Combining two local searches with crossover

Abstract

The Traveling Salesman Problem (TSP) is one of the most well-known optimization problems. Ejection Chain Methods (ECM) and the Lin-Kernighan (LK) heuristic are the state-of-art local search (LS) algorithms for solving the TSP. Multi-Neighborhood Search (MNS) is known to be especially suitable for hybridization with Evolutionary Computation (EC). Hybridizing two different LS algorithms with each other (LS-LS) can combine their mutual advantages and lead to better performance. We introduce the new concept of LS-LS-X hybrids, which combines two different LS algorithms with a crossover operator. We enhance the two best LS-LS hybrids, ECM-LK and LK-MNS, with Order Based Crossover and Heuristic Crossover. We hybridize these LS-LS-X algorithms with an Evolutionary Algorithm, the most prominent EC method, and obtain highly-efficient (memetic) EC-LS-LS-X algorithms. We conduct a large-scale experimental study with many different algorithm setups on all 110 symmetric instances of the TSPLib benchmark set. We find that the LS-LS-X hybrids have significantly better performance than the original LS-LS and their component algorithms. They even outperform several memetic EC-LS-LS and EC-LS algorithm setups. The EC-LS-LS-X hybrids are the best hybrid EA-based TSP solvers by a large margin in our experiment and the wide range of algorithms available in the popular TSP Suite.