(74d) GOSSIP: Decomposition Software for the Global Optimization of Nonconvex Two-Stage Stochastic Mixed-Integer Nonlinear Programs

Kannan, R., Massachusetts Institute of Technology
Barton, P. I., Massachusetts Institute of Technology
Stochastic programming provides a natural way of incorporating uncertainty in model parameters, and has been receiving increasing attention in the process systems engineering literature [1â??6]. Despite rapid advances in decomposition techniques for solving nonconvex two-stage stochastic mixed-integer nonlinear programs (MINLPs) [1, 7, 8], there is, to the best of our knowledge, no publicly available software framework which implements these techniques. Motivated by the above, we introduce GOSSIP, a decomposition framework for the global optimization of two-stage stochastic MINLPs.

GOSSIP includes subroutines for reformulating user input, detecting special structure, automatic construction of the subproblems required by the decomposition techniques, automatic construction of relaxations, and bounds tightening [9â??12]. The decomposition framework includes implementations of nonconvex generalized Benders decomposition (NGBD) [7, 8], Lagrangian relaxation [1, 13], and a modified Lagrangian relaxation algorithm. The option of solving the extensive form of the two-stage stochastic MINLP using a global optimization solver is also included. Solver links to several state-of-the-art optimization software are part of GOSSIP and are used to solve the various subproblems used by the decomposition techniques.

A library of test instances of two-stage stochastic MINLPs from the literature is composed, and the capabilities of GOSSIP are demonstrated over this diverse set of problems.

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