Table 3 shows the results of problems of size 50k to 100k variables. CPLEX was unable to find the best-known solution to any of these problems in the time limit of 6 hours. AlphaQUBO quickly provided best known solutions for all problems, outperforming CPLEX in terms of solution quality and time. Note that these QUBO models are the largest reported on in the literature to date.
ID
Vars
Constraints
Density
CPLEX (OFV)
CPLEX (Time)
alphaQUBO (OFV)
alphaQUBO (Time)
spp50k
50,000
10,000
25
76903
18144
76402
2315
spp60k
60,000
12,000
25
92293
16060
91912
2876
spp70k
70,000
14,000
25
109168
19084
108112
272
spp80k
80,000
16,000
25
125139
18600
123890
175
spp90k
90,000
18,000
25
140223
15278
139269
1804
spp100k
100,000
20,000
25
154694
19509
154351
622
Table 3
Key Takeaway:
alphaQUBO solves large combinatorial optimization problems quickly and efficiently. This is clearly shown in the benchmark with CPLEX.
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