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Solving Mixed Integer Bilinear Problems Using MILP Formulations

Akshay Gupte, Shabbir Ahmed, Myun Seok Cheon, Santanu Dey
2013 SIAM Journal on Optimization  
In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and  ...  We present the convex hull of the underlying mixed integer linear set.  ...  Particular thanks for encouraging us to experiment on more instances, helping us simplify the proof of Proposition 3.4, and for correcting an earlier version of Proposition 2.3.  ... 
doi:10.1137/110836183 fatcat:72ipukixhzbpzfz4lbnwfwr66u

A New Mixed Integer Linear Programming Formulation for Protection Relay Coordination Using Disjunctive Inequalities

Srinivas STP, K Shanti Swarup
2019 IEEE Power and Energy Technology Systems Journal  
Many linear (LP), nonlinear (NLP), mixed integer nonlinear (MINLP), mixed integer linear (MILP), and quadratically constrained quadratic programming (QCQP)-based formulations have been presented in the  ...  This paper proposes a new MILP-based formulation using disjunctive inequalities.  ...  Mixed integer nonlinear programming (MINLP) is proposed in [13] where I p values are assumed as integer variables and TDS parameters are considered to be continuous and solved using Seeker's algorithm  ... 
doi:10.1109/jpets.2019.2907320 fatcat:fmpwphglpvep5hq5hqxauhgs3i

Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

Pedro M. Castro, Ignacio E. Grossmann
2014 Journal of Global Optimization  
This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem.  ...  We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized.  ...  The short-term scheduling problem can be formulated as a discrete-time mixed-integer nonlinear programming formulation [1] , where the only source of nonlinearities is eq.  ... 
doi:10.1007/s10898-014-0162-6 fatcat:5cbgmc7e6zgtpmevftgxpsbhde

A Conic Integer Programming Approach to Constrained Assortment Optimization under the Mixed Multinomial Logit Model [article]

Alper Sen, Alper Atamturk, Philip Kaminsky
2017 arXiv   pre-print
Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations.  ...  In contrast, we develop a novel conic quadratic mixed-integer formulation.  ...  In contrast, we show that by formulating this problem in a non-traditional manner, as a conic quadratic mixed-integer program, large instances of the capacitated version of the problem can be solved directly  ... 
arXiv:1705.09040v2 fatcat:hvvnsgzhrnd6bi3pabgiyakmli

Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms [article]

Yifu Chen, Christos T. Maravelias, Xiaomin Zhang
2022 arXiv   pre-print
These methods convert the original nonconvex optimization problems into mixed-integer linear programs (MILPs).  ...  Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms.  ...  optimization problem into a mixed-integer linear program (MILP).  ... 
arXiv:2207.03699v1 fatcat:h5uorvpqsnfhnd37vrkh3upise

Technical Note—A Conic Integer Optimization Approach to the Constrained Assortment Problem Under the Mixed Multinomial Logit Model

Alper Şen, Alper Atamtürk, Philip Kaminsky
2018 Operations Research  
Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations.  ...  In contrast, we develop a novel conic quadratic mixed-integer formulation.  ...  By contrast, we show that by formulating this problem in a nontraditional manner, as a conic quadratic mixed-integer program, large instances of the capacitated version of the problem can be solved directly  ... 
doi:10.1287/opre.2017.1703 fatcat:ift2gp63iff2hbp2h2hyv653z4

Tightening piecewise McCormick relaxations for bilinear problems

Pedro M. Castro
2015 Computers and Chemical Engineering  
This can be obtained through a mixed-integer linear programming formulation relying on the concept of piecewise McCormick relaxation.  ...  While it involves solving hundreds or even thousands of linear bound contracting problems in a pre-processing step, the benefit from having a tighter formulation more than compensates the additional computational  ...  E-mail address: pmcastro@fc.ul.pt nonlinear (MINLP) type, alternative algorithms can be used that have in common the generation of linear (LP) or mixed-integer linear (MILP) relaxations of the original  ... 
doi:10.1016/j.compchemeng.2014.03.025 fatcat:a7vj4tjoovbupoqzkh3zmdex5a

Tight Convex Relaxation for TEP Problem: A Multiparametric Disaggregation Approach

Shahin Goodarzi, mohsen gitizadeh, Ali Reza Abbasi, Matti Lehtonen
2020 IET Generation, Transmission & Distribution  
In this context, first, the TEP problem is formulated as a mixed-integer bilinear problem by representing the complex bus voltage in its rectangular coordinates.  ...  The AC power flow equations are quadratic and hence the TEP problem can be formulated as a mixed-integer quadratically constrained programme.  ...  These equations are quadratic and hence the TEP problem can be formulated as a mixed-integer quadratically constrained programme (MIQCP).  ... 
doi:10.1049/iet-gtd.2019.1270 fatcat:lheo525275btxgeg26ibdbwp4a

