What is GAMSPy?#

GAMSPy combines the high-performance GAMS execution system with the flexible Python language, creating a powerful mathematical optimization package. It serves as a bridge between the expressive Python language and the robust GAMS system with its extensive collection of integrated solvers, enabling you to create and solve complex mathematical models effortlessly. This allows creating full pipelines in Python by using your favorite packages for preprocessing (e.g. data cleaning) and postprocessing (e.g. visualization) along with GAMSPy.

What is GAMSPy?

Why is GAMSPy fast?#

GAMSPy delegates the expensive assignment and solve statements to the GAMS execution system. Set-based operations are at the core of the GAMSPy and GAMS execution system. For example, in many optimization libraries, you would write your equations as shown in the Other Libraries block below:

import other_library as ol
from numpy.random import uniform

m = ol.Model()
m.i = ol.Set(records=range(500))
m.i = ol.Set(records=range(1000))
data = uniform(0, 1, (500, 1000))
data[data > 0.01] = 0
m.a = ol.Parameter(m.i, m.j, records=data)
m.b = ol.Parameter(m.i, records=uniform(0,1, 500))
m.x = ol.Variable(m.i, m.j)

def e_definition(m, i):
  return sum(m.a[i, j] * m.x[i, j] for j in m.j) >= m.b[i]
m.e = ol.Equation(m.i, definition=e_definition)

import gamspy as gp
from numpy.random import uniform

m = gp.Container()
i = gp.Set(m)
j = gp.Set(m)
a = gp.Parameter(m, domain=[i, j])
b = gp.Parameter(m, domain=[i])
x = gp.Variable(m, domain=[i, j])
e = gp.Equation(m, domain=[i])
e[i] = gp.Sum(j, a[i, j] * x[i, j]) >= b[i]

data = uniform(0, 1, (500, 1000))
data[data > 0.01] = 0
i.setRecords(range(500))
j.setRecords(range(1000))
a.setRecords(data)
b.setRecords(uniform(0, 1, 500))

With the approach of other libraries, you iterate over all items of I and J. This approach has certain disadvantages:

  • It can get pretty verbose for long statements with many loops which decreases the readability.

  • The performance might suffer severely (depending on the implementation) when iteratating through many and sometime unnecessary items. Python loops are known to be very slow.

In contrast, the GAMSPy implementation employs set-based operations, which results in:

  • Concise and easier to read definitions.

  • GAMSPy definitions closely resemble mathematical notation that you would put in a paper making it easier to correctly code mathematical equations.

  • Great performance since the actual operation is performed by GAMS using robust and highly optimized low level code utilizing sparsity in the model’s data.

See also

Performance in Optimization Models: A Comparative Analysis of GAMS, Pyomo, GurobiPy, and JuMP

Model Instances vs. Mathematical Models#

Creating robust, readable, and maintainable models is an art rooted in algebraic formulation. The ability to express mathematical models in a language that retains the essence of algebraic notation and is machine-processable is paramount.

With this goal in mind GAMSPy has been developed to be able to generate mathematical models instead of model instances. Think of a mathematical model as a pure representation of mathematical symbols, devoid of specific data. In contrast, a model instance is the unrolled and constant folded representation of a model with its actual data. In a model instance, sum expressions are resolved into its individual components, and equation domains are resolved to individual scalar equations.

Mathematical Model

\[\sum_{i \in \mathcal{I}} \frac{p_{i,j} - q_i}{a_j} \cdot x_{i,j} \le \sum_{k \in \mathcal{K}} d_{k,j} \hspace{1cm} \forall \: j \in \mathcal{J}\]

Model Instance

\[ \begin{align}\begin{aligned}5 \cdot x_{i1,j1} + 3 \cdot x_{i2,j1} + 2 \cdot x_{i3,j1} \le 7\\2 \cdot x_{i1,j2} + 6 \cdot x_{i2,j2} + 4 \cdot x_{i3,j2} \le 10\end{aligned}\end{align} \]

Especially for complex models with many variables and equations, a model instance can become hard to manage. Therefore, GAMSPy leverages the concept of a standalone, data independent, and indexed representation of a mathematical model, which is very close to the original mathematical algebraic formulation.

Sparsity#

A key aspect of any modeling language is how it handles sparse multidimensional data structures. Many optimization problems are subject to a particular structure in which the data cube has a lot of zeros and only a few non-zeros, a characteristic referred to as sparsity. In optimization problems, it is often necessary to account for complex mappings of indices to subsets.

While you might be used to taking on the full responsibility to make sure only the relevant combinations of indices go into your variable definition in the Python modeling world, we especially focused on transferring the convenience and mindset of GAMS into Python by designing GAMSPy. As a result, GAMSPy automatically takes care of generating variables only for the relevant combinations of indices based on the algebraic formulation. This feature is particularly useful when working with a large multidimensional index space, where generating all possible combinations of indices would be both computationally expensive and unnecessary. GAMSPy handles this task quietly in the background, allowing us to focus on the formulation of the model.

Which backends does GAMSPy support?#

GAMSPy currently supports three backends: your local GAMS installation, GAMS Engine and NEOS Server. The default backend is the local GAMS installation that comes with GAMSPy. With GAMS Engine backend, you can run hundreds of jobs in the cloud in parallel to speed up your pipeline. You can also send your jobs to the NEOS Server, a free service for solving optimization problems. Make sure you understand the NEOS Terms of Use before you use this backend.

GAMSPy is also integrated with GAMS MIRO, allowing you to create fully interactive applications. The extensive visualization options in GAMS MIRO support decision-making based on optimization.

GAMS MIRO

Interoperability of GAMSPy#

A mathematical optimization model written in GAMSPy can be converted to GAMS or LaTeX format. Converting GAMSPy models to GAMS can be useful for rapid prototyping in GAMSPy and converting the model to GAMS to utilize certain features of GAMS (e.g., EMP-SP models) that are missing in GAMSPy. GAMSPy to LaTeX conversion can be convenient for including your model in an academic paper or verifying that the equations you have written match your mathematical intentions.

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