the multiple traveling salesman problem (mtsp) is a generalization of the famous traveling salesman problem (tsp), where more than one salesman is used in the solution. although the mtsp is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. this paper presents an efficient and evolutionary optimization algorith...

The multiple traveling salesman problem (MTSP) is a generalization of the famous traveling salesman problem (TSP), where more than one salesman is used in the solution. Although the MTSP is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. This paper presents an efficient and evolutionary optimization algorith...

Helsgaun has introduced and implemented the lower tolerances (α-values) for an approximation of Held-Karp’s 1-tree with the purpose to improve the Lin-Kernighan’s Heuristic (LKH) for the Symmetric TSP (STSP). The LKH appears to exceed the performance of all STSP heuristic algorithms proposed to date. In this paper we improve the Helsgaun’s LKH based on an approximation of Zhang and Looks’ backb...

In recent years, several heuristics have been proposed for the hardware/software partitioning problem. One of the most promising directions is the adaptation of the Kernighan-Lin algorithm. The Kernighan-Lin heuristic was originally developed for circuit partitioning, but it has been adapted to other domains as well. Moreover, numerous improvements have been suggested so that now several varian...

This report describes an implementation of the Lin-Kernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397-city problem (th...

We present an “adaptive multi-start” genetic algorithm for the Euclidean traveling salesman problem that uses a population of tours locally optimized by the Lin-Kernighan algorithm. An all-parent cross-breeding technique, chosen to exploit the structure of the search space, generates better locally optimized tours. Our work generalizes and improves upon the approach of Boese et al. [2]. Experim...

Multi-trial Lin-Kernighan-Helsgaun 2 (LKH-2) is widely considered to be the best Interated Local Search heuristic for the Traveling Salesman Problem (TSP) and has found the best-known solutions to a large number of benchmark problems. Although LKH-2 performs exceptionally well on most instances, it is known to have difficulty on clustered instances of the TSP. Generalized Partition Crossover (G...

The Chained Lin-Kernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, where nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) network-based framework the resulting tours are modified and exchanged with neighboring nodes. We show that ...

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-...