A novel discrete network design problem formulation and its global optimization solution algorithm

David Z.W. Wang, Haoxiang Liu, W.Y. Szeto
2015 Transportation Research Part E: Logistics and Transportation Review  
A global optimization method employing linearization, outer 17 approximation and range reduction techniques is developed to solve the formulated model. 18  ...  In this paper, we address a novel yet general discrete network design problem formulation 14 that aims to determine the optimal new link addition and their optimal capacities simultaneously, 15 which answers  ...  Formulate the R-MILP problem with the incumbent range of7 variables and the current subset of corner-points. Solve the R-MILP problem to Update the subset of corner-points.  ... 
doi:10.1016/j.tre.2015.04.005 fatcat:53hfk6b33zadtpk7p7e7eyhcvy

Global optimization of bilinear programs with a multiparametric disaggregation technique

Scott Kolodziej, Pedro M. Castro, Ignacio E. Grossmann
2013 Journal of Global Optimization  
algorithms that are used to solve bilinear programming problems.  ...  mixed-integer problems and faster solution times for similar optimality gaps.  ...  Note that if the convex functions h q (x) are linear, problem (P') represents a mixed integer linear program (MILP). Otherwise it corresponds to an MINLP.  ... 
doi:10.1007/s10898-012-0022-1 fatcat:wjkz74623vhofahvjyckcetzi4

An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands

Axel Nyberg, Ignacio E. Grossmann, Tapio Westerlund
2012 AIChE Journal  
Introduction In this article we present an effective mixed-integer linear programming (MILP) formulation for design of a multi-echelon stochastic inventory system with uncertain customer demands.  ...  In this short note we first reformulate the mixed-integer nonlinear programming (MINLP) model presented in You and Grossmann [2010] and , using an alternative linearization scheme leading to a model  ... 
doi:10.1002/aic.13977 fatcat:77gvmxa7nnco7ol4egcxzslgvi

An outer-approximation algorithm for generalized maximum entropy sampling

Han-Lim Choi, Jonathan P. How, Paul I. Barton
2008 2008 American Control Conference  
An outerapproximation algorithm is developed for this formulation that obtains the optimal solution by solving a sequence of mixedinteger linear programs.  ...  A new mixedinteger semidefinite program (MISDP) formulation is proposed to handle a GMES problem with a jointly Gaussian distribution over the search space.  ...  Mixed-Integer Semidefinite Program Formulation This work poses the following mixed-integer semidefinite program (MISDP), which is a mixed-integer convex program (MICP), to address (GMES) described in the  ... 
doi:10.1109/acc.2008.4586756 dblp:conf/amcc/ChoiHB08 fatcat:y4nycpkjhbe7xlihj754ilwzhe

Relaxations of Multilinear Convex Envelopes: Dual Is Better Than Primal [chapter]

Alberto Costa, Leo Liberti
2012 Lecture Notes in Computer Science  
Bilinear, trilinear, quadrilinear and general multilinear terms arise naturally in several important applications and yield nonconvex mathematical programs, which are customarily solved using the spatial  ...  This requires a convex relaxation of the original problem, obtained by replacing each multilinear term by appropriately tight convex relaxations.  ...  A sequence of k − 1 Fortet's linearizations will then yield a Mixed-Integer Linear Programming (MILP) formulation of the original multilinear term.  ... 
doi:10.1007/978-3-642-30850-5_9 fatcat:2acrmdbcrjanbjbbhjmmogzsc4

Optimal scheduling of chiller plant with thermal energy storage using mixed integer linear programming

Kun Deng, Yu Sun, Amit Chakraborty, Yan Lu, Jack Brouwer, Prashant G. Mehta
2013 2013 American Control Conference  
At each time step, the MPC problem is represented as a large-scale mixed integer nonlinear programming (MINLP) problem.  ...  We propose a heuristic algorithm to search for suboptimal solutions to the MINLP problem based on mixed integer linear programming (MILP), where the system dynamics is linearized along the simulated trajectories  ...  (14) is a mixed integer linear programming (MILP) problem, with N * n c binary variables and N * (3n c + 7) real variables.  ... 
doi:10.1109/acc.2013.6580284 fatcat:cipmejkhfrd67ey6zzdvbwma4e

Advances in Logic-Based Optimization Approaches to Process Integration and Supply Chain Management [chapter]

Ignacio E. Grossmann
2005 Chemical Engineering  
In particular, recent advances are presented in the modeling and solution of nonlinear mixed-integer and generalized disjunctive programming, global optimization and constraint programming.  ...  Discrete/continuous optimization problems, when represented in algebraic form, correspond to mixedinteger optimization problems that have the following general form:  ...  of the wellbehaved mixed-integer constraints.  ... 
doi:10.1002/0470025018.ch11 fatcat:4lgp6f3llbcfhlatqg2dhockoy
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