学科发展研究(2012-2013)分述
运筹学
2014年04月02日

  一、概述

  运筹学是自20世纪三四十年代发展起来的一门新兴交叉学科。它主要研究人类对各种资源的运用及筹划活动,以期通过了解和发展这种运用及筹划活动的基本规律和方法,发挥有限资源的最大效益,达到总体最优的目标。运筹学的学科体系主要包含模型、理论和算法三大部分。从问题的形成开始到构造模型、理论分析、提出解案、进行检验、建立控制,直至付诸实施为止的所有环节构成了运筹学研究的全过程。运筹学的应用范围遍及工农业生产、经济管理、工程技术、国防安全、自然科学等各个方面和领域。

  经过七十多年的发展,运筹学已经逐步形成了一套系统的研究和解决实际问题的方法,它可以概括为以下五个阶段:

  (1) 构建所关心问题的数学模型,将一个实际问题表示为一个运筹学问题;

  (2)分析问题(最优)解的性质和求解问题的难易程度,寻求合适的求解方案;

  (3)设计求解相应问题的算法,并对算法的性能进行理论分析;

  (4)编程实现算法,并分析模拟数值结果;

  (5)判断模型和解法的有效性,提出解决原始实际问题的具体实施方案。

  二、本学科发展历程

  1937年,英国物理学家E.C. Williams 研究雷达在实战军事行动中的使用,给出了“运筹学”这一名词。第二次世界大战期间,英国军方为了有效地运用新研制的雷达系统来对付德国飞机的空袭,从政府研究部门和高校抽调了一批科学家,进行新战术试验和战术效率的研究,这标志着现代运筹学的诞生。之后,美国和加拿大的军事部门也相继成立了若干运筹学研究小组。

  现代运筹学被引入中国是在20世纪50年代后期。1956年,钱学森在中国科学院力学研究所成立了中国第一个运筹学小组。当时,运筹学在中国的应用集中在运输问题上,其中代表性工作有“打麦场的选址问题”和“中国邮路问题”。在文革期间,华罗庚亲自率领“小分队”到农村、工厂讲解基本的优化技术和统筹方法,足迹遍布二十余个省,促进了运筹学在我国的普及和推广。

  20世纪六、七十年代,许国志和越民义等中国运筹学的开拓者们在排队论的瞬时概率性态问题、非线性规划梯度算法收敛问题、组合优化中的排序问题等取得了一批重要成果,得到了国外同行的关注和好评。相关成果在1978年全国科学大会上获得大会奖,也为中国运筹学的发展打下了坚实的基础,同时培养了一批运筹学的学科带头人和研究骨干。

  自20世纪80年代以来,随着改革开放,国内外学术交流不断增加。中国运筹学有了快速地发展,取得了一批有国际影响的理论和应用成果。特别是运筹学工作者因在组合优化、生产系统优化、图论、非线性规划和城市交通领域的突出贡献,曾先后获得国家自然科学奖二等奖五项;因在经济信息系统评估和粮食产量预测方面取得突出成绩,曾先后获得国际运筹学会联合会运筹学进展奖一等奖二项。与此同时,中国运筹学在国际上的影响日益增强。1982年,中国运筹学会成为国际运筹学会联合会的成员国;1999年,中国运筹学会在北京成功举办了国际运筹学会联合会第十五届大会。

  三、本学科近年来突出成果

  近五年以来,中国运筹学工作者在数学规划、博弈论、随机优化、排序论、供应链管理和计算系统生物学等运筹学的主要研究领域和方向开展了大量的研究工作,取得了一批具有国际影响的理论成果。与此同时,他们还积极与企业密切合作,开展了一系列运筹学方法的应用项目与实践活动。在移动通信、钢铁制造、医疗服务和航空客运等领域推动了相关行业的技术革新与进步,形成了多项具有自主知识产权的优化技术和系统,产生了良好的经济与社会效益。

  中国科学院研究生院郭田德领导的团队与广州移动通信公司合作,利用运筹学的优化模型和方法为其提供了一整套一种双网融合无线网络规划方法,为电信运营商的无线网络精细化管理服务,避免现在靠人工经验进行基站优化的不可靠性及低效率。2009年始该项目的成果已经在全国3个城市推广应用,系统已经在中国移动集团广东、北京和河北等公司得到了应用,并在亚运场馆移动网络规划建设中发挥重要作用,取得了较好的经济效益和社会效益。

