(575b) Parallel Global Optimization for Nlp and Minlp Programming Problems | AIChE

(575b) Parallel Global Optimization for Nlp and Minlp Programming Problems


Polisetty, P. K. - Presenter, University of South Carolina, Dept. of Chemical Engineering
Gay, D. M. - Presenter, Sandia National Laboratory
Hart, W. - Presenter, Sandia National Laboratories


     The objective of this work is to develop efficient large scale parallel methods for global optimization of nonconvex nonseparable nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. Finding global optima of nonconvex nonlinear optimization problems has been an important topic for many researchers. Branch-and-bound [2, 6, 3] and Outer-Approximation algorithms [1, 4] can be used for solving MINLP problems to global solutions. Existing optimization routines when implemented sequentially may require large amount of time in determining global solutions. Significant speed-up can be attained by implementing these techniques on parallel machines.

     Several commercial software tools are already available for solving NLP and MINLP problems. However, existing tools can be expensive and difcult to extend or adapt and may not support parallel searches. An overview of GNLP, an object-oriented open source software package for global nonlinear programming on parallel machines is presented. GNLP can be applied to a wide range of industrial and scientific applications. GNLP is a branch-and-bound based code for rigorous optimization of algebraically specified nonlinear functions subject to nonlinear constraints, involving bounded continuous or discrete variables. GNLP builds on PICO's facilities for parallel computing, rewrites expression graphs to obtain convex or linear bounding functions, and uses some facilities from COCONUT [10]. COCONUT is another open-source global optimization project developed within academic framework and can support the use of various bounding strategies and AMPL for automatic differentiation.

     GNLP is integrated with various public domain LP solvers and IPOPT [9], an open source NLP optimization solver for determining locally optimal solutions that can be used as upper bounds during branch-and-bound implementation. Linear Programming (LP) based relaxations for nonconvex nonlinear expressions can be generated using reformulation technique of McCormick and Smith [5, 7] combined with linearization strategy of Tawarmalani and Sahinidis [8]. Additionally, LP based relaxations can also be generated using COCONUT's interval slopes and exclusion box techniques [10]. The advantage of using multiple lower bounding techniques is that tighter relaxations can be generated which can signicantly decrease the partitioning during branch-and-bound algorithm. PICO's parallel MILP branch-and-bound framework can be used in obtaining global solutions to nonconvex NLP problems. Current work under progress includes extension of PICO's branch-andbound capabilities to obtain global solutions to MINLP problems and implementing Outer-Approximation algorithms in parallel framework. Further, various heuristics for parallel variable bound contraction, parallel incumbent generation techniques are under consideration. Computational results from work in progress will be presented.


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