Abstract: An improved adaptive genetic algorithm is proposed to solve the problem in which traditional genetic algorithm has deficiencies in global search and convergence speed. It modifies the adaptive technology by adopting the crossover and mutation operator adaptive adjusting with the number of iterations and fitness of populations. And the traditional selection operator based on roulette is replaced by new selection operator and improved elite reservation strategy to increase the probability of the global best answer and speed up the convergence rate. Through the experiments of optimization for common functions, the improved algorithm can enhance the number of elite and show the better global optimal ability and faster convergence ability. Based on this, the improved algorithm is applied in the array optimization of MIMO radar. Through the grid coding and using the bi-fitness function considering both sidelobe level and mainlobe width, the better synthetical performance of the array pattern for MIMO radar can be obtained, which will be more available in practice. Simulation results verify that the proposed algorithm is effective.dimensional cases. The 9th and 11th degree symmetric quadrature formulae W⁽⁴⁾₅ and W⁽⁴⁾₆ for fourdimensional hypercubs, and the 9th and 11th degree symmetric quadrature formulae W^(6)*₅ and W^(6)*₆ for sixdimensional hypercubs is deduced. Compared to the same degree Gaussian quadrature formulae, these formulae need much less function evaluations. The number of function evaluations of W⁽⁴⁾₅ and W⁽⁴⁾₆ are 185 and 505, and the number of function evaluations of W^(6)*₅ and W^(6)*₆ are 465 and 1825 respectively. The deduced four and six dimensional formulae are used respectively in calculating impedance elements of RWG Galerkin moment method for arbitrary conducting surface objects and extensive RWG Galerkin moment method for inhomogeneous dielectric objects. The calculated results show that when the mesh cells’ electrical length is less than λ/4 , the quardrature relative precision of formulae W⁽⁴⁾₅ and W⁽⁴⁾₆are about 1e-6 for four dimensional, while that of formulae  W^(6)*₅ and W^(6)*₆are about 1e-4 for six dimensional.