  东北大学唐立新领导的团队与上海宝山股份有限公司合作,针对钢铁企业降低生产及物流成本的迫切需求,钢铁企业生产与物流调度问题的特征,建立了多个原创性的运筹学模型,提出了三层次优化方案及智能优化方法,解决了现有优化方法难以有效解决复杂工业问题的难点。该项目已获得国家发明专利十余项,国家软件著作登记近20项。与宝钢等大型企业合作,开发了多个具有我国自主知识产权的决策支持系统,其中一些系统已在上海宝山钢铁股份有限公司及上海梅山钢铁股份有限公司成功应用。

  近年来,中国运筹学界在国际运筹学界的地位也不断加强。中国运筹学会的两位前任理事长章祥荪、袁亚湘先后代表亚太运筹学会出任国际运筹学会联合会副主席,此外,在2014年第27届国际数学家大会上,袁亚湘将做邀请报告。

  四、本学科国内外发展的比较及思考

  目前,相当多的运筹学工作者都有很强的数学背景或者在数学系任职。因为数学理论和方法是运筹学最主要的方法和工具,所以他们中的很多人对运筹学的发展做出了重要贡献。然而,一些在数学系任职的运筹学工作者,他们的研究渐渐地脱离了现实。这对运筹学的健康发展尤其不利,特别是在中国,大多数从事运筹学研究的人在数学系任教。如何消除不良的学术氛围的影响,做出对运筹学的发展有实质性贡献的工作,这是中国运筹学界面临的一个挑战。

  随着运筹学的快速发展和学科体系的建立,管理科学与运筹学之间的差异逐渐显现。例如,美国运筹学会和管理科学学会分别于1952年和1953年成立。他们在意识到管理科学与运筹学之间这些差异的同时,也清楚地认识到两者之间的密切联系,更重要的是强化联系比强调差异能更好地促进这两个学科的共同发展。两个学会在各自成立四十多年以后,于1995年合并为美国运筹学与管理科学学会。目前,在中国的学科体系下,运筹学与控制论是作为一级学科数学下的一个二级学科,管理科学与工程是管理学门类下的一个一级学科。而在国家自然科学基金委员会的学部体制下,运筹学相关的项目主要是由数理学部受理,而管理科学相关的项目主要是由管理科学部受理,它是与数理学部平级的(这与美国自然基金委员会的设置不同)。由此可以看出,在某种程度上管理科学更具有相对独立性,也更受到重视,而运筹学涉及的范围更加广泛,是更具有交叉性的一个二级学科。如何看待和处理运筹学与管理科学之间的联系与区别,使得运筹学和管理科学都能更好地协调发展,这是中国运筹学界今后面临的另一个挑战。

  运筹学在二次世界大战时期逐渐形成,期间许多运筹学工作者的出色工作,使得运筹学产生了巨大的影响。二战结束以后,他们中的许多人转到高校,纷纷建立运筹或相关的系,也有不少到民用领域服务的。这些运筹学前辈在各自的新岗位上继续从事着运筹学方面的教育、研究和实践推广。最近十几年,中国运筹学实践和推广方面的工作开展得不多,大多数运筹学工作者的重心在理论研究方面。造成这种现象的原因包括:(1)运筹学工作者对运筹学发展的认知问题,没有充分意识到实践和推广工作的重要性;(2)实践和推广工作非常繁复,甚至艰苦,特别是与各行各业具有不同知识层次和结构的人沟通时的困难。(3)国家和单位的学术及科研评价和奖励机制下实践和推广工作未得到应用的认可和承认。如何协调运筹学研究和教学与推广和实践的关系,广泛和深入地开展运筹学实践和推广工作,这是中国运筹学界今后面临的又一个挑战。

  困扰运筹学发展的一个问题是,如何评价一项运筹学的成果。运筹学学术研究的目标与实际应用的目标有着根本的差别,只有身处他们各自所服务的组织、奖励体系和生活方式中才能体会得到。不容置疑,仅仅以否能在顶级杂志上发表论文及发表论文的篇数的多少来衡量一项运筹学成果的意义的大小和研究者的水平的高低,不仅是十分不恰当的而且是非常有害的。特别是在中国近年来过分强调SCI论文的学术环境下,无法对运筹学应用方面的成果做出公正的评价。如何尽最大可能地摆脱目前不科学的科研成果评价体系,是中国运筹学界所面临的再一个挑战。

