Maximum stable set formulations and heuristics based on continuous optimization

Maximum stable set formulations and heuristics based on continuous optimization

The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of co...

Heuristics for Maximum Clique and Independent Set

Heuristics For Maximum Clique And Independent Set

Formulations for the Stable Set Polytope

We give a simple algorithm for the weighted stable set problem of an arbitrary graph which yields an extended formulation for its stable set polytope The algorithm runs in polynomial time for the class of distance claw free graphs These are the graphs such that for each node neither its neighbour set nor the set of nodes at distance two contain a stable set of size three The extended formulatio...

Derivative-based hybrid heuristics for continuous-time simulation optimization

The topic of simulation–optimization has not been fundamentally tackled by many continuous-time modeling and simulation tools, yet. Common simulation-based optimization problems are usually coupled with standard optimization algorithms like any other simulation-free nonlinear optimization problems. While such couplings are usually based on many state-of-the-art software engineering concepts wit...