A feasibility-preserving local search operator for constrained discrete optimization problems

Meta-heuristic optimization approaches are commonly applied to many discrete optimization problems. Many of these optimization approaches are based on a local search operator like, e.g., the mutate or neighbor operator that are used in evolution strategies or simulated annealing, respectively. However, the straightforward implementations of these operators tend to deliver infeasible solutions in constrained optimization problems leading to a poor convergence. In this paper, a novel scheme for a local search operator for discrete constrained optimization problems is presented. By using a sophisticated methodology incorporating a backtracking-based ILP solver, the local search operator preserves the feasibility also on hard constrained problems. In detail, an implementation of the local serach operator as a feasibility-preserving mutate and neighbor operator is presented. To validate the usability of this approach, scalable discrete constrained testcases are introduced that allow to calculate the expected number of feasible solutions. Thus, the hardness of the testcases can be quantified. Hence, a sound comparison of different optimization methodologies is presented.