Dear Experts,
I am looking for a solution for a convex optimization problem (linear programming) and I am thinking about evolutionary algorithms. Do you think it would be helpful?
for a linear programming problem, the simplex method converges in a finite no. of iterations if there is no degeneracy and a bounded feasible region. it operates by moving from one extreme point to another reducing the cost function along the way, because optimal solution for such an LPP lies at an extreme point only.
In using evolutionary algorithms, there is no guarantee of convergence or convergence can take a very large number of iterations.
Dear Mahshid
Dobopam answered to perfection your question
If the problem is feasible or bounded, the Simplex will find the optimum
I will only add that the simplex looks for the best solution following the vertexes of a polygon, a polyhedron, or a polytope, as per the fundamental theorem of LP, depending on the number of alternatives, that contain all feasible solutions. There is no guessing here.
This is the reason by which LP is the only method in MCDM that can determine if a problem is or not feasible. All the other methods assume that it is feasible, and then, may yield solutions that are unreal
If the problem is unfeasible, LP will tell it by writing a warning to the DM.
Dear Debopam Ghosh and Nolberto Munier
Thanks for your great guide, by the way, is there another optimal solution rather than using the simplex method?
From my point of view, one of the reasons is the subjectivity in all methods, except in LP, which works without weights, assumptions, or preferences. The Simplex algorithm, developed by Dantzig in 1948, based on the work of Kantorovich (1939), which was awarded the Nobel prize in 1956 for his invention of LP, was nominated as one of the ten best algorithms in the XXth Century. No other MCDM method doesn't even come close to LP
In LP everything is mathematically supported. The DM has the great responsibility of selecting the criteria and establishing, from the point of view of real issues, limits for them. His contribution is essential in analyzing the final results which are completely objective, but that can be modified, even rejected by the DM.
It is not the same to work on a solid base that one uncertain based on subjectivity
Remember one thing, LP is the only method, except perhaps CRITIC, that always gives the same result, no matter who is applying it. Obviously, this does not apply to any other method
Dear Debopam
I agree with you, however, I understand that it is more difficult than the Simplex, albeit more powerful than the Simnplex
Most LPs arising in practice can be solved quickly using simplex. For very large and/or degenerate instances, interior point methods (IPMs) may be faster. Many solvers (e.g., CPLEX, Gurobi, Xpress, MOSEK) allow the user to try several methods.
Dear Adam N. Letchford , Silvia Carvalho
, Nolberto Munier , and Debopam GhoshThanks for your amazing answers, so helpful.
I would like to invite you to have a look on the following links.
SSO: https://www.mathworks.com/matlabcentral/fileexchange/92150-sperm-swarm-optimization-sso
HSSOGSA: https://www.mathworks.com/matlabcentral/fileexchange/92130-hssogsa?s_tid=srchtitle
MOSFP: https://github.com/sh7adeh1990/MOSFP
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