Authors:
Ehsan Iranmanesh
and
Ramesh Krishnamurti
Affiliation:
Simon Fraser University, Canada
Keyword(s):
Linear Ordering Problem, Linear Programming, Integer Linear Program, Mixed Integer Program Heuristic.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Artificial Intelligence
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Linear Programming
;
Methodologies and Technologies
;
Network Optimization
;
Operational Research
;
Optimization
;
Pattern Recognition
;
Scheduling
;
Software Engineering
;
Symbolic Systems
Abstract:
The Linear Ordering Problem is a classic optimization problem which can be used to model problems in graph theory, machine scheduling, and voting theory, many of which have practical applications. Relatively recently, there has been some success in using Mixed Integer Program (MIP) heuristic for NP-hard optimization problems. We report our experience with using a MIP heuristic for the problem. Our heuristic generates a starting feasible solution based on the Linear Programming solution to the IP formulation for the Linear Ordering Problem. For each starting solution, a neighborhood is defined, again based on the LP solution to the problem. A MIP solver is then used to obtain the optimal solution among all the solutions in the neighborhood. The MIP heuristic shows promise for large problems of hard instances.