The Reformulation-based αGO Algorithm for Solving Nonconvex MINLP Problems – Some Improvements
نویسندگان
چکیده
The α-reformulation (αR) technique can be used to transform any nonconvex twice-differentiable mixedinteger 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 α global optimization (αGO) 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.
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