Evaluation of the Performance and Parameter Sensitivity of Constraint-Handling Techniques for a Genetic Algorithm-Based Watershed Management Problem

Handling constraints in Evolutionary Algorithms (EAs) can be a challenging issue. Because constraints are not handled directly, heuristics must be carefully designed and applied to guide the search toward feasible and good-performing solutions. Penalty functions are the most commonly used method to handle constraints in EAs. There are many possible formulations for penalty functions. One drawback of penalty functions is that they require time-consuming fine-tuning of the penalty parameters to effectively search for feasible solutions with good objective function values. Alternative techniques have also been reported in the literature, including multi-objective optimization techniques, which treat the constraints in single objective problems as additional objectives. In this paper, various constraint-handling techniques are applied to an EA-based watershed management problem to investigate their performance and sensitivity to fine-tuning parameters. The watershed management problem involves designing detention ponds in a system-wide manner in conjunction with land use allocation to provide a desired level of long-term system-wide pollutant removal at the least cost. The constraint-handling methods investigated include several penalty functions and alternative constraint-handling techniques. The associated fine-tuning parameters for each constraint-handling method are varied to investigate the sensitivity of the solution quality (feasibility and objective function value) to these parameters. The solution quality and its sensitivity to the constraint-handling parameters are compared. This comparison is intended to help provide guidelines for better-performing constraint-handling methods for a watershed management problem that can be successfully implemented without excessive fine-tuning requirements.