Implementation analysis of efficient heuristic algorithms for the traveling salesman problem

Abstract

-The state-of-the-art of local search heuristics for the traveling salesman problem (TSP) is chiefly based on algorithms using the classical Lin-Kernighan (L-K) procedure and the Stem-and-Cycle (S&C) ejection chain method. Critical aspects of implementing these algorithms efficiently and effectively rely on taking advantage of special data structures and on maintaining appropriate candidate lists to store and update potentially available moves. We report the outcomes of an extensive series of tests on problems ranging from 1,000 to 1,000,000 nodes, showing that by intelligently exploiting elements of data structures and candidate lists routinely included in state-of-the-art TSP solution software, the S&C algorithm clearly outperforms all implementations of the Lin-Kernighan procedure. Moreover, these outcomes are achieved without the use of special tuning and implementation tricks that are incorporated into the leading versions of the L-K procedure to enhance their computational efficiency.

Data structures and ejection chains for solving large-scale traveling salesman problems

“…The results obtained with this new implementation [5] on a testbed provided for the ''8th DI-MACS Implementation Challenge'' [5] clearly demonstrate the efficiency of the new implementation over the original version and, more importantly, establish the stem-and-cycle algorithm as one of the most efficient methods currently available for the TSP [3,6]. …”

“…The motivation for this study comes from the fact that the stem-and-cycle algorithm has proved to be extremely effective and competitive with the best algorithms for the TSP [3,6]. We therefore anticipated that the algorithm's efficiency when solving large scale problems can be improved by the implementation of a data structure specifically designed to reduce the computational complexity associated with the path reversal operations needed at each iteration of the algorithm.…”

Genetic operators for combinatorial optimization in TSP and microarray gene ordering

“…The systematic process of determining frag is described later in this section. As an example, let us consider a string P that is sliced into three random fragments (1-8), (9)(10)(11)(12)(13)(14) and (15)(16)(17)(18)(19)(20) for a 20-city problem. P = 1 2 3 4 5 6 7 8 |9 10 11 12 13 14| 15 16 17 18 19 20 For tour construction the first fragment (9-14) is chosen randomly.…”

“…Of particular interest are the GAs, due to the effectiveness achieved by this class of techniques in finding near optimal solutions in short computational time for large combinatorial optimization problems. The state-of-theart techniques for solving TSP with GA incorporates various local search heuristics including modified versions of LinKernighan (LK) heuristic [12][13][14][15]. It has been found that, hybridization of local search heuristics with GA for solving TSP leads to better performance, in general.…”

Improving the Efficiency of Helsgaun’s Lin-Kernighan Heuristic for the Symmetric TSP

“…Variations of this idea have been explored recently by Helsgaun [16], Schilham [26], and Tamaki [28]. Considering STSP heuristics, Helsgaun's LKH [16] appears to exceed all further algorithms including the multiple runs of Chained Lin-Kernighan and some other high-end STSP heuristics introduced by Applegate et al [1], Balas and Simonetti [2], Cook and Seymour [5], Gamboa et al [6,7], Kahng and Reda [18], Schilham [26], