MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance hybriddynamic_fixed
Fixed Finite Elements
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 1.47377778 (ALPHAECP) 1.47377778 (ANTIGONE) 1.47377778 (BARON) 1.47377778 (BONMIN) 1.47377778 (COUENNE) 1.47377778 (CPLEX) 1.47377778 (GUROBI) 1.47377778 (LINDO) 1.47377778 (SCIP) 1.47377778 (SHOT) |
| Referencesⓘ | Baumrucker, Brian and Biegler, L T, MINLP & MPCC Strategies for Optimization of a Class of Hybrid Dynamic Systems, 2009. |
| Sourceⓘ | del_asl_miqp.gms from minlp.org model 27 |
| Applicationⓘ | Hybrid Dynamic Systems |
| Added to libraryⓘ | 24 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 71 |
| #Binary Variablesⓘ | 10 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 11 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 11 |
| #Nonlinear Nonzeros in Objectiveⓘ | 11 |
| #Constraintsⓘ | 79 |
| #Linear Constraintsⓘ | 79 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 178 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 11 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 11 |
| #Blocks in Hessian of Lagrangianⓘ | 11 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 2.0000e-01 |
| Maximal coefficientⓘ | 2.0000e+00 |
| Infeasibility of initial pointⓘ | 3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 80 60 10 10 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 72 62 10 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 190 179 11 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,objvar;
Binary Variables b11,b12,b13,b14,b15,b16,b17,b18,b19,b20;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80;
e1.. -(sqr((-1.66666666666667) + x71) + 0.2*sqr(x51) + 0.2*sqr(x52) + 0.2*sqr(
x53) + 0.2*sqr(x54) + 0.2*sqr(x55) + 0.2*sqr(x56) + 0.2*sqr(x57) + 0.2*
sqr(x58) + 0.2*sqr(x59) + 0.2*sqr(x60)) + objvar =E= 0;
e2.. - x31 + x41 =E= 0.2;
e3.. - x32 + x42 =E= 0.2;
e4.. - x33 + x43 =E= 0.2;
e5.. - x34 + x44 =E= 0.2;
e6.. - x35 + x45 =E= 0.2;
e7.. - x36 + x46 =E= 0.2;
e8.. - x37 + x47 =E= 0.2;
e9.. - x38 + x48 =E= 0.2;
e10.. - x39 + x49 =E= 0.2;
e11.. - x40 + x50 =E= 0.2;
e12.. - x21 + x51 - 0.2*x61 =E= 0;
e13.. - x22 + x52 - 0.2*x62 =E= 0;
e14.. - x23 + x53 - 0.2*x63 =E= 0;
e15.. - x24 + x54 - 0.2*x64 =E= 0;
e16.. - x25 + x55 - 0.2*x65 =E= 0;
e17.. - x26 + x56 - 0.2*x66 =E= 0;
e18.. - x27 + x57 - 0.2*x67 =E= 0;
e19.. - x28 + x58 - 0.2*x68 =E= 0;
e20.. - x29 + x59 - 0.2*x69 =E= 0;
e21.. - x30 + x60 - 0.2*x70 =E= 0;
e22.. x1 - 2*b11 =E= -1;
e23.. x2 - 2*b12 =E= -1;
e24.. x3 - 2*b13 =E= -1;
e25.. x4 - 2*b14 =E= -1;
e26.. x5 - 2*b15 =E= -1;
e27.. x6 - 2*b16 =E= -1;
