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c('Seattle','New-York') = 0.40;
is a valid GAMS assignment statement.
The same parameter can be assigned a value more than once. Each assignment statement takes effect immediately and
overrides any previous values. (In contrast, the same parameter may not be declared more than once. This is a GAMS error
check to keep you from accidentally using the same name for two different things.)
The right-hand side of an assignment statement can contain a great variety of mathematical expressions and built-in functions.
If you are familiar with a scientific programming language such as FORTRAN or C, you will have no trouble in becoming
14 A GAMS Tutorial by Richard E. Rosenthal
comfortable writing assignment statements in GAMS. (Notice, however, that GAMS has some efficiencies shared by neither
FORTRAN nor C. For example, we were able to assign c(i,j) values for all (i,j) pairs without constructing 'do loops'.)
The GAMS standard operations and supplied functions are given later. Here are some examples of valid assignments. In all
cases, assume the left-hand-side parameter has already been declared and the right-hand-side parameters have already been
assigned values in previous statements
GAMS是灵活而强大的.模型可以非常方便的从一个计算机平台移到另外一个,只要GAMS已经在每个平台被安装好.GAMS很容易进行敏感度分析.使用者能够方便的规划模型来求解一个成分的不同值,然后生成一个输出报告,列出了每种情况的解决方案特征.模型能够同时被开发和文档化,因为GAMS允许使用者包含解释性的文本来作为任意符号和等式的定义和解释.
GAMS不断的在被增强和扩展.2.25版本包含了多个语言扩展,例如在一个循环中的SOLVE声明,INCLUDE声明,IF-ELSE声明,和使用PUT声明进行报告编写的功能.其它的加强包括增加的系统集成特征,性能改善,新的子系统,和另外的计算机平台支持.
当前版本2.50包括一个基于Intel Windows平台(95/98/ME和NT/2K/XP)的集成开发环境(IDE).GAMS 2.50的新的分发包含新的语言特征和新发表的全新/更新的求解器,一年至少4次.请检查版本声明.
示例:
从的1963书(由George Dantzig编写)中提取的一个运输问题,用来描述GAMS的有效性.这个模型只是模型库中的部分,模型库中还包含了大量的完整GAMS模型.
支持模型的类型:
GAMS模型类型包括LP,MIP和NLPs的不同形式.这里列出了GAMS支持的所有的模型类型.
GAMS 的发展背景
GAMS 是"General Algebraic Modeling System"(一般性代数仿真系统)的缩写,早是由美国的世界银行(World Bank)的 Meeraus 和 Brooke [Brooke, Kendrickm and Meeraus, 1992]所发展。"GAMS"事实上并不代表任何佳化数值算法,而只是一个语言的使用者接口,利用 GAMS 可以很容易建立、修改、除错你的佳化模型输入文件,而输入档经过编译后,成为较低阶的佳化数值算法程序所能接受的格式,再加以执行并写出输出档。
数值算法方面,对线性与非线性规划问题,GAMS 使用由新南韦尔斯大学的Murtagh、及史丹福大学的 Gill、Marray、Saunders、Wright 等所发展的 MINOS [Murtagh and Saunders, 1983] 算法。MINOS是 "Modular In-core Non-linear Optimization System"的缩写,这个算法综合了缩减梯度法和准牛顿法,是为大型、复杂的线性与非线性问题设计的算法。对混合整数规划问题,则采用亚历桑那大学的 Marsten 及巴尔第摩大学的 Singhal[1987]共同发展的 ZOOM(Zero/One Optimization Method)算法。
In Section The Dollar Condition, we describe how to use the dollar operator to impose restrictions on the summation operator
so that only the elements of i and j that satisfy specified conditions are included in the summation.
Products are defined in GAMS using exactly the same format as summations, replacing Sum by Prod. For example,
prod(j, x(i, j))
is equivalent to: Pjxi j.
Summation and product operators may be used in direct assignment statements for parameters. For example,
GAMS was developed to improve on this situation by:
• Providing a high-level language for the compact representation of large and complex models
• Allowing changes to be made in model specifications simply and safely
• Allowing unambiguous statements of algebraic relationships
• Permitting model descriptions that are independent of solution algorithms
2 Basic Features of GAMS
2.1 General Principles
The design of GAMS has incorporated ideas drawn from relational database theory and mathematical programming and
has attempted to merge these ideas to suit the needs of strategic modelers. Relational database theory provides a structured
framework for developing general data organization and transformation capabilities. Mathematical programming provides a
way of describing a problem and a variety of methods for solving it. The following principles were used in designing the
system:
1. All existing algorithmic methods should be available without changing the user's model representation. Introduction of
new methods, or of new implementations of existing methods, should be possible without requiring changes in existing
models. Linear, nonlinear, mixed integer, mixed integer nonlinear optimizations and mixed complementarity problems
can currently be accommodated.
2. The optimization problem should be expressible independently of the data it uses. This separation of logic and data
allows a problem to be increased in size without causing an increase in the complexity of the representation.
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