运筹学与控制论【参考】.docVIP

恒速机下的有限资源博弈排序最优性研究 摘要 排序问题是一类组合最优化问题,由于排序问题中的处理机、任务或作业是有限的,绝大部分排序问题是从有限个可行解中找出一个最优解,使目标函数达到极小. 本文主要研究有限资源的博弈排序问题,我们考虑的资源是相同的,博弈的社会成本是实用的.在恒速机博弈排序模型中,每一个工件都可以自主选择一个合适的机器来加工它自己,这样每个工件的目标就是使它自己的成本最小.工件的成本是指它所选择的那台机器的总完工时间.本文的结构安排如下： 第一章为绪论部分,主要介绍了排序问题、博弈论和纳什均衡问题、博弈排序的产生背景和主要内容以及后两章内容需要用到的一些预备知识. 第二章考虑了恒速机下的博弈排序模型.在纳什均衡中,在每个工件的策略都不改变的情况下,任何一个工件都不能通过单方面的改变自己的策略来降低它的成本,但是纳什均衡不一定是最优的,实际上还常常与最优值存在很大差距.在这里我们使用（the price of anarchy）（the price of stability） Abstract Scheduling problem is a kind of combinatorial optimization problems, due to the processor task or assignment is limited, so most of the scheduling problems is to find an optimal solution from limited feasible solutions, as to achieve the minimum of the objective function. In this paper, we investigate resource allocation games for job scheduling when the resource are limited. The resource we considered are identical and the social costs of the games are utilitarian. In terms of machine scheduling, assignment of jobs to machines in which selfish agents, representing individual jobs, select machines for processing the jobs, and each job will be minimize its cost. The structure of this article is as follows: The first chapter is an introduction, it mainly introduces the combinatorial optimization problems, the background of game scheduling and some preliminary knowledge. In the second chapter, we consider the load balancing game in uniform machines. A Nash equilibrium(NE) is a strategy profile, in any NE assignment, no job can reduce its cost by unilaterally changing its machine. But in terms of a given social objective, such an Nash equilibrium is not necessarily, indeed can often be far from optimal. We use the notions of the price of anarchy() and the price of stability() to analyze the quality of NE solutions.when the The objective function is Total completion time,we prove theand the. When the objective function is the makespan, we prove the . In the third chapter, we consider a system w