The Reformulation-based aGO Algorithm for Solving Nonconvex MINLP Problems – Some Improvements

• Main Authors: A. Lundell, T. Westerlund
• Format: Article
• Language: English
• Published: AIDIC Servizi S.r.l. 2013-06-01
• Series: Chemical Engineering Transactions
• Online Access: https://www.cetjournal.it/index.php/cet/article/view/6615

The a-reformulation (aR) technique can be used to transform any nonconvex twice-differentiable mixed-integer nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is implemented in the a global optimization (aGO) algorithm solving the specified problem type to global optimality as a sequence of reformulated subproblems where the piecewise linear functions are refined in each step. The tightness of the underestimator has a large impact on the efficiency of the solution process, and in this paper it is shown how it is possible to reduce the approximation error by utilizing a piecewise quadratic spline function defined on smaller subintervals. The improved underestimator is also applied to test problems illustrating its performance.