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Note that this simple example reveals some modeling practices that we regard as good habits in general and that are consistent
with the design of GAMS. First, all the entities of the model are identified (and grouped) by type. Second, the ordering
of entities is chosen so that no symbol is referred to before it is defined. Third, the units of all entities are specified, and,
fourth, the units are chosen to a scale such that the numerical values to be encountered by the optimizer have relatively small
absolute orders of magnitude. (The symbol $K here means thousands of dollars.)
The names of the types of entities may differ among modelers. For example, economists use the terms exogenous variable
and endogenous variable for given data and decision variable, respectively. In GAMS, the terminology adopted is as follows:
indices are called sets, given data are called parameters, decision variables are called variables, and constraints and the
objective function are called equations.
The GAMS representation of the transportation problem closely resembles the algebraic representation above. The most
important difference, however, is that the GAMS version can be read and processed by the computer.
Table 1: Data for the transportation problem (adapted from Dantzig, 1963) illustrates Shipping Distances from Plants to
Markets (1000 miles) as well as Market Demands and Plant Supplies.
通用代数建模系统(GAMS)是数学编程和优化的建模系统。它由一个语言编译器和一个稳定的集成各种高性能的求解器组成。GAMS适用于复杂的、大规模的建模应用,并允许您创建大的维护模型以很快的适应新的情况。
立的模型和求解器
提供**过25个广泛和多样化的求解器组合,包括所有预期的商业化求解器。
LP/MIP/QCP/MIQCP: CPLEX, GUROBI, MOSEK, XPRESS
NLP: CONOPT, IPOPTH, KNITRO, MINOS, SNOPT
MINLP: ALPHAECP, ANTIGONE, BARON, DICOPT, OQNLP, SBB
混合互补问题求解器(MCP)、平衡约束数学规划求解器(MPEC)和约束非线性系统求解器(CNS)
免费到每个GAMS系统中的 (比如 BONMIN (MINLP), CBC (LP, MIP), COUENNE (MINLP), IPOPT (NLP)。教育版还包括了SCIP和SOPLEX。
选择使用的求解器非常简单---只要改变一行代码或者调整一个选项设置就可以了。想要比较求解器的性能或者看有什么改进的可能,也不需要做任何的设置。同样的,模型类型可以轻松切换(比如:线性和非线性),尝试不同的公式也非常的*。通过使用GAMS,您可以得到一个广泛类型的模型和求解器的环境。
立的模型和数据
你可以编写立的模型数据,包括各种不同来源的数据,从ASCII到Excel或者Access 以及其他各种来源。比如使用GDX(GAMS数据交换)文件格式。GDX文件可以保存一个或多个GAMS符号的值,比如集、参数变量和方程。GDX文件可以为GAMS模型准备数据、展示GAMS模型的结果、使用不同的参数为这同一个模型保存结果等。GDX文件不能保存一个模型的公式或者执行语句。GDX文件二进制文件,可在不同平台进行移植。
ALPHAECP
AMPL
ANTIGONE 1.1
BARON
BDMLP
BENCH
BONMIN 1.8
CBC 2.9
CONOPT 3
CONOPT 4
CONVERT
COUENNE 0.5
CPLEX 12.7
DE
DECIS
DICOPT
EXAMINER
GAMSCHK
GLOMIQO 2.3
GUROBI 7.0
GUSS
IPOPT 3.12
JAMS
KESTREL
KNITRO 10.0
基于扩展平面切割(ECP)方法的MINLP求解器
在AMPL模型系统中使用求解器时与GAMS模型连接
MINLP确定性全局优化
成熟**解决方案的分支和减少优化向导
任意GAMS系统都配备了LP和MIP求解器
实用方便的GAMS求解器和验证方案
COIN-OR MINLP求解器执行各类分支定界和外逼近算法
高性能LP/MIP求解器
大型的NLP求解器
大型的NLP求解器
将模型转换成其他语言的标量模型的框架
(MI)NLP确定性全局优化
高性能LP/MIP求解器
产生和解决包括EMP/SP中的随机规划的确定等价
大规模随机规划求解器
求解MINLP模型框架
检查解点并评估其优点的工具
GAMS求解线性规划问题时对结构和解决方案属性的检查系统
混合整数二次模型分支定界全局优化
高性能LP/MIP求解器
有效解决多个相关模型实例的框架(收集更新分散的求解方案)
大规模非线性规划的内点优化算法
扩展数学规划求解器(包括LogMIP)
本地GAMS系统使用远程NEOS求解器框架
大型NLP求解器
求解器 描述
03
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
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