5

There are competitions for constraint satisfaction solvers. Some problems there can be readily translated to IP solvers as well. See e.g., MiniZinc challenge which has taken place yearly since 2008 or the XCSP competition.


4

There are no competitions targeting general integer programming or mixed integer programming, but there are (or were) benchmarks, such as the MIPLIB (linear) and the MINLPLIB (nonlinear). There are competitions for subsets (PB, SAT, max-SAT) and for constraint programming, as you and other answers pointed out. You can find many competitions (DIMACS ...


3

There was a Pseudo-Boolean solver competition from 2005-2012, but (as far as I can tell) nothing since then. Integer Linear Programming is a subset of Pseudo-Boolean programming. See the 2012 competition page for results and links to other competition results.


3

This sounds to me like the Knapsack problem where $z$ is the weight of each item, $Z$ is the capacity of the knapsack, $g$ the value of the item, and $G$ the value to be achieved. The problem is NP-complete but solvable, using dynamic programming, in pseudo-polynomial time $O(n \cdot W)$ where $W = \max_{(z,g) \in R}(g)$. You can prove that the Knapsack ...


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