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Find the shortest possible route that visits each city exactly once and returns to the origin city.

Assign colors to the vertices of a graph so that no two adjacent vertices are of the same color. The goal is to minimize the number of colors used.

Generalization of the Traveling Salesman Problem. The objective is to find the optimal set of routes for a fleet of vehicles delivering to a given set of customers such that the total route cost is minimized.

Given a set of elements and a collection of sets containing these elements, identify the smallest collection of sets such that every element in the universe of sets is contained in at least one set of the collection.

Optimization where some or all of the variables are required to be integers. The goal is to find the values of the integer variables that maximize or minimize the objective function while satisfying the constraints.

Find a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Identify the best locations for facilities to minimize transportation costs while considering constraints like distance, capacity, and customer demand.

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

A variant of the Maximum Weighted Bipartite Matching problem. Aim is to assign jobs to workers in such a way as to maximize the total profit or minimize the total cost, given that each job can be assigned to exactly one worker and vice versa.