Optimization.SimplexTwoPhase Function

Linear optimization by Two-Phase Simplex algorithm.

Pascal

function SimplexTwoPhase(const A: TMtx; const b: TVec; const c: TVec; const relations: String; const AFinal: TMtx; const X: TVec; const Indexes: TVecInt; out SolutionType: TLPSolution; Minimize: boolean = true; const Verbose: TStrings = nil): double;

File

Optimization

Description

Solves the following optimization problem:

where rel holds the relation signs. For example, relation string ' < = > ' means the constraints system consists of one inequality ' <= ', one equality ' = ' and one more inequality ' >= '.

Optionally, you can also assign TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring.

See Also

SimplexDual, SimplexLP

Example

Solve the following LP problem:

f(x) = x1+x2+2*x3-2*x4

subject to:

x1+2x <= 700

2x2-8x4 <= 0

x2-2x3+x4 > 1

x1+x2+x3+x4 = 1

which translates to using two-phase simplex method:

Uses MtxExpr, Optimization, Math387; procedure Example; var A, AF: Matrix; b,c,indexes,x: Vector; sol: TLPSolution; f: double: begin A.SetIt(4,4,false,[1,1,0,0 0,2,0,-8, 0,1,-2,1, 1,1,1,1]); b.SetIt(false,[700,0,1,1]); c.SetIt(false,[1,1,2,-2]); f := SimplexTwoPhase(A,b,c,'<<>=',AF,x,indexes,sol,true,nil); end;

#include "MtxExpr.hpp" #include "Math387.hpp" #include "Optimization.hpp" void __fastcall Example; { sMatrix A,Af; sVector b,c,x,indexes; TLPSolution sol; A.SetIt(4,3,false, OPENARRAY(double,(1,1,0,0 0,2,0,-8, 0,1,-2,1, 1,1,1,1))); b.SetIt(OPENARRAY(double,(700,0,1,1))); c.SetIt(OPENARRAY(double,(1,1,2,-2))); // Find minimum using above system double f = SimplexTwoPhase(A,b,c,"<<>=",Af,x,indexes,sol,true,NULL); }

Optimization, Functions, Example, See Also

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