From Svenleyffer

This file briefly describes the MINLP test problems.

## Contents |

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.

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.

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).

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

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

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.

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.

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.

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.

Pure integer NLP due to Hans D. Mittelman, Arizona State University, mittelmann@asu.edu.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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