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GAMS是一款佳化的计算机数值分析商业软件。这种商业软件相当普遍,如 LINDO、DOT 等,以矩阵运算见长的 MATLAB 计算机软件亦有发展"optimization tool box",可以解各种非线性佳化问题的数值解。这里要介绍的GAMS,则是以简单清楚的使用者接口和强健稳定的数值分析能力见长。
通用代数建模系统(GAMS)是特别为建模线性,非线性和混合整数优化问题而设计的.本系统对于大型的,复杂的问题特别有帮助.GAMS可以运行在个人计算机、工作站、大型机和**级计算机上.
GAMS允许使用者通过制定简单的设置来把精力放在建模问题上.至于特定机器和系统软件执行的费时的细节将由GAMS系统来处理.
GAMS对于处理大型的,复杂的,需要多次修订才能终确定模型的的问题特别有帮助.系统以高 度简洁和自然的方式来建模问题.使用者能够快速和方便的更改公式,能从一个求解器转到另一个,甚至稍加费心就能从线性转换到非线性.
GAMS让使用者把精力集中到建模上.通过排除考虑纯技术上的机器特定的问题的需要,比如地址计算,存储分配,子程序链接,和输入输出和流程控制,GAMS增加了用于概念化和运行模型,和分析结果的时间.GAMS本身构建了良好的建模习惯,通过请求简明而的实体和关系的规范.GAMS语言形式上和通常使用的编程语言相似.因此对于那些有编程检验的使用者将非常熟悉.
使用GAMS,数据仅仅需要一次就能在熟悉的列表和表格形式中输入.模型以简练的代数声明来描述,对于人和机器都很*读懂.非常相关的约束的整个都被输入到一个声明中.GAMS自动生成每个约束等式,并让使用者处理例外情况,假使那里一般来说是不需要的.在模型中的声明能够被重用,而不需要更改代数式,当其它的实例是相同的或出现了相关问题.错误的位置和类型会在尝试解决方案前被查明.GAMS处理动态模型,包括时间序列,滞后,及暂时终点的提示和处理.
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GAMS Summation (and Product) Notation
Before going into equation definition we describe the summation notation in GAMS. Remember that GAMS is designed for
standard keyboards and line-by-line input readers, so it is not possible (nor would it be convenient for the user) to employ the
standard mathematical notation for summations.
The summation notation in GAMS can be used for simple and complex expressions. The format is based on the idea of always
thinking of a summation as an operator with two arguments: Sum(index of summation, summand) A comma separates
the two arguments, and if the first argument requires a comma then it should be in parentheses. The second argument can be
any mathematical expression including another summation.
As a simple example, the transportation problem contains the expression
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,
Model and Solve Statements
The word model has a very precise meaning in GAMS. It is simply a collection of equations. Like other GAMS entities, it
must be given a name in a declaration. The format of the declaration is the keyword model followed by the name of the
model, followed by a list of equation names enclosed in slashes. If all previously defined equations are to be included, you
can enter /all/ in place of the explicit list. In our example, there is one Model statement:
model transport /all/ ;
This statement may seem superfluous, but it is useful to advanced users who may create several models in one GAMS run. If
we were to use the explicit list rather than the shortcut /all/, the statement would be written as
model transport / cost, supply, demand / ;
The domains are omitted from the list since they are not part of the equation name. The list option is used when only a subset
of the existing equations comprises a specific model (or sub-model) being generated.
Once a model has been declared and assigned equations, we are ready to call the solver. This is done with a solve statement,
which in our example is written as
solve transport using lp minimizing z ;
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