LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
On the optimality of the random hyperplane rounding technique for max cut
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
An improved hybrid genetic algorithm for the generalized assignment problem
Proceedings of the 2004 ACM symposium on Applied computing
A low-level hybridization between memetic algorithm and VNS for the max-cut problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hybridizing the cross-entropy method: An application to the max-cut problem
Computers and Operations Research
Advanced Scatter Search for the Max-Cut Problem
INFORMS Journal on Computing
Solving Max-Cut to optimality by intersecting semidefinite and polyhedral relaxations
Mathematical Programming: Series A and B
Matheuristics: Hybridizing Metaheuristics and Mathematical Programming
Matheuristics: Hybridizing Metaheuristics and Mathematical Programming
Hybrid metaheuristics in combinatorial optimization: A survey
Applied Soft Computing
The core concept for the multidimensional knapsack problem
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
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The Max-Cut problem is a classical NP-hard combinatorial optimization problem. It consists of dividing the vertices of a weighted graph into two subsets, such that the sum of the weights of the edges connecting the two subsets is maximized. Although semidefinite relaxation algorithms for Max-Cut have been proved to be of high quality and offer performance guarantees, in practice, metaheuristic algorithms are still the first option to solve large Max-Cut instances. In this paper, we present the first effort at combining semidefinite programming (SDP) with metaheuristic algorithm (Memetic Algorithm) to solve the Max-Cut problem. Based on the solution of semidefinite relaxation, we use Goemans-Williamson Algorithm to seed high quality solutions to the initial population for the memetic algorithm. Experimental results on well-known benchmark problems show that our new hybrid algorithm is capable of obtaining better solutions in the initial population generation stage than previous algorithms, and the overall performance of our algorithm is better than one of the best existing algorithms. Besides, new best solutions for 14 benchmark problems were found by our algorithm.