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Introduction
1 Motivation
Substantial progress was made in the 1950s and 1960s with the development of algorithms and computer codes to solve
large mathematical programming problems. The number of applications of these tools in the 1970s was less then expected,
however, because the solution procedures formed only a small part of the overall modeling effort. A large part of the time
required to develop a model involved data preparation and transformation and report preparation. Each model required many
hours of analyst and programming time to organize the data and write the programs that would transform the data into the
form required by the mathematical programming optimizers. Furthermore, it was difficult to detect and eliminate errors
because the programs that performed the data operations were only accessible to the specialist who wrote them and not to the
analysts in charge of the project.
OsiMosek
OsiXpress
PATHNLP
PATH
PYOMO
SBB
SCIP 3.2
SNOPT
SOPLEX 2.2
XA
XPRESS 28.01
全局--局部非线性优化求解套件
随机求解器,包括一个无限制版本的LINDOGLOBAL
成熟全局解决方案的MINLP求解器
在LINGO模型系统中使用求解器求解GAMS模型的链接
混合邻域搜索算法
GAMS线性回归求解器
MCP求解器
NLP求解器
大型LP/MIP加锥凸非线性规划系统
全局优化的多启动方法
使用其他GAMS NLP求解器把MPEC转换成NLP
全局优化的多头启动方法
Bare-Bone与CPLEX连接
Bare-Bone 与Gurobi连接
Bare-Bone与 Mosek 连接
Bare-Bone与 Xpress 连接
凸面问题的大规模NLP求解器
大规模MCP求解器
在PYOMO模型系统中使用求解器求解GAMS模型的链接
求解MINLP模型的分支定界算法
高性能约束整数规划求解器
基于NLP求解器的大规模SQP算法
高性能LP求解器
大规模LP/MIP求解器
高性能LP/MIP求解器
GAMS
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.
GAMS lets you place explanatory text (shown in lower case) throughout your model, as you develop it. Your comments are automatically incorporated into the output report, at the appropriate places.
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