MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance faclay80
single-row facility layout problem modeled as a quadratic linear ordering problem An instance of the single-row facility layout problem is formally defined by n one-dimensional facilities with given positive lengths and pairwise non-negative weights. The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem can be modeled as a quadratic objective over linear ordering variables.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -10830269.50000000 (BARON) 128395.37250000 (COUENNE) -6947106.40600000 (CPLEX) 1052292.92100000 (GUROBI) 2204030.50000000 (LINDO) 136000.95770000 (SCIP) 160886.65000000 (SHOT) |
| Referencesⓘ | Anjos, Miguel F, Kennings, Andrew, and Vannelli, Anthony, A semidefinite optimization approach for the single-row layout problem with unequal dimensions, Discrete Optimization, 2:2, 2005, 113-122. |
| Sourceⓘ | POLIP instance quadratic_linear_ordering/AnKeVa_2005_80dept_set1 |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 3161 |
| #Binary Variablesⓘ | 3160 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 3160 |
| #Nonlinear Binary Variablesⓘ | 3160 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 164321 |
| #Linear Constraintsⓘ | 164320 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 496121 |
| #Nonlinear Nonzeros in Jacobianⓘ | 3160 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 307788 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3160 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3160 |
| Average blocksize in Hessian of Lagrangianⓘ | 3160.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.4328e+04 |
| Infeasibility of initial pointⓘ | 3.092e+06 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |