Hello..

I correct two typos, read again about Mixed integer linear programming
and linear programming..

Mixed integer linear programming problems are much harder to solve than
linear programming problems. In terms of computational complexity, LP's
can be solved in polynomial time while solving MILP is an NP-Hard
problem. The known algorithms for solving MILP's have exponential worst
case complexity.

And read about a comparison of Open-Source Linear Programming Solvers
from Sandia National Laboratories:

https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2013/138847.pdf

And i think that Symphony is the best non-commercial MILP solver with an
ECLIPSE PUBLIC LICENSE here:

https://github.com/coin-or/SYMPHONY/blob/master/LICENSE

I think Symphony MILP solver has a decent performance, read here to
notice it:

http://strimas.com/prioritization/scip-performance/

But i have noticed that the sensitivity analysis in Symphony MILP solver
is part of the callable library and is not part of the command-line
Symphony MILP solver.

Also i think that CLP is the best non-commercial linear programming solver.

About my linear programming modeling examples in Object Pascal..

I have just updated my Linear programming modeling examples in Object
Pascal, and i have just included the last stable version of 64bit
Symphony MILP solver inside the zip file, so just pass it the MPS output
file from the object pascal example.

You can download it from:

https://sites.google.com/site/scalable68/linear-programming-modeling-examples-in-object-pascal

And about optimization..

Advances in integer optimization from 1988 to 2017:

– Improved algorithms and methods: 147,650 times faster

– Improved computing power: 17,120 times faster

– Overall improvement: 2,527,768,000 times faster

In practice, this means that solving a typical MILP problem would have
taken 80 years back in 1988, whereas today it only takes one second.
However, while MILP problem solving is nowadays standard technology,
MINLP problems still pose a challenge.This is motivating and inspiring
researchers in the field.

Read more here:

The world’s fastest

https://www.abo.fi/en/news/the-worlds-fastest/

Optimization is a special area within Mathematics and Engineering. The
idea of optimization is to find the best possible – or a sufficiently
good – solution to a problem given in the form of a mathematical
description of a system or process.

And about optimization, i have just included the 64 bit SYMPHONY solver
for mixed-integer linear programs (MILPs), with a batch file that
executes the MPS file, inside the zip file that you can download from here:

https://sites.google.com/site/scalable68/linear-programming-modeling-examples-in-object-pascal

And read my following webpage about my Linear programming formulation of
the Shortest-Route problem in object pascal to understand more:

http://pages.videotron.com/aminer/lp/linear.htm

Thank you,
Amine Moulay Ramdane.