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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.

2 votes

Optimal Graph Splitting

Both of these problems share many similarities with the partition problem for which there exists efficient greedy algorithms, dynamic programming approaches, and exact methods (see link).
Philippe Olivier's user avatar
1 vote

Distribution of a knapsack problem

The optimal value of $p(A)$ can easily be found by ordering the items by nonincreasing profits, and packing the first $M$ items into the knapsack. The average value of a packing is $(\sum_{i \in N}p_{ …
Philippe Olivier's user avatar