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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.