allcolor58

decomposition aggregations precedence variable_bound set_partitioning integer_knapsack general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Domenico Salvagnin 84376 197154 3.09698e-05 open allcolor 258.0* allcolor58.mps.gz

Prepack optimization model.

Location of instance in collection

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 84376 52982
Constraints 197154 139746
Binaries 2492 25480
Integers 78288 27038
Continuous 3596 464
Implicit Integers 0 1768
Fixed Variables 1160 0
Nonzero Density 3.09698e-05 4.64720e-05
Nonzeroes 515184 344080
Constraint Classification Properties
Original Presolved
Total 197154 140248
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 6356
Precedence 58464 31290
Variable Bound 58464 58464
Set Partitioning 14 468
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 0 0
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 502
Mixed Binary 854 0
General Linear 79358 43168
Indicator 0 0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

Nonzero entries of original problem

Nonzero entries of original problem

Matrix after trivial presolving

Nonzero entries after trivial presolving

Decomposed structure of original problem

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving

Decomposed structure after trivial presolving (dec-file)

value min median mean max
Components 1.462398
Constraint % 0.000716 3.53964 3.53964 7.07856
Variable % 0.007550 3.47571 3.47571 6.94387
Score 0.922285

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
6 258 258 0 0 0 Edward Rothberg 2021-12-28 This was obtained using the NoRel heuristic with Gurobi 9.5.
5 366 366 0 0 0 Edward Rothberg 2020-05-15 Obtained with Gurobi 9.0 using the solution improvement heuristic
4 439 439 0 0 0 Frederic Didier 2020-02-24 Obtained with Google OR-tools through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
3 988 0 0 0 Edward Rothberg 2020-02-17 Obtained with Gurobi 9.0 using the solution improvement heuristic
2 1157 0 0 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found using ODH|CPlex
1 3378 3378 0 0 0 - 2018-10-11 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to allcolor58 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance Status Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Objective Tags
allcolor10 hard 14872 476 13776 620 34014 89136 Domenico Salvagnin allcolor 6 decomposition aggregations precedence variable_bound set_partitioning integer_knapsack general_linear
neos-4532248-waihi easy 86842 86841 0 1 167322 525339 Jeff Linderoth neos-pseudoapplication-6 61.59999999999999 benchmark benchmark_suitable aggregations precedence set_partitioning cardinality binpacking knapsack mixed_binary
neos-4165869-wannon hard 31728 480 31248 0 85865 270474 Hans Mittelmann neos-pseudoapplication-44 293 precedence variable_bound set_partitioning set_packing invariant_knapsack integer_knapsack general_linear
uccase8 easy 37413 9576 0 27837 53709 214625 Daniel Espinoza uccase 11167.74532 benchmark_suitable aggregations variable_bound set_partitioning invariant_knapsack binpacking knapsack mixed_binary
uccase7 hard 33020 7224 0 25796 47132 335644 Daniel Espinoza uccase 26834.28427331005 aggregations precedence variable_bound set_partitioning invariant_knapsack binpacking knapsack mixed_binary

Reference

@article{FMS16,
    Author = {Matteo Fischetti and Michele Monaci and Domenico Salvagnin},
    Journal = {Discrete Optimization},
    Pages = {195--205},
    Title = {Mixed-Integer Linear Programming Heuristics for the PrePack Optimization Problem},
    Volume = {22},
    Year = {2016}}

@incollection{HMMMMR14,
    Author = {Hoskins, M. and R. Masson and G.G. Melanon and J.E. Mendoza and C. Meyer and L.-M. Rousseau},
    Booktitle = {Integration of AI and OR Techniques in Constraint Programming},
    Editor = {Simonis, H.},
    Pages = {136--143},
    Publisher = {Springer Berlin / Heidelberg},
    Series = {Lecture Notes in Computer Science},
    Title = {The {P}re{P}ack {O}ptimization {P}roblem},
    Volume = {8451},
    Year = 2014}
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