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A GAMS Tutorial by Richard E. Rosenthal
1 Introduction
The introductory part of this book ends with a detailed example of the use of GAMS for formulating, solving, and analyzing
a small and simple optimization problem. Richard E. Rosenthal of the Naval Postgraduate School in Monterey, California
wrote it. The example is a quick but complete overview of GAMS and its features. Many references are made to other parts
of the book, but they are only to tell you where to look for more details; the material here can be read profitably without
reference to the rest of the book.
The example is an instance of the transportation problem of linear programming, which has historically served as a 'laboratory
animal' in the development of optimization technology. [See, for example, Dantzig (1963) 1. ] It is a good choice for
illustrating the power of algebraic modeling languages like GAMS because the transportation problem, no matter how large
the instance at hand, possesses a simple, exploitable algebraic structure. You will see that almost all of the statements in the
GAMS input file we are about to present would remain unchanged if a much larger transportation problem were considered.
In the familiar transportation problem, we are given the supplies at several plants and the demands at several markets for a
single commodity, and we are given the unit costs of shipping the commodity from plants to markets. The economic question
is: how much shipment should there be between each plant and each market so as to minimize total transport cost?
The algebraic representation of this problem is usually presented in a format similar to the following
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,
设计不一样的规则
我们努力去适应,而非直接拿来。
GAMS专注于其核心竞争力:让用户创建可读性、可维护的模型,用好的求解方法解决任何问题。开放的体系结构和多个数据接口允许与外部系统无缝通信。
模型、求解器、数据、平台和用户界面立层,便于切换求解器、使用多个数据集、在多个平台运行以及将GAMS整合到现有的应用、结构和工作流中去。
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。
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Sets
Sets are the basic building blocks of a GAMS model, corresponding exactly to the indices in the algebraic representations of
models. The Transportation example above contains one Set statement:
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