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genetic algorithm is N, then the demand of the hybrid algorithm is N>M+1 During the optimization
process, if the GA is in the premature status, the hybrid algorithm will select M-t-1 individuals from the
population as the beginning of simplex. Then the simplex begins its optimization calculation. If the
simplex finds the solution satisfies (2.2), the optimization ends. Otherwise, simplex can find some
better solutions generally after a number of calculations. Then the hybrid algorithm will replace M+l
individuals selected randomly in the population with new better solutions found by simplex, and the
genetic algorithm continues. Use GA and simplex alternately until the best solution is found. The flow
chart of genetic algorithm - simplex is show in Fig. 1.
3. TEST FUNCTIONS AND HYBRID ALGORITHM TEST
In order to test the validity of the hybrid algorithm, seven complex test functions were selected. In the
test, the objective function is defined as O =
best value - function value
best value
. For the first four test
functions, only two-dimension cases were calculated, and for other three functions, both
two-dimension and multi-dimension cases were calculated.
3,1 Test Function
(1) Fi: Shubert function 3 (-10