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A Framework for Globally Optimizing Mixed-Integer Signomial Programs

JOURNAL OF optimization THEORY AND APPLICATIONS 2014年第3期161卷 905-932页

作者： Misener, Ruth Floudas, Christodoulos A. Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to epsilon-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures;introducing additional nonconvex terms to interlink expressions;integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree;designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.

关键词： Mixed-integer signomial optimization Global optimization numerical optimization software

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GloMIQO: Global mixed-integer quadratic optimizer

引用

JOURNAL OF GLOBAL optimization 2013年第1期57卷 3-50页

作者： Misener, Ruth Floudas, Christodoulos A. Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA

This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to -global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0.

关键词： Mixed-integer quadratically-constrained quadratic programs numerical optimization software Mathematical programming reformulations Branch-and-bound global optimization

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