Optimization for Multiobjective Optimal Control Problem and Its Application in 3D Horizontal Wells

The design for the 3-dimensional trajectory in horizontal wells is an optimal control system, where the state variables are azimuth and inclination and the control variables are radius, tool-face angle and length of curve. Here an multiobjective control system was given, whose performance indexes were the precision of hitting target and trajectory length. For the multiobjective system an improved GA was designed to provide the comprise solutions scattered uniformly over the Pareto frontier. We constructed multiple fitness functions to guide the search, where each one was equal to a weighted sum of two normalized performance indexes, and the weights of fitness function were selected by uniform design. In addition, a select operator was constructed to maintain the diversity of the population and generate a new generation. The algorithm had been applied to the optimal design for several wells in Oil Field of Liaohe, and the results illustrated its validity and advantages such as providing more compromise projects etc