# MINLP Comments

This file briefly describes the MINLP test problems.

#### batch

Optimal Design of Multiproduct Batch Plant. Source: G.R. Kocis & I.E. Grossmann, "Global OPtimization of Nonconvex Mixed Integer Nonlinear Programmming (MINLP) problems in Process Synthesis", Indust. Engng. Chem. Res., No. 27, pp 1407--1421, 1988.

#### c-reload-14

Small core reload pattern optimization problem for 14 fuel positions. Source: A.J. Quist, R. van Geemert, J.E. Hoogenboom, T. Illes, E. de Klerk, T. Terlaki, "Optimization of a Nuclear Reactor Core Reload Pattern Using Nonlinear Optimization and Search Heuristics", Technical Report, Delft University, 1997.

#### c-reload-q

Small core reload pattern optimization problem for 24, 25, 49 and 104 fuel positions respectively. Modelling a quadrant (rather than octant) of the core. Own problem generated from c-reload-14(a-f).

#### c-sched

Source: V. Jain & I.E. Grossmann, "Cyclic Scheduling of Continuous Parallel Units with Decaying Performance", AIChE Journal, 44, 1623-1636.

#### feedloc

Feed tray location & determination of optimum number of trays in a distillation column.

#### geartrain

Gear Train design problem. Source: E. Sangren, "Nonlinear Integer and Discrete Programming in Mechanical Design Optimization", Trans. ASME, J. Mech. Design 112, 223-229, 1990.

#### lbti-00

Optimal design of a load-bearing thermal insulation system. This model is discontinuous (model (P-0)) in Abhishek, Leyffer, andf Linderoth, "Modeling without Categorical Variables: A Mixed-Integer Nonlinear Program for the Optimization of Thermal Insulation Systems", Argonne MCS Preprint, ANL/MCS-P1434-0607, 2007.

#### lbti-01

Optimal design of a load-bearing thermal insulation system. This model is nonsmooth (model (P-1)) in Abhishek, Leyffer, andf Linderoth, "Modeling without Categorical Variables: A Mixed-Integer Nonlinear Program for the Optimization of Thermal Insulation Systems", Argonne MCS Preprint, ANL/MCS-P1434-0607, 2007.

#### lbti-02

Optimal design of a load-bearing thermal insulation system. This model is smooth (model (P-2)) in Abhishek, Leyffer, andf Linderoth, "Modeling without Categorical Variables: A Mixed-Integer Nonlinear Program for the Optimization of Thermal Insulation Systems", Argonne MCS Preprint, ANL/MCS-P1434-0607, 2007.

#### mittelman

Pure integer NLP due to Hans D. Mittelman, Arizona State University, [email protected].

#### optprloc

Optimal positioning of a new product in a multiattribute space: market of M existing products, set of N consumers in a multiattribute space of dimension K. Source: M. Duran & I.E. Grossmann, "An outer approximation algorithm for a class of mixed integer nonlinear programs", Mathematical Programming 36, pp. 307-339, 1986.

#### shale-gas

Shale gas production optimization of 6 wells connected to a compressor with upper and lower limit gas rate capacity constraints. The problem is to maximize the cumulative gas production over a period of time of 123 days.

Source: Shaurya Sharma, "Mixed-Integer Nonlinear Programming Heuristics Applied To A Shale Gas Production Optimization Problem", MSc. Thesis, Norwegian University of Science and Technology, 2013.

#### space

Model of 25 and 960 resp. bar space truss design.

1. Model discrete sizes as SOS-1 variables

2. Units kips, in; except for density in lbs/in^3

3. Optimum weight in lbs

Source: GAMS file by F. Tin-Loi, University of New South Wales, April 00.

#### space-r

Reduced model of 25 and 960 resp. bar space truss design (making use of ampl's defined variable capability to remove some variables from space(25,960)-r

1. Model discrete sizes as SOS-1 variables

2. Units kips, in; except for density in lbs/in^3

3. Optimum weight in lbs

Source: GAMS file by F. Tin-Loi, University of New South Wales, April 00.

#### space-i

Model of 960 bar space truss design from space-960-r with SOS 1 variables replaced by integer.

1. Units kips, in; except for density in lbs/in^3

2. Optimum weight in lbs

Source: GAMS file by F. Tin-Loi, University of New South Wales, April 00.

#### space-ir

Model of 960 bar space truss design. Combines space-960-r and space-960-i (i.e. integers replacing SOS & ampl's defined variables).

1. Units kips, in; except for density in lbs/in^3

2. Optimum weight in lbs

Source: GAMS file by F. Tin-Loi, University of New South Wales, April 00.

#### spring

Coil compression spring design problem, finds minimum volume of wire for the production of a coil compression spring. Using special ordered sets. Source: E. Sangren, "Nonlinear Integer and Discrete Programming in Mechanical Design Optimization", Trans. ASME, J. Mech. Design 112, 223-229, 1990.

#### stockcycle

Pure integer NLP which minimizes totall average stock cycle. Source: "A fast heuristic for minimizing total average cycle stock subject to practical constraints", E.A. Silver & I. Moon, JORS 50, 789-796, August 1999. Model uses SOS to express discrete variables.

#### synthes

Synthesis of processing system. Source: M. Duran & I.E. Grossmann, "An outer approximation algorithm for a class of mixed integer nonlinear programs", Mathematical Programming 36, pp. 307-339, 1986.

#### top1

Topology optimization for compliance minimization of statically loaded structures for 15 x 5, 30 x 10 and 60 x 20 finite element grid. Structure of type 1 (see picture). * This model still has a checkerboard solution pattern which can be eleminated, see model xxxx!*

Source: O. Sigmund, "A 99 line topology optimization code written in Matlab", Technical University of Denmark, October 1999. See also the TopOpt Homepage.

#### trimlon

Nonconvex MINLP arising from trim loss minimization in the paper industry. The problem is to produce a set of product paper rolls from raw paper rolls such that a cost function including the trim loss and the overall production cost is minimized.

There are several data files for different sized problems (e.g. trimlon2.dat is for 2 products, trimlon4.dat for 4 etc).

Source: I. Harjunkoski, T. Westerlund, R. P\"{o}rn and H. Skrifvars "Different transformations for solving non--convex trim loss problems by MINLP", European Journal of Operational Research 105 (1998) 594-603.

#### trimloss

Convex MINLP arising from trim loss minimization in the paper industry. The problem is to produce a set of product paper rolls from raw paper rolls such that a cost function including the trim loss and the overall production cost is minimized. *Square root reformulation of trimlon.mod*

There are several data files for different sized problems (e.g. trimloss2.dat is for 2 products, trimloss4.dat for 4 etc).

Source: I. Harjunkoski, T. Westerlund, R. P\"{o}rn and H. Skrifvars "Different transformations for solving non--convex trim loss problems by MINLP", European Journal of Operational Research 105 (1998) 594-603.

#### wind-fac

Model of the winding factor of the electrical machines due to Michal MICHNA, Polytechnika Gdanska, June 2000.