Embedding a Chained Lin-Kernighan Algorithm into a Distributed Algorithm

Abstract

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, were 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 distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050% above the optimum, compared to CLK's average solution of 0.119% above the optimum given the same total CPU time (10 4 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033% above the optimum and the CLK algorithm 0.099%.

Evolutionary algorithm for the k-interconnected multi-depot multi-traveling salesmen problem

“…This perturbs the Lin-Kernighan solution creating three independent random walks of a given length from a vertex v in the neighborhood of this solution. According to [8], this type of kicking strategy presents better results than other strategies suggested in [2].…”

Solving the routing and wavelength assignment problem with a multilevel distributed memetic algorithm

“…Distributing computation is an active field of research, as it offers the possibility to find solutions in less real-time [21]. For exact algorithms, this approach is mandatory to find optimal solutions in realistic time frames due to their prohibitive computation time requirements.…”

Fourier descriptors for 2-Opt and 3-Opt heuristics for traveling salesman problem

“…Figure 4 shows an example of a single 2-Opt swap. By proceeding around the tour, the salesman visits each city A, and an edge AB is defined by a path from A to its directly connected neighbor city, u (12) u (13) u' (12) u'(13) (12) D (13) u' (12) u'(13) B, on the tour. Then, on the tour, given a city A and its edge AB, consider every city C and its edge CD until an edge CD is found so that the length/ cost of (AB þ CD) is larger than (AC þ BD).…”

“…Lin and Kernighan [25] developed a simple and elegant approach (LK algorithm), which is one of the most successful approaches for solving TSP. Following the LK algorithm, other approaches (Martin and Otto [26], Johnson and McGeoch [20], Fisher and Merz [11][12][13]) have been proposed, where the 2-Opt and 3-Opt heuristics are an essential part. Even in the tour merging algorithm proposed by Cook and Seymour [9], k-Opt-based heuristics, such as chained LK (proposed by Martin et al [27]) or LKH (proposed by Helsgaun [18]), are adopted as the underlying TSP solver.…”