The problem of strongly nonlinear constrained optimization is an extremely difficult topic with comprehensive engineering background in the field of optimization. It is still crucial how to explore effective and efficient optimizers for seeking the global optima of the problem. Therefore, to cope with the difficulty of solving function optimization problems with strongly nonlinear constraints, this work develops a state matrix transition-based improved fly visual evolutionary neural network, by integrating the inspiration of population evolution with the information-processing mechanism of the fly visual system. In the design of the model, the input is a grayscale image which matches with a state matrix at any moment. Each grayscale denotes the object value of a candidate so-called state; an improved fly visual feed forward neural network is designed to not only generate a global learning rate, but also effectively deal with the constraints of the problems, relying upon the property of hierarchical information-processing of the visual system; each state is transformed into another one by a strategy of state transition with the help of the learning rate and the whale's location update strategy. The theoretical analyses show that the computational complexity of the visual evolutionary neural network is decided only by the resolution of each input image. The comparative experiments validate that the neural network has major advantages in optimization quality and important reference value for solving engineering optimization problems.