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An algorithm for nonlinear optimization problems with binary variables

Walter Murray, Kien-Ming Ng
2008 Computational optimization and applications  
One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables.  ...  Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables.  ...  nonlinear optimization problems with binary variables.  ... 
doi:10.1007/s10589-008-9218-1 fatcat:uj62ggkkczc2bmgygvhf4uv5fe

Computational experience with dicopt solving MINLP problems in process systems engineering

G.R. Kocis, I.E. Grossmann
1989 Computers and Chemical Engineering  
This paper discusses an implementation of the Outer-Approximation/Equality -Relaxation algorithm for solving MINLP problems that arise in process systems engineering.  ...  Computational experience in solving fifteen MINLP problems with DICOPT is reported.  ...  Computer times on an IBM-3090/600 are typically of the order of only 2-100 seconds for problems with up to 60 0-1 variables and 410 variables and constraints.  ... 
doi:10.1016/0098-1354(89)85008-2 fatcat:fitw5sah35gmldwgtjaj7z74i4

Predictive Control of Nonlinear Hybrid Systems Using Generalized Outer Approximation

Naresh N. Nandola, Sharad Bhartiya
2008 IFAC Proceedings Volumes  
This paper presents an efficient optimization algorithm for mixed integer nonlinear programming (MINLP) problem resulting from multiple partially linearized (MPL) model based control of nonlinear hybrid  ...  The algorithm uses structural information of the canonical MPL framework and derives comparatively easier quadratic programming (QP) primal problem as well as an MILP master problem for generalized outer  ...  The master problem results in an MILP whose solution is a lower bound of the MINLP. The master problem also produces the value of the binary variables for next iteration.  ... 
doi:10.3182/20080706-5-kr-1001.00612 fatcat:pwb6zee5wvb2lk5n2ruuigxmri

A Review of Piecewise Linearization Methods

Ming-Hua Lin, John Gunnar Carlsson, Dongdong Ge, Jianming Shi, Jung-Fa Tsai
2013 Mathematical Problems in Engineering  
for obtaining an approximated global optimal solution.  ...  How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory.  ...  Developing an efficient polynomial time algorithm for solving nonconvex problems by piecewise linearization techniques is still a challenging question.  ... 
doi:10.1155/2013/101376 fatcat:zqbkl6b2ibdebb4bkoddiknccu

Global optimization of MINLP problems in process synthesis and design

C.S. Adjiman, I.P. Androulakis, C.A. Floudas
1997 Computers and Chemical Engineering  
it allows to solve the underestimating problems to global optimality using the GBD algorithm or the OA algorithm, provided that the binary variables participate separably and linearly.  ...  The conditions imposed on the functionality of the binary variables differ for each method : linear and mixed bilinear terms can be treated with the SMIN-BB; mixed nonlinear terms whose continuous relaxation  ...  and not necessarily separable binary variables; the Generalized Benders Decomposition algorithm, GBD (Geoffrion, 1972; Floudas et al., 1989) , is designed for problems with a convex continuous part and  ... 
doi:10.1016/s0098-1354(97)87542-4 fatcat:iqgiswkqdrfvreg6s5ygc7isra

Global Optimization of MINLP Problems in Process Synthesis and Design

C Adjiman
1997 Computers and Chemical Engineering  
it allows to solve the underestimating problems to global optimality using the GBD algorithm or the OA algorithm, provided that the binary variables participate separably and linearly.  ...  The conditions imposed on the functionality of the binary variables differ for each method : linear and mixed bilinear terms can be treated with the SMIN-BB; mixed nonlinear terms whose continuous relaxation  ...  and not necessarily separable binary variables; the Generalized Benders Decomposition algorithm, GBD (Geoffrion, 1972; Floudas et al., 1989) , is designed for problems with a convex continuous part and  ... 
doi:10.1016/s0098-1354(97)00089-6 fatcat:miaj3o2omfdblh4r5g6ecp6pkm

Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method

Yoon Young Kim, G.-W. Jang, Sang Jun Nam
2006 IEEE Transactions on robotics  
The key idea of the proposed method is to formulate the inverse kinematics problem of a binary manipulator as an optimization problem with real design variables, in which the real variables are forced  ...  In this case, numerically efficient inverse kinematics algorithms for binary manipulators usually require impractically large memory size for the real-time calculation of the binary states of all joints  ...  ACKNOWLEDGMENT The authors appreciate discussions with Prof. F. C. Park at Seoul National University during this investigation.  ... 
doi:10.1109/tro.2005.858864 fatcat:ihjpxqk25vbgndew5amt3uhpji

