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mutation. Elitist strategy means that the best individual has been found will always be kept in the
population. The simple genetic algorithm with elitist strategy is convergence^.
For many multi-parameters optimization problems, some algorithms have to calculate the grad of the
function. But in nonlinear optimization problems, the grad of function can not be expressed
analytically, and can only be calculated approximately. This will not only increase the calculating cost
but also depress the precision of the solution. Simplex is a multi-dimensions local optimization
algorithm which does not calculate the grad of the objective function. It has the advantages of easy
implement, good searching ability in local area and simplicity of operation on computers.
Simple genetic algorithm is one of the widely used optimization algorithms. But has the disadvantage
of low searching efficiency problem, especially for multi-dimension and high precision demanded
problems. Many efforts have been put by researchers to speed up the convergence of the genetic
algorithm. For example, Cui 3 has obtained some improvement by combing GA with simulated
annealing algorithm. In order to improve the search capability, a hybrid optimization algorithm was
developed in this paper which combines the genetic algorithm and the simplex. In the proposed
algorithm, the convergence is guaranteed by genetic algorithm, and simplex can speed up the
optimization. Further more, the validity of this hybrid algorithm was checked by seven test functions
and compared with other two algorithms. The result shows that the proposed hybrid algorithm has high
searching efficiency.
2. GENETIC ALGORITHM - SIMPLEX
Premature is the main factor that affects the speed of convergence of GA. To cope with it, genetic
algorithm-simplex is presented, and the main procedure is shown in Fig 1.
2.1 Objective Function and Initial Population
In many actual engineering optimization problems, observed data are used to identify the parameters.
For example, as the observed data are Fc(i), i=l,2,-,M, M is the number of the parameters that to be
identified in the model, the objective function can be defined as:
in which, F L (i) is the theoretic value. If the model space is B, its size is K, the objective of optimization
is to find a special model, and its M parameters meet the condition,
(2.1)
$ ^ s (2.2)
where s is convergence precision, is a pre-chosen, small positive number.