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
An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem
Journal of Global Optimization
A Template for Scatter Search and Path Relinking
AE '97 Selected Papers from the Third European Conference on Artificial Evolution
Scatter Search: Methodology and Implementations in C
Scatter Search: Methodology and Implementations in C
Variable neighborhood search for the linear ordering problem
Computers and Operations Research
Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search
Operations Research
Evaluating las vegas algorithms: pitfalls and remedies
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
A population-based strategic oscillation algorithm for linear ordering problem with cumulative costs
EvoCOP'13 Proceedings of the 13th European conference on Evolutionary Computation in Combinatorial Optimization
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Given a matrix of weights, the Linear Ordering Problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This well known NP-complete problem can also be formulated on a complete weighted graph, where the objective is to find an acyclic tournament that maximizes the sum of arc weights. The variant of the LOP that we target here was recently introduced and adds a cumulative non-linear propagation of the costs to the sum of the arc weights. We first review the previous methods for the LOP and for this variant with cumulative costs (LOPCC) and then propose a heuristic algorithm for the LOPCC, which is based on the Tabu Search (TS) methodology. Our method achieves search intensification and diversification through the implementation of both short and long term memory structures. Our extensive experimentation with 224 instances shows that the proposed procedure outperforms existing methods in terms of solution quality and has reasonable computing-time requirements.