Investigation of the traveling thief problem

Abstract

The Traveling Thief Problem (TTP) is a relatively new benchmark problem created to study problems which consist of interdependent subproblems. In this paper we investigate what the fitness landscape characteristics are of some smaller instances of the TTP with commonly used local search operators in the context of metaheuristics that uses local search. The local search operators include: 2-opt, Insertion, Bitflip and Exchange and metaheuristics include: multi-start local search, iterated local search and genetic local search. Fitness landscape analysis shows among other things that TTP instances contain a lot of local optima but their distance to the global optimum is correlated with its fitness. Local optima networks with respect to an iterated local search reveals that TTP has a multi-funnel structure. Other experiments show that a steady state genetic algorithm with edge assembly crossover outperforms multi-start local search, iterated local search and genetic algorithms with different tour crossovers. At last we performed a comparative study using the genetic algorithm with edge assembly crossover on relatively larger instances of the commonly used benchmark suite. As a result we found new best solutions to almost all studied instances.