Optimal vertical alignment analysis for highway design

Critical length of grade control, fixed-elevation points, and nonoverlapping of horizontal and vertical curves are three common requirements in the vertical alignment design of roads. These three forms of constraints are, however, usually not addressed in the conventional road alignment optimization analysis because of the complexity in considering them in the mathematical formulation and solution of the problem. This paper illustrates that the artificial intelligence technique of genetic algorithms can be adopted to handle these three forms of constraints effectively. The formulation of the genetic-algorithm computer program and the method of solution are explained. The validity of the optimization algorithm is verified against a dynamic programming solution. Examples are presented to illustrate the application of the genetic-algorithm program to problems involving critical length of grade requirements, fixed-elevation control, and nonoverlapping of horizontal and vertical curves. These three constraints were found to have significant effects on the computed optimal alignments and the associated construction costs.