In the Traveling Purchaser Problem with Incompatibility Constraints (TPP-IC), there is a depot and a set of markets. The purchaser must purchase a list of required items, where each item is available at specific markets. Item prices vary between markets, and there are travel costs associated with moving between them. Some items are incompatible due to their nature and cannot be transported together in the same route. The obejctive of the TPP-IC is to determine a set of minimum-cost routes—accounting for both purchasing and travel costs—that: start and end at the depot; collect all required items, and do not transport incompatible items in the same route.