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.

A comprehensive benchmark set and heuristics for the traveling thief problem

“…Furthermore, we intend to discover inherent regularity in interaction between components and their mutual influence. The preliminary results have recently been obtained in [5], where the potential benefit of methods considering interdependency between components was studied.…”

Cosolver2B: An efficient local search heuristic for the Travelling Thief Problem

“…Cosolver is an abstract algorithm proposed in [2] to solve TTP. The idea behind the algorithm is simple.…”

“…An Evolutionary Algorithm and a Random Local Search were proposed in [13] to provide a starting point to other researchers. In [2], an approach named Cosolver was introduced to solve TTP by separating the sub-problems and managing a communication between them. Lastly, an interesting work on TTP introduces many complexity reduction techniques in order to solve very large instances in a time budget of 10 minutes [11].…”

“…In this paper, we follow the ideas proposed in [2] and [11] to propose further improvements and introduce an algorithm based on the Cosolver framework that can solve TTP instances efficiently.…”

Approximate Approaches to the Traveling Thief Problem

“…The resulting algorithm significantly outperforms the three iterative and constructive algorithms originally presented in [10]. Bonyadi et al [4] are the first to attempt to solve both components of the TTP in parallel, instead of sequentially. The authors design a coevolutionary approach called CoSolver in which modules responsible for either the TSP part or the KP part communicate with each other.…”