# fhnw-sq3

### infeasiblefeasibilityprecedenceset_partitioninginteger_knapsackgeneral_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Simon Felix 2450 167 1.80178e-02 hard fhnw-sq Infeasible fhnw-sq3.mps.gz

Combinatorial toy feasibility problem: Magic square. This instance is hard for all MIP solvers, but can be solved by customized codes. Infact, infeasibility can be deduced from a look at the model as explained by Ed Klotz: "But the easiest way is just by looking at the model itself. It's a magic square problem with a few side constraints. Just remove the side constraints, and for that matter you can even remove remove the constraints on the sums of the diagonals of the square. So you are left to fill in a 7x7 magic square where the row sums are an even number (1544). If you look at the 49 values to place in the square, exactly 2 of them are odd. Regardless of where you place them, you are guaranteed to have at least 2 rows or columns involving one odd and 6 even numbers. Those rows cannot possibly add up to an even number, so no feasible solution exists.""

# Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 2450 2450
Constraints 167 167
Binaries 2401 2401
Integers 49 49
Continuous 0 0
Implicit Integers 0 49
Fixed Variables 0 0
Nonzero Density 0.0180178 0.0180178
Nonzeroes 7372 7372
Constraint Classification Properties
Original Presolved
Total 183 183
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 4 4
Variable Bound 0 0
Set Partitioning 98 98
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 16 16
Mixed Binary 0 0
General Linear 65 65
Indicator 0 0

# Structure

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

value min median mean max
Components 1.662758
Constraint % 0.598802 0.705256 0.598802 4.19162
Variable % 1.918370 2.088890 1.918370 7.67347
Score 0.308520

# Best Known Solution(s)

No solution available for fhnw-sq3 .

# Similar instances in collection

The following instances are most similar to fhnw-sq3 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
fhnw-sq2 hard 650 625 25 0 91 1968 Simon Felix fhnw-sq 0 feasibility precedence set_partitioning integer_knapsack general_linear
neos-5125849-lopori easy 8130 8040 90 0 453 20938 Jeff Linderoth neos-pseudoapplication-42 0 feasibility benchmark_suitable aggregations set_partitioning set_packing equation_knapsack general_linear
fiball easy 34219 33960 258 1 3707 104792 MIPLIB submission pool -- 138 benchmark decomposition benchmark_suitable aggregations precedence set_partitioning general_linear
neos-3004026-krka easy 17030 16900 130 0 12545 41860 Jeff Linderoth neos-pseudoapplication-38 0 benchmark feasibility benchmark_suitable set_partitioning general_linear
neos-1354092 easy 13702 13282 420 0 3135 187187 NEOS Server Submission neos-pseudoapplication-47 46 benchmark decomposition benchmark_suitable variable_bound set_partitioning general_linear

## Reference

No bibliographic information available

Last Update Mai 20, 2021 by Philipp Wellner
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