A VNS metaheuristic with stochastic steps for Max 3-cut and Max 3-section (Q1954820)

Summary: A heuristic algorithm based on VNS is proposed to solve the Max 3-cut and Max 3-section problems. By establishing a neighborhood structure of the Max 3-cut problem, we propose a local search algorithm and a variable neighborhood global search algorithm with two stochastic search steps to obtain the global solution. We give some numerical results and comparisons with the well-known 0.836-approximate algorithm. Numerical results show that the proposed heuristic algorithm can obtain efficiently the high-quality solutions and has the better numerical performance than the 0.836-approximate algorithm for the NP-Hard Max 3-cut and Max 3-section problems.