GAMS (General Algebraic Modeling System)

GAMS (General Algebraic Modeling System) is a high-level modeling system specifically designed for mathematical programming and optimization. It was first introduced in the early 1980s by Alexander Meeraus at the World Bank as a tool for solving complex linear, nonlinear, and mixed-integer optimization problems. The language is designed to work with large-scale models, particularly in fields such as economics, engineering, energy, agriculture, and management science. Its primary purpose is to help modelers formulate mathematical problems and then solve them using various optimization solvers.

What makes GAMS unique is its ability to handle a wide variety of mathematical problems by providing a consistent environment for model formulation and solution. It supports various optimization types, including linear programming (LP), nonlinear programming (NLP), mixed-integer programming (MIP), dynamic optimization, and more. This makes it a flexible tool for researchers and professionals working with complex mathematical models across diverse domains.

The structure of GAMS is relatively straightforward. A GAMS program consists of declarations of sets, parameters, variables, and equations, followed by model definition and execution commands to solve the model. The language emphasizes ease of use, allowing the modeler to concentrate on the mathematical structure of the problem rather than algorithmic details.

Here is an example of a simple linear programming problem formulated in GAMS:

Sets
  i /1*3/;
  
Parameters
  a(i) / 1 1, 2 2, 3 3 /;
  
Variables
  x(i), z;
  
Equations
  objective, constraint;
objective .. z =e= sum(i, a(i) * x(i));
constraint .. sum(i, x(i)) =l= 10;
Model simpleModel /all/;
Solve simpleModel using lp maximizing z;

In this example, a simple linear optimization model is defined. The objective equation maximizes the value of z, and the constraint ensures that the sum of variables x(i) is less than or equal to 10. The model is then solved using linear programming (lp).

GAMS is particularly beneficial when working with:

Large-scale models: It is ideal for handling optimization problems that involve thousands of variables and constraints.
Scenario analysis: GAMS is frequently used to explore multiple scenarios and perform sensitivity analysis, often used in energy planning and economic modeling.
Complex economic and engineering systems: Professionals in fields like energy, transportation, and agriculture use GAMS to model complex systems and optimize resource use and planning.

Many industries use GAMS for decision-making processes, such as power systems optimization, logistics, investment planning, and resource allocation. Given its extensive library of solvers and its ability to handle multiple types of optimization problems, GAMS remains a popular tool in academic research and industry, offering both flexibility and scalability for optimization challenges.

Codes