Relaxation strategy for the structural optimization of process flow sheets

Gary R. Kocis, Ignacio E. Grossmann
1987 Industrial & Engineering Chemistry Research  
This paper presents an Equality Relaxation variant to the Outer-Approximation algorithm for solving mixed-integer nonlinear programming (MINLP) problems that arise in structural optimization of process  ...  The proposed algorithm has the important capability of being able to explicitly handle nonlinear equations within MINLP formulations that have linear integer variables and linear/nonlinear continuous variables  ...  the optimal value of the binary variables.  ... 
doi:10.1021/ie00069a026 fatcat:meftt2gvqfagjduytpuwh32dke

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

Sebastian Sager
2009 Journal of Process Control  
In model-based nonlinear optimal control switching decisions that can be optimized often play an important role.  ...  Optimization algorithms need to take the discrete nature of the variables that model these switching decisions into account.  ...  We introduce an additional variable, e.g., for ω i (t) · ω j (t): ω ij (t) := 1 if ω i (t) = ω j (t) = 1 0 else The new binary variables can be incorporated into the optimization problem by adding the  ... 
doi:10.1016/j.jprocont.2009.03.008 fatcat:uza4dupvnzaanghamyc6piyrpa

Page 7919 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Summary: “ELSO is an environment for the solution of large-scale optimization problems. With ELSO the user is required to provide only a code for the evaluation of a partially separable function.  ...  It has been shown recently that some properties of the maximum weight stable set problem hold true in the more general setting of binary integer programs with two variables per inequality.  ... 

Real-coded genetic algorithm for system identification and controller tuning

K. Valarmathi, D. Devaraj, T.K. Radhakrishnan
2009 Applied Mathematical Modelling  
In the proposed genetic algorithm, the optimization variables are represented as floating point numbers.  ...  This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants.  ...  In this work the problem of controller tuning is formulated as an optimization problem.  ... 
doi:10.1016/j.apm.2008.11.006 fatcat:iaxqvwmns5ad5clkb3ei4cbvne

Symmetry-exploiting cuts for a class of mixed-0/1 second-order cone programs

Sarah Drewes, Sebastian Pokutta
2014 Discrete Optimization  
We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints.  ...  For example in [7] lift-and-project based cuts for mixed 0/1 conic programming problems have been studied.  ...  ACKNOWLEDGEMENTS The authors are indebted to the two anonymous referees for the helpful comments.  ... 
doi:10.1016/j.disopt.2014.04.002 fatcat:tmaguogruzcibn5kbwbj5xyah4

Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

Vassilis M. Charitopoulos, Lazaros G. Papageorgiou, Vivek Dua
2017 Engineering  
In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being  ...  For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.  ...  Compliance with ethics guidelines Vassilis M. Charitopoulos, Lazaros G. Papageorgiou, and Vivek Dua declare that they have no conflict of interest or financial conflicts to disclose.  ... 
doi:10.1016/j.eng.2017.02.008 fatcat:c3wzwbusenbatlrgmllcvrnnru

Convex separable optimization is not much harder than linear optimization

D. S. Hochbaum, J. George Shanthikumar
1990 Journal of the ACM  
This paper presents a general-purpose algorithm for converting procedures that solves linear programming problems with or without integer variables, to procedures for solving the respective nonlinear separable  ...  An algorithm for finding an c-accurate optimal continuous solution to the nonlinear problem that is polynomial in log( l/c) and the input size and the largest subdeterminant of the constraint matrix is  ...  The authors are grateful to Ilan Adler for several stimulating discussions that motivated the work done in this paper.  ... 
doi:10.1145/96559.96597 fatcat:lkqrg236dvfzhjcxkn5umtet4u

MINLP OPTIMIZATION OF STEEL FRAMES [chapter]

Uroš Klanšek, Tomaž Žula, Zdravko Kravanja, Stojan Kravanja
2007 Volume 3 Number 3  
The Modified Outer-Approximation/ Equality-Relaxation algorithm and a two-phase MINLP optimization approach were applied for the optimization.  ...  It performs the discrete optimization of discrete decisions simultaneously with the continuous optimization of continuous parameters.  ...  The MILP optimization master problem predicts a new vector of binary variables.  ... 
doi:10.18057/ijasc.2007.3.3.5 fatcat:dzpztz3qyfg5vaxfwtsfl6sevi
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