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Title: An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

Journal Article · · Journal of Global Optimization
ORCiD logo [1];  [2];  [2];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Clemson Univ., SC (United States). Dept. of Industrial Engineering
+ Show Author Affiliations

We develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE; LANL Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1514953
Report Number(s):
LA-UR--17-25666
Journal Information:
Journal of Global Optimization, Journal Name: Journal of Global Optimization Journal Issue: 4 Vol. 74; ISSN 0925-5001
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

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  • PROCEEDINGS LEGO – 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP, AIP Conference Proceedings https://doi.org/10.1063/1.5090004
conference January 2019
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97 MATHEMATICS AND COMPUTING
MILP-based methods
McCormick
adaptive partitioning
global optimization
mixed-integer nonlinear programs
piecewise relaxations
sequential optimization-based bound-tightening