Do you Know algorism ESGP
Hi all
I have trouble with problem
Min f1(x) = 0.225x1 + 2.2x2 + 0.8x3 + 0.1x4 + 0.05x5 + 0.26x6
Min f2(x) = 10x1 + 20x2 + 120x3
Min f3(x) = 24x1 + 27x2 + 15x4 + 1.1x5 + 52x6
Subject to:
720x1 + 107x2 + 7080x3 + 134x5 + 1000x6 > 5000
0.2x1 + 10.1x2 + 13.2x3 + 0.75x4 + 0.15x5 + 1.2x6 > 12.5
344x1 + 1460x2 + 1040x3 +75x4 + 17.4x5 +240x6 > 2500
18x1 + 151x2 + 78x3 + 2.5x4 + 0.2x5 + 4x6 > 63
x1 < 6
x2 < 1
x3 < 0.25
x4 < 10
x5 < 10
x6 < 4
I dont now the algorism to solve this problem. anyone to know the algorism to solve? please help me to solve the problem
Thanks all
You have a multi objective LP to solve...
One way to to create a new function g(x) = w1*f1(x)+w2*f2(x)+w3*f3(x)
and Min g(x)...
here w1, w2, w3 are weights or relative importance of each objective.
Alternately, you can look up some literature on Goal Programming...
Sandie
Hi sandie384
I real want to find x1,x2,x3,x4,x5,x6... satisfy the F1(x),f2(x)..and the subjects.
This is mutiple objectives linear programming problem . I hear some name of the algorism (e.g Efficient Solution Via Goal Programming (ESGP), Linear goal Programming (LGP)), but I have not the algorism to solve this problems. I realy want solve this problems, it urgent. If you know the problems, please help me to solve it.
Thanks.
I would approach the problem as follows...
1. Solve 3 LPs for each of the objective functions independently. Let the Optimal values of the objective function be F1*, F2*, F3* respectively. this is simple enough, just do a simplex 3 times!
2. Now to set up the Goal Programming problem
Let D1 = F1(x) - F1*
D2 = F2(x) - F2*
D3 = F3(x) - F3*
3. Solve the new LP
min D1 + D2 + D3
Subject to:
720x1 + 107x2 + 7080x3 + 134x5 + 1000x6 > 5000
0.2x1 + 10.1x2 + 13.2x3 + 0.75x4 + 0.15x5 + 1.2x6 > 12.5
344x1 + 1460x2 + 1040x3 +75x4 + 17.4x5 +240x6 > 2500
18x1 + 151x2 + 78x3 + 2.5x4 + 0.2x5 + 4x6 > 63
x1 < 6
x2 < 1
x3 < 0.25
x4 < 10
x5 < 10
x6 < 4
Essentially we are trying to minimize the total deviation from the individual optima...
This should give you a pretty good solution...
You can also play arond with this problem by saying
Min D1/F1* + D2/F2* + D3/F3* .... To allow for relative importance between the 3 objectives you listed.
Would this work?
S
