Constraint handling for genetic algorithms in optimal remediation design

There often is difficulty enforcing the given constraints when applying a genetic algorithm (a flexible stochastic search method) to optimal ground-water remediation design problems. This paper compares two methods for constraint handling within the genetic algorithm framework. The first method, the additive penalty method (APM), is a commonly used penalty function approach in which a penalty cost proportional to the total constraints violation is added to the objective function. The second method, the multiplicative penalty method (MPM), multiplies the objective function by a factor proportional to the total constraints violation. The APM and MPM, using constant and generation-varying constraint weights, are applied to two pump-and-treat design examples. Overall, the application of the APM resulted in infeasible solutions with small-to-moderate total constraints violations. With the MPM, a set of feasible and near-optimal policies was readily identified for both examples. Additionally, the MPM converges to the solution faster than the APM. These results demonstrate that the MPM is a robust method, capable of finding feasible and optimal or near-optimal solutions while using a range of weights.