Mathematical model and genetic algorithm for the traveling thief problem

In this article, two well-known combinatorial optimization problems are discussed, namely the Traveling Thief Problem (TTP), which is a combination of the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). Deciphering such multicomponent optimization problems is difficult not only because of the strict optimization problems involved, but also because of the interdependencies between the different components in particular. The purpose of this problem is to form a collection plan, according to which a thief visits all cities and determines which items should be taken from which city in order to get the maximum benefit. A mathematical model has been developed for the problem under consideration, and two different genetic algorithms have been developed because large-sized problems cannot be solved with the proposed mathematical model. The performances of the developed algorithms were tested using test problems of different properties.