  运筹学经过几十年的发展,现在分支越来越多,方向越分越细,理论越来越艰深,运筹学工作者之间的合作变得越来越难。对某一个问题,不同的运筹学工作者建立了不同的模型,使用了不同的方法。这就更需要合作,从不同的角度处理同一个问题,才能给出完整的解答。如何形成团队,并开展有效的合作,是中国运筹学界所面临的第五个挑战。

  我国现行的教育和科研体制几乎将学科分类推到了极致,这不利于运筹学这样一个具有交叉性的、应用基础性的学科发展。从谷歌、脸书等例子来看,信息服务产业中许多最有创造的想法都来自于年青人。而我们国家中学里的应试式教育和大学里的灌输式教育都极大地抑制了年青人的创造性。我国许多运筹学工作者还没有认识到自己研究领域的作用在不断扩大,从而限制了他们培养学生和吸引更多学生的能力。我国整个运筹学界需要共同努力,积极参与和推动重新设计大学数学科学课程,并改进数学界与外界保持联系的机制,吸引更多的学生们到运筹学领域,储备更多的高端人才,满足未来运筹学发展的需求。如何实现这个目标,是中国运筹学界面临的第六大挑战。

  五、本学科发展趋势

  遵循大多数学科发展的一般规律,数学的发展和进步通常是由内部因素和外部因素共同驱动的。本世纪随着科学技术的日新月异的发展,经济的全球化,可以预测在探索生命和社会发展规律的过程中将形成崭新的数学,而运筹学将在这一过程中起到重要作用,并形成新的交叉领域与学科增长点。

  20世纪中期,随着蛋白质空间结构的解析和DNA双螺旋结构的发现,形成了以遗传信息载体核酸和生命功能执行者蛋白质为主要研究对象的分子生物学。而21世纪初人类基因组计划的完成,标志着生命科学研究进入了一个崭新的后基因组时代。运筹学已经逐步应用到生物信息学和系统生物学等诸多新兴的生命科学研究领域,并且发挥着重要的作用。一方面,线性规划、非线性规划和整数规划在蛋白质结构比对和结构预测中作为重要工具经常使用;另一方面,现代生命科学对运筹学理论和方法提出了新的需求和巨大的挑战。当然,系统生物学要成为一门独立的分支学问需建立自己的“公理系统”、“基本理论”以及实验和算法体系,运筹学将在这一过程中起到其独特的作用。

  网络科学是21世纪刚刚兴起的一个新的交叉学科。它以复杂网络为主要研究对象,通过对复杂网络特性的提取和刻画,探究其所反映的复杂系统的普遍规律。运筹学的各个分支,特别是最优化方法和图论已在网络科学中发挥了重要作用。今后十年内,网络科学预期在网络生成模型和网络演化特征的刻画方面将有重大的突破,并成为应用科学的主流性分支。网络科学目前尚处于实证研究为主的阶段,它要真正成为一门独立的科学分支,必须建立其基础理论、运算理论,以及从目前的实证地从实际世界中提炼网络模型,发展到应用网络理论去建立自然界的或技术性的系统,使其具有特定的性质。在这一过程中,运筹学可以成为一个主要的工具。

  管理科学从其一开始就与运筹学有着密切的关系,其早期的重点是用运筹学的方法来研究有管理背景的实际问题。管理科学不仅为运筹学的研究和实践提供了一个很好的应用领域,而且它也为运筹学的发展提供了很多挑战性的课题。未来几个具有代表性的研究方向包括:(1)管理科学中的一些实证研究;(2)风险管理问题;(3)一些经典的随机存储问题;(4)多服务台随机排队模型广泛应用于银行的顾客服务。