e28.. x7 - 2*b17 =E= -1;
e29.. x8 - 2*b18 =E= -1;
e30.. x9 - 2*b19 =E= -1;
e31.. x10 - 2*b20 =E= -1;
e32.. 2*b11 - x51 =L= 2;
e33.. 2*b12 - x52 =L= 2;
e34.. 2*b13 - x53 =L= 2;
e35.. 2*b14 - x54 =L= 2;
e36.. 2*b15 - x55 =L= 2;
e37.. 2*b16 - x56 =L= 2;
e38.. 2*b17 - x57 =L= 2;
e39.. 2*b18 - x58 =L= 2;
e40.. 2*b19 - x59 =L= 2;
e41.. 2*b20 - x60 =L= 2;
e42.. 2*b11 - x51 =G= 0;
e43.. 2*b12 - x52 =G= 0;
e44.. 2*b13 - x53 =G= 0;
e45.. 2*b14 - x54 =G= 0;
e46.. 2*b15 - x55 =G= 0;
e47.. 2*b16 - x56 =G= 0;
e48.. 2*b17 - x57 =G= 0;
e49.. 2*b18 - x58 =G= 0;
e50.. 2*b19 - x59 =G= 0;
e51.. 2*b20 - x60 =G= 0;
e52.. - x31 + x32 =E= 0.2;
e53.. - x32 + x33 =E= 0.2;
e54.. - x33 + x34 =E= 0.2;
e55.. - x34 + x35 =E= 0.2;
e56.. - x35 + x36 =E= 0.2;
e57.. - x36 + x37 =E= 0.2;
e58.. - x37 + x38 =E= 0.2;
e59.. - x38 + x39 =E= 0.2;
e60.. - x39 + x40 =E= 0.2;
e61.. - x21 + x22 - 0.2*x61 =E= 0;
e62.. - x22 + x23 - 0.2*x62 =E= 0;
e63.. - x23 + x24 - 0.2*x63 =E= 0;
e64.. - x24 + x25 - 0.2*x64 =E= 0;
e65.. - x25 + x26 - 0.2*x65 =E= 0;
e66.. - x26 + x27 - 0.2*x66 =E= 0;
e67.. - x27 + x28 - 0.2*x67 =E= 0;
e68.. - x28 + x29 - 0.2*x68 =E= 0;
e69.. - x29 + x30 - 0.2*x69 =E= 0;
e70.. - x30 - 0.2*x70 + x71 =E= 0;
e71.. x1 + x61 =E= 2;
e72.. x2 + x62 =E= 2;
e73.. x3 + x63 =E= 2;
e74.. x4 + x64 =E= 2;
e75.. x5 + x65 =E= 2;
e76.. x6 + x66 =E= 2;
e77.. x7 + x67 =E= 2;
e78.. x8 + x68 =E= 2;
e79.. x9 + x69 =E= 2;
e80.. x10 + x70 =E= 2;
* set non-default bounds
x1.lo = -1; x1.up = 1;
x2.lo = -1; x2.up = 1;
x3.lo = -1; x3.up = 1;
x4.lo = -1; x4.up = 1;
x5.lo = -1; x5.up = 1;
x6.lo = -1; x6.up = 1;
x7.lo = -1; x7.up = 1;
x8.lo = -1; x8.up = 1;
x9.lo = -1; x9.up = 1;
x10.lo = -1; x10.up = 1;
x21.fx = -2;
x31.fx = 0;
x51.lo = -2; x51.up = 2;
x52.lo = -2; x52.up = 2;
x53.lo = -2; x53.up = 2;
x54.lo = -2; x54.up = 2;
x55.lo = -2; x55.up = 2;
x56.lo = -2; x56.up = 2;
x57.lo = -2; x57.up = 2;
x58.lo = -2; x58.up = 2;
x59.lo = -2; x59.up = 2;
x60.lo = -2; x60.up = 2;
* set non-default levels
x1.l = -1;
x2.l = -1;
x3.l = -1;
x4.l = -1;
x5.l = -1;
x6.l = -1;
x7.l = -1;
x8.l = -1;
x9.l = -1;
x10.l = -1;
x22.l = -2;
x23.l = -2;
x24.l = -2;
x25.l = -2;
x26.l = -2;
x27.l = -2;
x28.l = -2;
x29.l = -2;
x30.l = -2;
x32.l = 1;
x33.l = 1;
x34.l = 1;
x35.l = 1;
x36.l = 1;
x37.l = 1;
x38.l = 1;
x39.l = 1;
x40.l = 1;
x41.l = 1;
x42.l = 1;
x43.l = 1;
x44.l = 1;
x45.l = 1;
x46.l = 1;
x47.l = 1;
x48.l = 1;
x49.l = 1;
x50.l = 1;
x51.l = -2;
x52.l = -2;
x53.l = -2;
x54.l = -2;
x55.l = -2;
x56.l = -2;
x57.l = -2;
x58.l = -2;
x59.l = -2;
x60.l = -2;
x71.l = 1;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc