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# Time-Dependent Traveling Salesman Problem

### Article Outline

Keywords

Keywords TDTSP - Benders decomposition - Convexification - Multistage optimization

Given a list of cities, the classical traveling salesman problem is aimed at finding the least cost tour through the cities. The time-dependent traveling salesman problem is a generalization of the traveling salesman problem where the cost of travel between cities is also dependent on the order in which they are traversed. We now provide a more formal description of the two problems. Consider a set of cities 𝒩 = {1, …, *n*} and a mapping, *D*: 𝒩 × 𝒩 → **R**, that associates with each ordered city-pair a cost incurred when a travel/transition is undertaken starting from the first city and ending at the second city. The data may be pictorially visualized