Inequality Constraints in Facility Location and Related Problems

In this paper we propose an annealing based framework to incorporate inequality constraints in optimization problems such as facility location, simultaneous facility location with path optimization, and the last mile delivery problem. These inequality constraints are used to model several application specific size and capacity limitations on the corresponding facilities, transportation paths and the service vehicles. We design our algorithms in such a way that it allows to (possibly) violate the constraints during the initial stages of the algorithm, so as to facilitate a thorough exploration of the solution space; as the algorithm proceeds, this violation (controlled through the annealing parameter) is gradually lowered till the solution converges in the feasible region of the optimization problem. We present simulations on various datasets that demonstrate the efficacy of our algorithm.