Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
Simulated annealing: theory and applications
Simulated annealing: theory and applications
Optimal linear labelings and eigenvalues of graphs
Discrete Applied Mathematics
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
An introduction to genetic algorithms
An introduction to genetic algorithms
The Unified Modeling Language reference manual
The Unified Modeling Language reference manual
A greedy genetic algorithm for the quadratic assignment problem
Computers and Operations Research
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Bipartite Drawings and the Linear Arrangement Problem
SIAM Journal on Computing
A Multi-scale Algorithm for the Linear Arrangement Problem
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Divide-and-conquer approximation algorithms via spreading metrics
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Experiments on the minimum linear arrangement problem
Journal of Experimental Algorithmics (JEA)
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The optimal linear arrangement problem is defined as follows: given a graph G, find a linear ordering for the vertices of G on a line such that the sum of the edge lengths is minimized over all orderings. The problem is NP-complete and it has many applications in graph drawing and in VLSI circuit design. We introduce a genetic hillclimbing algorithm for the optimal linear arrangement problem. We compare the quality of the solutions and running times of our algorithm to those obtained by simulated annealing algorithms. To obtain comparable results, we use a benchmark graph suite for the problem. Our experiments show that there are graph classes for which the optimal linear arrangement problem can be efficiently approximated using our genetic hillclimbing algorithm but not using simulated annealing based algorithms. For hypercubes, binary trees and bipartite graphs, the solution quality is better and the running times are shorter than with simulated annealing algorithms. Also the average results are better. On the other hand, there also are graph classes for which simulated annealing algorithms work better.