Computational Results for an Efficient Implementation of the GOP Algorithm and Its Variants
Recently, Floudas and Visweswaran (1990, 1993) proposed a global optimization algorithm (GOP) for the solution of a large class of nonconvex problems through a series of primal and relaxed dual subproblems that provide upper and lower bounds on the global solution. Visweswaran and Floudas (1995a) proposed a reformulation of the algorithm in the framework of a branch and bound approach that allows for an easier implementation. They also proposed an implicit enumeration of all the nodes in the resulting branch and bound tree using a mixed integer linear (MILP) formulation, and a linear branching scheme that reduces the number of subproblems from exponential to linear. In this paper, a complete implementation of the new versions of the GOP algorithm, as well as detailed computational results of applying the algorithm to various classes of nonconvex optimization problems is presented. The problems considered including pooling and blending problems, problems with separation and heat exchanger networks, robust stability analysis with real parameter uncertainty, and concave and indefinite quadratic problems of medium size.
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