By Frederick J Munster; Maine. Dept. of Economic and Community Development
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One sided penalty function called the barrier function have been proposed but can lead to constraints violently oscillating between feasibility and violation on successive iterations. Reliable algorithms for weighted inequality constraints are complex and unwieldy compared to the Lagrange multipliers. 2 Algorithms for the constrained optimization can be developed from the consideration of the necessary and sufficient conditions for a constrained optimum point. In the solution, a linear combination of the active constraint gradients is equal and oposite to the merit function gradient.
6 49 Linear normalization Davis in  describes the scaling method that can be used in both the minimization problems and the maximization problems. The algorithm for the linear normalization consists of the following steps: Step 1: Order the individuals of the population so that the best individual is the first and the worst individual is the last one. If the optimization problem is the minimization problem then the best individual has the smallest merit function value. Step 2: The individual with the best merit function is assigned a constant predefined value (the staring value for the linear normalization).
Most GA applications use fixed length, fixed order bit strings to encode individuals. Some people in the genetic algorithms field have come to believe that the bit strings should be used as encoding technique whenever they apply a genetic algorithm. However, in recent years, there have been experiments with other kinds of representation of individuals in the genetic algorithms like the floating point numbers. 1 Representation of individuals with the binary numbers The representation of individuals with the binary numbers use the bit strings (string of binary digits 1 or 0) for encoding of possible solutions to the problem.