Implicit constraints handling for efficient search of feasible solutions

Real-world optimization problems usually involve constraints and sometimes even finding a single feasible solution is a challenging task. This study introduces a new approach for implicitly handling constraints. The proposed approach reduces the consideration of infeasible solutions by directly updating variable bounds with constraints, which is called the boundary update (BU) method. Two illustrative examples are used to explain the proposed approach, followed by applying it to mathematical and engineering constrained optimization problems. Finally, a surrogate-based problem and a large-dimensional and highly constrained problem are used to evaluate the BU method on these types of problems. The BU method is coupled with seven well-known evolutionary and mathematical optimization algorithms and the results show that the proposed BU method is a practical and effective approach and leads to better solutions with fewer function evaluations in nearly all cases, particularly for population-based optimization algorithms. This study should motivate optimization researchers and practitioners to pay more attention to the direct handling of constraints, rather than constraint handling by penalty or other fix-ups.