Result: A Randomized Algorithm for Finding Local Maximum Cuts

This paper describes a new randomized algorithm for calculating local maximum cuts of the maximum cut problems in graph theory. The new algorithm transforms the maximum cut problem into a new form by using fuzzy logic technique. The transformation enables the algorithm to use the first-order derivative method to find optimal values for discrete non-linear optimization problems. This paper proves that the solution of the new algorithm satisfies the ϵ−δ condition. The algorithm converts decimal solution points to integer solution points by using the defuzzification technique. This paper also proves that the defuzzification maintains the local maximum value. The new algorithm is compared with IBM ILOG CPLEX. The numerical experiments indicate that the performance of the new algorithm is better than that of IBM ILOG CPLEX for finding local maximum cuts.