Linear programming based on neural networks for radiotherapy treatment planning

In this paper, we propose a neural network model for linear programming tha t is designed to optimize radiotherapy treatment planning (RTP). This kind of neural network can be easily implemented by using a kind of 'neural' ele ctronic system in order to obtain an optimization solution in real time. We first give an introduction to the RTP problem and construct a non-constrai nt objective function for the neural network model. We adopt a gradient alg orithm to minimize the objective function and design the structure of the n eural network for RTP. Compared to traditional linear programming methods, this neural network model can reduce the time needed for convergence, the s ize of problems (i.e., the number of variables to be searched) and the numb er of extra slack and surplus variables needed. We obtained a set of optimi zed beam weights that result in a better dose distribution as compared to t hat obtained using the simplex algorithm under the same initial condition. The example presented in this paper shows that this model is feasible in th ree-dimensional RTP.