Evaluation of Alternative Penalty Function Implementations in a Watershed Management Design Problem

Genetic algorithms (GAs) provide a convenient framework to search for good solutions for a wide range of problems that are typically difficult to solve by means of traditional optimization techniques. Their application in solving real-world engineering problems is becoming increasingly popular. A common drawback of this procedure is its poor ability to handle constraints while searching for good solutions. The watershed management problem addressed in this paper includes a significant number of constraints. After evaluating that special constraint handling operators and procedures reported in the GA literature are insufficient to handle these constraints, penalty function-based generalized techniques for handling constraints within GAs are chosen as the most likely approach. A systematic investigation of alternative implementations of penalty functions to handle the constraints that are typical in watershed management problems is carried out. Based on a case study involving a watershed in High Point, North Carolina, comparisons are made among a set of penalty functions with respect to the performance of the genetic algorithm in consistently finding good solutions that meet the specified constraints.