Design¶
Each family consists of 15 source instances from BOBILib. Every
source instance yields one instance per combination of q (the number of follower
variables with a piecewise-linear objective term) and p (the number of pieces per
term). Every instance is solved with an integer leader, as in BOBILib, and with a
continuous leader. Instances are named <BOBILib instance>__q<q>__p<p>.
Every method ran on every instance with a time limit of 3,600 s.
Xu–Wang¶
Origin. A stratified random sample (seed 20261002) of 8 instances with n = 60 and 7 instances with n = 10 among the BOBILib Xu–Wang instances with at least 4 negative-cost followers.
Source instances: bmilplib_10_1, bmilplib_10_2, bmilplib_10_3, bmilplib_10_5, bmilplib_10_6, bmilplib_10_7, bmilplib_10_8, bmilplib_60_1, bmilplib_60_2, bmilplib_60_3, bmilplib_60_4, bmilplib_60_5, bmilplib_60_7, bmilplib_60_8, bmilplib_60_9.
Piecewise-linear construction. q ∈ {1, 2, 3, 4} and p ∈ {2, 4, 8} (12 combinations). The PWL terms are placed on the q negative-cost follower variables, largest objective swing first. Breakpoints are uniform with relative interior perturbation 0.5; at most 4,096 regional assignments (p^q) per instance.
Leader types. integer leader: as in BOBILib (180 instances); continuous leader: the same instances with the leader's integrality relaxed and its bounds kept (180 instances).
Knapsack interdiction¶
Origin. All 15 BOBILib knapsack-interdiction instances of difficulty “easy” with at least 30 leader variables.
Source instances: K5030W07.KNP, K5030W09.KNP, K5030W12.KNP, interdiction35-10, interdiction35-8, interdiction35-9, interdiction40-10, interdiction40-7, interdiction40-8, interdiction45-10, interdiction45-9, interdiction50-10, interdiction50-8, interdiction55-10, interdiction55-9.
Piecewise-linear construction. q ∈ {1, 2, 3, 4} and p ∈ {2, 4, 8} (12 combinations). The PWL terms are placed on the q negative-cost follower variables, largest objective swing first. Breakpoints are uniform with relative interior perturbation 0.5; at most 4,096 regional assignments (p^q) per instance.
Leader types. integer leader: as in BOBILib (180 instances); continuous leader: the same instances with the leader's integrality relaxed and its bounds kept (180 instances).