  服务科学近年来在国内引起人们普遍关注。它基于服务经济的管理理念,是一门研究管理与被管理关系的、旨在形成二者良性互动的和谐关系的新学科方向。服务中最关键的要素是人的行为。对于不含人的“机械”系统,系统的行为是“完全理性”的。运用经典的运筹学、统计学和信息学对这类系统可以进行比较令人满意的理论分析,并相应地提出了较理想的解决策略。但对于涉及人的系统,人的行为表现出一些特有的现象,人们并不总是追求“效用最大”,而是会根据对环境的认知和自己有限的思维,做出“让自己满意的选择”,亦即人的行为的一个最基本特征是“有限理性”。因此,经典的运筹学、统计学和信息学不能被直接于应用以人为中心的服务系统。为此,未来需要研究的重要课题是:如何将行为科学与经典的运筹学相结合,建立“行为运筹学”的理论体系,为以人为中心的服务系统的性能分析、最优设计和最优控制奠定理论基础。

  大数据是指无法在一定时间内用常规软件工具对其内容进行抓取、管理和处理的数据集合。数据成本的下降助推了数据量的增长,新的数据源和数据采集技术的出现大大增加了数据的类型,数据间复杂的相互联系使大数据的处理变得异常困难。大数据的分析和研究不应停留在获得概率分布结果,也不应满足于对细节问题的数据挖掘,而是应争取从大数据中获得新知识,实现社会科学的“变革式”进步。数据分析的主要手段就是给数据建立起数学结构,这种数学结构可以是多方面的:拓扑的、几何的、或代数的。所以,数据科学给数学也带来了许多根本性的问题。数据和数,方程以及图形一样,也将成为数学研究的基本元素之一。

       

 Operations Research

 

Overview of Operations Research

Operations Research (OR) is an interdisciplinary subject emerged in 1930s. As a formal discipline, OR originated in the efforts of military planners during World War II. In the World War II era,OR was defined as a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. Other names for it included operational analysis and quantitative management. In the decades after the war, with expanded techniques and growing awareness of the field at the close of the war, OR was no longer limited to only operational, but was extended to encompass equipment procurement, training, logistics and infrastructure. OR also grew in many areas other than the military once scientists learned to apply its principles to the civilian sector. With the development of the simplex algorithm for linear programming in 1947 and the development of computers over the next three decades, OR can now solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently. Today OR is used by virtually every business and government throughout the world and remains an active area of academic research.

OR mainly studies how tofind optimal or satisfactory solutions through mathematical and computational theories and methods for social and engineering systems. Sometimes the term management science is used as synonyms for operations research. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, OR arrives at optimal or near-optimal solutions to complex decision-making problems. In a nutshell, OR is the discipline of applying advanced analytical methods to help make better decisions. To achieve these results, OR professionals draw upon the latest analytical technologies, including (1) simulation that enables people to try out approaches and test ideas for improvement, (2) optimization that narrows people’s choices to the very best when there are virtually innumerable feasible options and comparing them is difficult, and (3) probability and statistics that help people to measure risk, mine data to find valuable connections and insights, test conclusions, and make reliable forecasts.

A typical methodology of OR could be summarized as following phases: (1) define and formulate a mathematical model for the problem of interest; (2) study the properties of the solutions to the resulting mathematical problem and hardness to find them; (3) develop an algorithm for deriving solutions to the problem and analyze the performance of the proposed algorithm in terms of time efficiency and solution accuracy; (4) implement the algorithm in simulated environment and study the results obtained in simulations; (5) determine the effectiveness of the proposed model and algorithm and give a practical method for solving the original problem. It needs to emphasize that those phases are not independent and carried out sequentially; sometimes some of them have to be repeated many times before the problem is solved.

The major sub-disciplines in modern OR include mathematical programming, queuing theory, game theory, inventory theory, logistics and stochastic models / processes. Typical problems that OR professionals are interested include the problems of allocation, facility location, assignment, project planning, routing, scheduling, supply chain management and so on.

OR overlaps with other disciplines, notably industrial engineering and operations management. It is often concerned with determining a maximum (such as profit, performance, or yield) or minimum (such as loss, risk, or cost). OR encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queuing theory, Markov decision processes, economic methods, data analysis, statistics, neural networks, expert systems, and decision analysis. Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system.

Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science. OR professionals faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power.

