Random-key cuckoo search for the travelling salesman problem

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in both spaces using L\'evy flights. The performance of the proposed RKCS is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that RKCS is superior to some other metaheuristic algorithms

A hyperheuristic approach based on low-level heuristics for the travelling thief problem

In this paper, we investigate the use of hyper-heuristics for the travelling thief problem (TTP). TTP is a multi-component problem, which means it has a composite structure. The problem is a combination between the travelling salesman problem and the knapsack problem. Many heuristics were proposed to deal with the two components of the problem separately. In this work, we investigate the use of automatic online heuristic selection in order to find the best combination of the different known heuristics. In order to achieve this, we propose a genetic programming based hyper-heuristic called GPHS*, and compare it to state-of-the-art algorithms. The experimental results show that the approach is competitive with those algorithms on small and mid-sized TTP instances.Mohamed El Yafrani, Marcella Martins, Markus Wagner, Belaïd Ahiod, Myriam Delgado, Ricardo Lüder

A fitness landscape analysis of the travelling thief problem

Local Optima Networks are models proposed to understand the structure and properties of combinatorial landscapes. The fitness landscape is explored as a graph whose nodes represent the local optima (or basins of attraction) and edges represent the connectivity between them. In this paper, we use this representation to study a combinatorial optimisation problem, with two interdepend components, named the Travelling Thief Problem (TTP). The objective is to understand the search space structure of the TTP using basic local search heuristics and to distinguish the most impactful problem features. We create a large set of enumerable TTP instances and generate a Local Optima Network for each instance using two hill climbing variants. Two problem features are investigated, namely the knapsack capacity and profit-weight correlation. Our insights can be useful not only to design landscape-aware local search heuristics, but also to better understand what makes the TTP challenging for specific heuristics.Mohamed El Yafrani, Marcella S. R. Martins, Mehdi El Krari, Markus Wagner, Myriam R. B. S. Delgado, Belaïd Ahiod, Ricardo Lüder