On the edge of feasibility: A case study of the particle swarm optimizer

In many real-world constrained optimization problems (COPs) it is highly probable that some constraints are active at optimum points, i.e. some optimum points are boundary points between feasible and infeasible parts of the search space. A method is proposed which narrows the feasible area of a COP to its boundary. In the proposed method the thickness of the narrowed boundary is adjustable by a parameter. The method is extended in a way that it is able to limit the feasible regions to boundaries where at least one of the constraints in a given subset of all constraints is active and the remaining constraints might be active or not. Another extension is able to limit the search to cases where all constraints in a given subset are active and the rest might be active or not. The particle swarm optimization algorithm is used as a framework to compare the proposed methods. Results show that the proposed methods can limit the search to the requested boundary and they are effective in locating optimal solutions on the boundaries of the feasible and infeasible area.