The

constrained optimization problem can again be solved using the penalty method.

For the latter case we formulated a

constrained optimization problem where various constraints and parameters were considered in order to obtain a minimum-length path.

In this paper, to obtain the fitness function for proposed GA, the

constrained optimization problem (here, it is the maximization of constrained Redundancy allocation problem) is converted to an unconstrained optimization problem for handling of constraints by a new penalty function technique.

When BSAISA deals with

constrained optimization problems, the code in line (8) and line (40) in Pseudocode 1 should consider objective function value and constraint violation simultaneously, and SA[epsilon] is applied to choose a better solution or best solution in line (42) and lines (47)-(48).

Economic Load Dispatch is defined as the sharing of load equally in generating The dynamic economic dispatch problem is a high-dimensional complex

constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost.

The basic idea of these methods is to change, modify or convert the

constrained optimization problem into an unconstrained optimization problem by adding or subtracting a penalty value to or from the objective (Ashok and Chandrugupta, 2011).

More precisely, the constrained fuzzy-valued optimization problem with both fuzzy-valued objective function and constraints was converted to a general

constrained optimization problem, based on its underlying fuzzy-valued functions.

Many different methods have been applied to solve OPF, which is a large scale, nonlinear,

constrained optimization problem. Previously, OPF problems were solved with mathematic based traditional methods such as Gardient Method [2], Newton based Methods [3], Linear Programming [4], Quadratic Programming [5], Interior Point Method [6] and Nonlinear Programming [7].

Constrained Optimization Problem. In general, a

constrained optimization problem can be stated as follows:

[Step 6]: Update the counter l + [left arrow] l + 1 and go back to the step 3 if l < [l.sub.max] x Otherwise, stop algorithm and take the best position vector as an optimal solution which minimize the

constrained optimization problem (20).

By this means, the

constrained optimization problem can be formulated as follows: