All real-world optimization problems are constrained, at least implicitly if not explicitly. Constrained optimization is the optimization of an objective function in the presence of constraints on the solution. Without loss of generality, a constrained optimization problem can be written as:
This problem includes (m+p) constraints, m of which are inequality constraints and p of which are equality constraints. The set of x that satisfies all (m+p) constraints is called the feasible set, and the set of x that violates one or more constraints is called the infeasible set:
Constraints could be linear or nonlinear, and the objective of a constrained evolutionary algorithm is to minimize f(x) while at the same time satisfying the constraints gi (x) and hj (x).
Overview of the chapter
In this chapter, we discuss how to modify BBO for constrained optimization problems. Section 9.1 provides notation and concepts that often arise in constrained optimization. Section 9.2 introduces several popular constraint-handling approaches used in EAs, which are also suitable for BBO. Section 9.3 shows how we can combine BBO with these popular constraint-handling methods to obtain constrained BBO algorithms, and presents a comparative study of these constrained BBO algorithms ...