we use strip packing method for it and give an approximation algorithm with asymptotic performance ratio no more than 1 . 6 第一个算法利用装箱问题中的ff ( firstfit )算法求解极大化按期完工工件数的平行机排序问题pm d _ j = d n - u _ j ，该近似算法具有渐近性能比下界。第二个近似算法利用二维装箱中strippacking问题的算法求解以极小化makespan为目标的带并行工件的平行机排序问题，该算法的渐近性能比具有下界1 . 5和上界1 . 6 。
This is the fundamental for latter study . according to the preempt - resume model , a statistic algorithm for p2 prmp cmax is given . secondly , we use the two models to study the dynamic single - machine scheduling problems of minimizing total flow time and of minimizing total timetable - length and develop on - line optimal dispatching rules , which consider only available information 第三，我们研究了排序问题1 | r _ j ， prmp | somw _ j ( 1 - e ~ ( - ac ) )的动态在线调度问题，考虑该问题在中断?重复和中断?安装重复模型下的动态在线排序问题，给出了只考虑当前可用信息的在线调度规则。
In this paper , we presented a kind of pga which is based on distributed computation of the network for solving identical parallel machine scheduling problem with constraint , and computational results show that endga can not only save the optimization time evidently but also largely improve the optimization quality , which provides an effective solution to massive complicated optimization problems 在本文中,我们实现了一个解决带约束条件的并行多机调度问题的分布式网络pga 。实验表明, endga能显著节约寻优的时间,大大提高寻优的质量,为解决巨量优化问题提供一个可行的解决方法。
As an example , the parallel machine scheduling problem is mapped on a non - constrained matrix construction graph , and a aco algorithm is proposed to solve the parallel machine scheduling problem . comparison with other best - performing algorithm , the algorithm we proposed is very effective . the finite deterministic markov decision process corresponding to the solution construction procedure of aco algorithm is illustrated in the terminology of reinforcement learning ( rl ) theory 本章最后提出了解决并行机调度问题的蚁群算法，该算法把并行机调度问题映射为无约束矩阵解构造图，并在算法的信息素更新过程中应用了无约束矩阵解构造图的局部归一化蚂蚁种子信息素更新规则，与其他几个高性能算法的仿真对比试验证明这种方法是非常有效的。
Abstract : in this paper , we discussed a new kind of single machine scheduling problems with controllable processing times . the objective function being considered was the sum of weighted completion times of all jobs plus the maximum dissatisfaction of all jobs ' processing times that deviated from their specified ones . we presented a polynomial algorithm to solve the problem 文摘:本文讨论了一类新的加工时间可控的单机排序问题.我们所考虑的目标函数由所有工件的加权完工时间之和与对所有工件的实际加工时间偏离额定加工时间的最大不满意程度这两部分组成.对此问题,我们提出了一个多项式算法
In a non - preemptive static scheduling problem , all job parameters are known . scheduling decisions , which only the characteristics of jobs known to be in the system at a given point are called on - line optimal scheduling . seeing the importance of single machine scheduling problem , we take it as our object and study the dynamic condition of single machine problems 在做决策之前，所有任务的信息都是已知的情况下做出的排序称为静态离线最优排序，在做决策的时间点上，只知道当前可排任务的信息而做出的最优排序称为在线最优排序。
An approximation algorithm a2 - 1 with absolute performance ratio 3 / 4 is proposed and the asymptotic performance ratio of a2 - 1 applied to the problem in which machines require prepare times is 2 / 3 . another problem is two parallel machines scheduling to maximize the number of just in time jobs . for this problem we give a polynomial time optional algorithm in the case early penalty is larger or equal to late penalty , and it is proofed to be np - had when early penalty is less than late penalty 第二章所讨论的另一个问题是带提前和延误惩罚的两台机排序极大化justintime完工工件数问题，当提前惩罚大于或等于延误惩罚时，本文提出了该问题的一个多项式时间最优算法a _ ( 2 - 2 ) ，从而证明了该问题是一个p问题，当提前惩罚小于延误惩罚时，我们证明了该问题是一个np难的问题。
