Solving Linear Programming Problem in SymPy

[Shekhar Prasad Rajak]

Hello,

This thread is about the solving Linear/Non linear Programming problem. This topic is related to Optimization Technique, Operations Research.

Linear programming (LP) (also called linear optimization) is a method to achieve the best

outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by

linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).

Currently I don't see any method to solve these kinds of problems in SymPy. Most of the time we use simplex method or its

expansion to solve them.

Example:

Maximize z = 12x+40y

subjected to :

  x+y<=16

  x+3y<=36

  x<=10

  x>=0

  y>=0

find x,y and maximum value of z.

Soln : (x, y) = (0,12) and maxi value at this point is 480.

Let me know if there is already some way to solve these using SymPy methods or it is good idea to implement it.

Related links :

Linear Programming: https://en.wikipedia.org/wiki/Linear_programming

Simplex method: https://en.wikipedia.org/wiki/Simplex_algorithm

Wolfram: http://reference.wolfram.com/language/tutorial/ConstrainedOptimizationLinearProgramming.html

SciPy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html

Other tools: http://stackoverflow.com/questions/10697995/linear-programming-in-python

--

Shekhar

[Jason Moore]

Shekar,

Here is an example that uses sympy to let a user specify linear program optimization problems symbolically and then it is solved numerically:

https://github.com/biosustain/optlang

Here is another package I wrote that does NLP for optimal control systems.

https://github.com/csu-hmc/opty

Jason
moorepants.info
+01 530-601-9791

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[Shekhar Prasad Rajak]

Thanks Jason for sharing the links. They are good.

--

Shekhar

Jason
moorepants.info
+01 530-601-9791

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[Denis Akhiyarov]

The de-facto standard for solving linear programming problems in Python are PuLP and Pyomo. Pyomo can also handle non-linear problems and even differential equations. In fact, Pyomo calls into SymPy for differentiation! Pyomo was heavily inspired by AMPL.
Now if you want to ensure convexity of your problem, then go for CVX(PY).
Recently scipy added linear programming, but I have not seen much use for it.

[Shekhar Prasad Rajak]

Thanks Denis. 

I personally feel that SymPy must have similar functions which uses(wrote with) internal methods of SymPy.

--

Shekhar

[Donaldson Tan]

Does Sympy have a backend to interface with Pyomo?

[Chris Smith]

There are now functions for doing linear programming in the `simplex.py`. Here is a similar question at SO with answer: https://stackoverflow.com/a/77045152/1089161

/c