Solution Repair by Inequality Network Propagation in LocalSolver

Abstract

This paper focuses on optimization problems whose constraints comprise a network of binary and ternary linear inequalities. These constraints are often encountered in the fields of scheduling, packing, layout, and mining. Alone, small-neighborhood local search algorithms encounter difficulties on these problems. Indeed, moving from a good solution to another requires small changes on many variables, due to the tight satisfaction of the constraints.The solution we implemented in LocalSolver is a kind of constraint propagation: when the solution obtained after a local transformation is infeasible, we gradually repair it, one constraint at a time. In order to extend the local transformation rather than cancel it, we impose never to go back on the decision to increase or decrease the value of a variable. We show that the success of this repair procedure is guaranteed for a large class of constraints.We apply this method to several scheduling problems, characterized by precedences and disjunctive resource constraints. We give numerical results on the Job Shop, Open Shop and Unit Commitment Problems, and show that our repair algorithm dramatically improves the performance of our local search algorithms.