Bandwidth packing: a tabu search approach
Management Science
Distances between traveling salesman tours
Discrete Applied Mathematics
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
A glimpse at the metaphysics of Bongard problems
Artificial Intelligence
A Bionomic Approach to the Capacitated p-Median Problem
Journal of Heuristics
Diversity-Guided Evolutionary Algorithms
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
Linear gate assignment: a fast statistical mechanics approach
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Pareto autonomous local search
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
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Discrete mathematicians, operations researchers and computer scientists have been developing local search models to solve combinatorial optimization problems for the last decades. A major concern in this development has been to keep the algorithms with a high level of search diversity. There is, however, a lack of precision and definition in what is actually meant by "local search diversity". Authors have continually referred to such terms without any attempt of actually defining or modeling diversity. We propose two metrics for a structure of diversity based on distance metrics between solutions. The first metric is an absolute one in that it measures the diversity of the explored solutions given the whole of the solution space. The second one considers the level of diversity that might be theoretically achievable under each specific number of solutions explored. Finally, a discussion of the computational complexity of the proposed metrics is also provided.