A guided tour of Chernoff bounds
Information Processing Letters
Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
Go with the winners for graph bisection
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Hill-climbing finds random planted bisections
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Genetic Algorithm and Graph Partitioning
IEEE Transactions on Computers
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
Minimum spanning trees made easier via multi-objective optimization
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
The one-dimensional Ising model: mutation versus recombination
Theoretical Computer Science
On the effect of populations in evolutionary multi-objective optimization
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Approximating covering problems by randomized search heuristics using multi-objective models
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Simulated annealing for graph bisection
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
IEEE Transactions on Evolutionary Computation
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
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Evolutionary algorithms have been analyzed for many optimization problems during the last decade in order to understand their behavior. Recently, the application of multi-objective evolutionary algorithms for several single-objective problems has been investigated. The graph bisection problem (GBP), which is to partition the nodes of a given graph into two equal-sized subsets such that the number of edges crossing between these subsets is minimal, belongs to the group of single-objective NP-hard problems. Heuristics like Simulated Annealing have been proven to perform well on certain graph models. For evolutionary algorithms in contrast mostly experimental results exist. This paper proposes two evolutionary algorithms for GBP, a (1+1) EA and a multi-objective approach. The proposed algorithms are analyzed on two classes of instances in order to provide a first theoretical analysis of evolutionary algorithms for GBP as well as to point out their advantages and disadvantages. Each class causes one algorithm to struggle with a local optimum leading to expected exponential optimization time, while the other one finds the optimal solution within polynomial time. Experimental results are used to support the theoretical analysis.