On Risk-Averse Weighted k-Club Problems

In this work, we consider a risk-averse maximum weighted k-club problems. It is assumed that vertices of the graph have stochastic weights whose joint distribution is known. The goal is to find the k-club of minimum risk contained in the graph. A stochastic programming framework that is based on the formalism of coherent risk measures is used to find the corresponding subgraphs. The selected representation of risk of a subgraph ensures that the optimal solutions are maximal k-clubs. A combinatorial branch-and-bound solution algorithm is proposed and solution performances are compared with an equivalent mathematical programming counterpart problem for instances with k = 2.

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