[Libreoffice-bugs] [Bug 100916] Solver does not find the optimal solution

[bugzilla-daemon at bugs.documentfoundation.org]

https://bugs.documentfoundation.org/show_bug.cgi?id=100916

--- Comment #10 from Todor Balabanov <todor.balabanov at gmail.com> ---
DEPS solver is hybrid heuristic optimizer. It is based on Differential
Evolution and Particle Swarm Optimization. 

If you look a little bit more of DE's chart-flow diagram you will see that DE
works well with high dimensional spaces:

http://www1.icsi.berkeley.edu/~storn/de2.jpg

The example given in this bug report has only two variables (radius and
height), which means that this is two-dimensional space. The constraint of 1000
volume makes the situation even worse. We call this kind of constraints "hard
constraints", because usually they are difficult to be satisfied. 

DE is in the group of the genetic algorithms. It has crossover operation:

https://www.obitko.com/tutorials/genetic-algorithms/crossover-mutation.php

When you have only two variables your chromosomes have only two components.
Literally you do not have what to crossover. It is absolutely expected that DE
will perform bad in such situations. 

I am not good in PSO part of the solver, but PSO is an optimization heuristics
in the rank of DE. Even if you check the source code you will see that PSO has
pretty similar implementation to DE. This means that PSO also is not proper for
low-dimensional problems.

I am not using Microsoft Excel (generally I am not using Windows) and it is
difficult for me to test this example in Excel, but there is no direct
correspondence between Excel solvers and Calc solvers. It does not matter that
Excel solves this example efficiently. First of all most of the source code in
Microsoft's products is closed. May be they are using some kind of DE, GA, PSO
or something else, but may be they are using also something extra, which is
particularly implemented for low-dimensional cases.

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