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Assuming that the weights are non-negative, the maximum cut problem can be formulated by the following mixed-integer program (Kahruman, Kolotoglu, Butenko, & Hicks, 2007):
The optimal solution vector x defines a graph partition 
(if 
then 
, otherwise 
) that has the maximum cut value. Let 
denote a cost of a cut corresponding to the solution vector x.
Local search based methods require an initial solution 
to start the chain of local improvements until the local optimum is obtained. GES provides an intelligent mechanism of generating initial solutions for local search based methods. Its metaheuristic framework proved to be extremely efficient for a variety of combinatorial problems (Pardalos, Prokopyev, Shylo, & Shylo, 2008; Shylo, Prokopyev, & Shylo, 2008).