More facets from fences for linear ordering and acyclic subgraph polytopes
Discrete Applied Mathematics
A new heuristic algorithm solving the linear ordering problem
Computational Optimization and Applications
Intensification and diversification with elite tabu search solutions for the linear ordering problem
Computers and Operations Research
New Facets of the Linear Ordering Polytope
SIAM Journal on Discrete Mathematics
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Tabu Search
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem
Journal of Global Optimization
Data Allocation on Wireless Broadcast Channels for Efficient Query Processing
IEEE Transactions on Computers
Fences Are Futile: On Relaxations for the Linear Ordering Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization
INFORMS Journal on Computing
Lagrangian heuristics for the linear ordering problem
Metaheuristics
New Approximation Techniques for Some Linear Ordering Problems
SIAM Journal on Computing
Context-Independent Scatter and Tabu Search for Permutation Problems
INFORMS Journal on Computing
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Designing a hybrid genetic algorithm for the linear ordering problem
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
A hybrid data mining GRASP with path-relinking
Computers and Operations Research
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The linear ordering problem (LOP) is an $\mathcal{NP}$ -hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.