optimizing a multi objective problem

[Archiver]

hi
first i should briefly explain you my problem.
in an electrical system i want to minimize the cost in parallel to
minimizing voltage deviation, for this we have two choices:
1- modeling voltage deviation as an cost object an add it to all cost
of system then minimize this equation:
Cost_total=cost_generation+cost_VoltageDeviation;


2- modeling system by two equation as below:
cost_generation and Vlotage_deviation

then minimize both in one simulation.

i want to use the second method. would u guide me?
bests

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[Archiver]

Hi,

Typically, for a multi-objective problem, you do not get a single solution. The usual procedure is to generate a trade-off surface between the two objectives (which is called as the Pareto surface). You can learn about this from a standard optimization textbook.

There are two options for you to solve your problem.

1. Use a weight for each of the objective function to formulate a single objective such as:
a * Cost + b * Voltage deviation
and then minimize the problem in a single objective. You would have to solve multiple problems with different weights to get the Pareto surface.

2. Convert one of the objectives into constraint and again solve multiple problems with different bounds on this constraint. This is known as the constraint method and should also give you the Pareto surface. You can find the theory again in a standard textbook.

- Yogendra.



On Wed, May 20, 2009 at 8:26 AM, Alireza wrote:


hi
first i should briefly explain you my problem.
in an electrical system i want to minimize the cost in parallel to
minimizing voltage deviation, for this we have two choices:
1- modeling voltage deviation as an cost object an add it to all cost
of system then minimize this equation:
Cost_total=cost_generation+cost_VoltageDeviation;


2- modeling system by two equation as below:
cost_generation and Vlotage_deviation

then minimize both in one simulation.

i want to use the second method. would u guide me?
bests




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