Boundary Search for Constrained Numerical Optimization Problems

The necessity of approaching the boundary between the feasible and infeasible search space for many constrained optimization problems is a paramount challenge for every constraint-handling technique. It is true that many of the stateof- the-art constraint-handling techniques performs well when facing constrained problems. However, it is a common situation that reaching the boundary between the feasible and infeasible search space could be a difficult task for some particular problems. Firstly, this chapter shows a general overview of the constraint-handling techniques based on a boundary approach and emphasizing a recent proposal applying a more general boundary operator. In addition, the chapter includes some particular considerations related to the implementation aspects of the boundary approach when facing problems with one o more constraints. Another important issue also considered here is about the implementation of this approach when taking into account different search engines. On this direction, some basic examples are depicted as guidelines for possible implementations under well-known metaheuristics as Evolutionary Algorithms (EAs), Particle Swarm Optimization (PSO), and Ant ColonyOptimization (ACO). To validate the boundary approach implemented under the above metaheuristics, an experimental study is presented in which well-known problems were considered. Finally, a brief summary of the chapter and some ideas for future works are given which could help the researchers interested in developing advanced constraint-handling techniques.