Socially inspired algorithms for the travelling thief problem

Abstract

Many real-world problems are composed of two or more problems that are interdependent on each other. The interaction of such problems usually is quite complex and solving each problem separately cannot guarantee the optimal solution for the overall multi-component problem. In this paper we experiment with one particular 2-component problem, namely the Traveling Thief Problem (TTP). TTP is composed of the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). We investigate two heuristic methods to deal with TTP. In the first approach we decompose TTP into two sub-problems, solve them by separate modules/algorithms (that communicate with each other), and combine the solutions to obtain an overall approximated solution to TTP (this method is called CoSolver ). The second approach is a simple heuristic (called density-based heuristic, DH) method that generates a solution for the TSP component first (a version of Lin-Kernighan algorithm is used) and then, based on the fixed solution for the TSP component found, it generates a solution for the KP component (associated with the given TTP). In fact, this heuristic ignores the interdependency between sub-problems and tries to solve the sub-problems sequentially. These two methods are applied to some generated TTP instances of different sizes. Our comparisons show that CoSolver outperforms DH specially in large instances.