Constraint-Handling Method for Function Optimization : Pareto Descent Repair Operator

Function optimization underlies many real-world problems and hence is an important research subject. Most of the existing optimization methods were developed to solve primarily unconstrained problems. Since real-world problems are often constrained, appropriate handling of constraints is necessary in order to use the optimization methods. In particular, the performances of some methods such as Genetic Algorithms (GA) can be substantially undermined by ineffective constraint handling. Despite much effort devoted to the studies of constraint-handling methods, it has been reported that each of them has certain limitations. Hence, further studies for designing more effective constraint-handling methods are needed. For this reason, we investigated the guidelines for a method to effectively handle constraints. The guidelines are that the method 1) takes the approach of repair operators, 2) monotonically decreases both the number of violated constraints and constraint violations, and 3) searches over the boundaries of violated constraints. Based on these guidelines, we designed a new constraint-handling method Pareto Descent Repair operator (PDR) in which ideas derived from multi-objective local search and gradient projection method are incorporated. Experiments comparing GA that use PDR and some of the existing constraint-handling methods confirmed the effectiveness of PDR.