Development of Operations Research in China

In 1955 Hsue-shen Tsien and Guo-zhi Xu gave the initial drive to the OR development in China after they returned China from the United States of America and in 1956 they established the first OR group in the institute of mechanics within Chinese Academy of Science. In late 1950s OR professionals in China focused on transportation and facility location problems. The world-wide famous Chinese postman problem was proposed by Mei-gu Guan in 1961. In 1960s Loo-keng Hua traveled around more than twenty provinces in China promoting the optimization and critical path methods in numerous factories and country sides. His hard work and unremitting efforts exerted great impact in China and even received praise from Tse-tung Mao. In 1970s OR group in the institute of mathematics within Chinese Academy of Sciences obtained many important results in the study of queuing theory, nonlinear programming and combinatorial optimization and trained many young teachers and students in these fields. They laid a solid foundation for OR development in China.

After China adopted the famous policy of reforming and opening to the outside world in 1978, OR development in China became faster as the international academic exchanges increased. Five important results were achieved in combinatorial optimization, the optimization of production system, graph theory, nonlinear programming and traffic management in cities and awarded the second-class prizes of national natural science, respectively. In addition, two Chinese OR groups won the first-class Prizes for OR in development of IFORS (International Federation of Operations Research Societies) in the evaluation of economic information system and the forecast of grain yields. At the same time Chinese impact in international OR community increased significantly. In 1982 OR society of China (ORSC) became one of the members of IFORS, and in 1985 became one for the founding members of APORS (the Association of Asia-Pacific Operational Research Society). Even more, in 1992 Guang-hui Hsu was elected as the vice-president of IFORS. In 1999 ORSC successfully conducted the fifteenth conference of IFORS at Beijing.

In recent five years, Chinese OR professionals have made lots of progresses in the main fields of OR including, mathematical programming, game theory, stochastic optimization, scheduling theory, supply chain management, computational system biology and so on, and some of them have already exert considerable impact in international OR community. In addition to that, Chinese OR professionals have put lots of effort in OR application by closely working with enterprises under some joint projects including, mobile network optimization, steel production and logistics, operating room scheduling and market forecasting of airline companies. The methods / techniques of independent intellectual property rights have been achieved, which greatly speeds up the innovation pace of enterprises involved. During this period, two ex-presidents of ORSC, Xiang-sun Zhang and Ya-xiang Yuan, were elected as the vice-presidents of IFORS representing APORS, respectively. Moreover, Ya-xiang Yuan, who is the academician of Chinese Academy of Sciences, will give an invited talk in the International Congress of Mathematicians at Korea in 2014.

Operations Research Development in Future

In addition to ascertaining that the internal vitality of the mathematical sciences is very impressive, the current study has found a striking expansion in their impact on other fields, as well as an expansion in the number of mathematical sciences subfields, such as OR, that are being applied to challenges outside of the discipline. This expansion has been ongoing for decades, but it has accelerated greatly over the past 10~20 years and will keep the same pace in the future. Some of these links develop naturally because so much of science and engineering now builds on mathematical modeling, computation and simulation for which the mathematical sciences are the natural language. In addition, data-collection capabilities achieved in recent years have expanded enormously and will continue to do so in the future, and the mathematical sciences are innately involved in distilling knowledge from all those data. However, mechanisms to facilitate linkages between mathematical scientists and researchers including OR professionals in other disciplines must be improved. This is particularly urgent in China where prevailing SCI journals / papers oriented research have prevented most of OR experts or graduate students to work with professionals in other areas focusing on some key problems of real importance and potential applications.

The impacts of mathematical science research can spread very rapidly in some cases, because a new insight can quickly be embodied in software without the extensive translation steps that exist between, say, basic research in biology and the use ofa collected data. When mathematical sciences research produces a new way to compress or analyze data, value financial products, process a signal from a medical device or military system, or solve the equations behind an engineering simulation, the benefit can be realized quickly. For that reason, even government agencies or industrial sectors that seem disconnected from the mathematical sciences have a vested interest in the maintenance of a strong mathematical sciences enterprise for the technology innovation. And because that enterprise must be healthy in order to contribute to the supply of well-trained individuals in science, technology, engineering, and mathematical fields, it is clear that everyone should be aware of the vitality of the mathematical sciences including OR.

In the future, OR will develop rapidly and fruitfully in some interdisciplinary areas including life science, network science, management science, behavior OR and service science, economics as well as big data science and technology. OR professionals will play a more important role not only helping solve some concrete scientific or technical problems but also establishing some new subjects of OR and enriching the tank of OR methods and techniques. In summary, OR will have another golden age when facing so many challenges and exciting opportunities in the next 10~20 years.