QUBO Instance Examples

Randomly generated QUBO Instances. All elements are selected from -1000 to 1000 (excluding 0) independently and uniformly at random.

• 1024 bits: r1k.csv.gz, r1k.utm.gz

• 2048 bits: r2k.csv.gz, r2k.utm.gz

• 4096 bits: r4k.csv.gz, r4k.utm.gz

• 8192 bits: r8k.csv.gz, r8k.utm.gz

• 16384 bits: r16k.csv.gz, r16k.utm.gz

• 32768 bits: r32k.csv.gz, r32k.utm.gz

Converted from WK2000_1.rud, a randomly generated complete graph with weight -1/+1.

• 2000 bits: k2000.csv.gz, k2000.utm.gz. Best known solution: -33337 (QUBO), 33337 (Max Cut)

Converted from randomly generated complete graphs. All edge weights are selected from -1000 to +1000 (excluding 0) independently and uniformly at random.

• 10000 bits: k10000.csv.gz, k10000.utm.gz

• 32768 bits: k32k.csv.gz, k32k.utm.gz

Converted from TSP instances in TSPLIB.

The first visiting city is fixed to city 1. The visiting order of remaining n-1 cities must be computed.

• 529 bits, Penalty=1000: gr24.csv.gz, gr24.utm.gz. Optimal solution:-21728(QUBO), 1272(TSP)

• 2209 bits, Penalty=1000: gr48.csv.gz, gr48.utm.gz. Optimal solution:-41954(QUBO), 5046(TSP)

• 2601 bits, Penalty=2000: berlin52.csv.gz, berlin52.utm.gz. Optimal solution:-94458(QUBO), 7542 (TSP)

• 5625 bits, Penalty=20000: pr76.csv.gz, pr76.utm.gz. Optimal solution:-1391841(QUBO), 108159(TSP)

• 14161 bits, Penalty=1000: gr120.csv.gz, gr120.utm.gz. Optimal solution:-112058(QUBO), 6942(TSP)

• 25500 bits, Penalty=1000: ch150.csv.gz, ch150.utm.gz. Optimal solution:-142472(QUBO), 6528(TSP)

Converted from QAP instances in QAPLIB.

• 400 bits, Penalty=100000000: tai20b.csv.gz, tai20b.utm.gz. Optimal solution:-1877544681(QUBO), 122455319(QAP)

• 676 bits, Penalty=10000000: bur26a.csv.gz, bur26a.utm.gz. Optimal solution:-254447561(QUBO), 5426670(QAP)

• 900 bits, Penalty=1000: nug30.csv.gz, nug30.utm.gz. Optimal solution:-23876(QUBO), 6124(QAP)

• 2500 bits, Penalty=1000000: tai50a.csv.gz, tai50a.utm.gz. Best known solution:-15058590(QUBO), 4941410(QAP)

• 10000 bits, Penalty=10000: sko100a.csv.gz, sko100a.utm.gz. Best known solution:-847998(QUBO), 152002(QAP)

• 22500 bits, Penalty=400000: tho150.csv.gz, tho150.utm.gz. Best known solution:-51866602(QUBO), 8133398(QAP)

The positions of n Queens are encoded in an nxn bit matrix so that the bit is1 if a queen is placed.

Since N-QUEEENS is a quite easy problem, it can be solved less than 1 second.

• 64 bits: nqueen8.csv.gz, nqueen8.utm.gz. Optimal solution: -8 (QUBO)

• 256 bits: nqueen16.csv.gz, nqueen16.utm.gz. Optimal solution: -16 (QUBO)

• 10000 bits: nqueen100.csv.gz, nqueen100.utm.gz. Optimal solution: -100 (QUBO)

• 32761 bits: nqueen181.csv.gz, nqueen181.utm.gz. Optimal solution: -181 (QUBO)