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
Lagrangian Smoothing Heuristics for Max-Cut
Journal of Heuristics
On greedy construction heuristics for the MAX-CUT problem
International Journal of Computational Science and Engineering
A discrete filled function algorithm for approximate global solutions of max-cut problems
Journal of Computational and Applied Mathematics
Hybridizing the cross-entropy method: An application to the max-cut problem
Computers and Operations Research
A Large Neighborhood Search Heuristic for Graph Coloring
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A global continuation algorithm for solving binary quadratic programming problems
Computational Optimization and Applications
Semidefinite Programming Heuristics for Surface Reconstruction Ambiguities
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
A Vector Assignment Approach for the Graph Coloring Problem
Learning and Intelligent Optimization
Advanced Scatter Search for the Max-Cut Problem
INFORMS Journal on Computing
Local search starting from an LP solution: Fast and quite good
Journal of Experimental Algorithmics (JEA)
Efficient implementation of quasi-maximum-likelihood detection based on semidefinite relaxation
IEEE Transactions on Signal Processing
A novel graph-based image annotation refinement algorithm
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 5
Linear and quadratic programming approaches for the general graph partitioning problem
Journal of Global Optimization
Solving the maxcut problem by the global equilibrium search
Cybernetics and Systems Analysis
Global optimality conditions and optimization methods for quadratic integer programming problems
Journal of Global Optimization
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
Expert Systems with Applications: An International Journal
A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem
Proceedings of the 14th annual conference on Genetic and evolutionary computation
A new discrete filled function method for solving large scale max-cut problems
Numerical Algorithms
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Memetic search for the max-bisection problem
Computers and Operations Research
A memetic approach for the max-cut problem
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part II
Path Relinking Scheme for the Max-Cut Problem within Global Equilibrium Search
International Journal of Swarm Intelligence Research
Breakout Local Search for the Max-Cutproblem
Engineering Applications of Artificial Intelligence
Max-k-Cut by the Discrete Dynamic Convexized Method
INFORMS Journal on Computing
A Continuous Relaxation Method for Multiuser Detection Problem
Wireless Personal Communications: An International Journal
Solving large scale Max Cut problems via tabu search
Journal of Heuristics
Probabilistic GRASP-Tabu Search algorithms for the UBQP problem
Computers and Operations Research
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The Goemans--Williamson randomized algorithm guarantees a high-quality approximation to the MAX-CUT problem, but the cost associated with such an approximation can be excessively high for large-scale problems due to the need for solving an expensive semidefinite relaxation. In order to achieve better practical performance, we propose an alternative, rank-two relaxation and develop a specialized version of the Goemans--Williamson technique. The proposed approach leads to continuous optimization heuristics applicable to MAX-CUT as well as other binary quadratic programs, for example the MAX-BISECTION problem.A computer code based on the rank-two relaxation heuristics is compared with two state-of-the-art semidefinite programming codes that implement the Goemans--Williamson randomized algorithm, as well as with a purely heuristic code for effectively solving a particular MAX-CUT problem arising in physics. Computational results show that the proposed approach is fast and scalable and, more importantly, attains a higher approximation quality in practice than that of the Goemans--Williamson randomized algorithm. An extension to MAX-BISECTION is also discussed, as is an important difference between the proposed approach and the Goemans--Williamson algorithm; namely, that the new approach does not guarantee an upper bound on the MAX-CUT optimal value.