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A Feedback Particle Swarm Optimization (FPSO) with a family of fitness functions is proposed to minimize sidelobe level (SLL) and control null. In order to search in a large initial space and converge fast in local space to a refined solution, a FPSO with nonlinear inertia weight algorithm is developed, which is determined by a subtriplicate function with feedback taken from the fitness of the best previous position. The optimized objectives in the fitness function can obtain an accurate null level independently. The directly constrained SLL range reveals the capability to reduce SLL. Considering both element positions and complex weight coefficients, a low-level SLL, accurate null at specific directions, and constrained main beam are achieved. Numerical examples using a uniform linear array of isotropic elements are simulated, which demonstrate the effectiveness of the proposed array pattern synthesis approach.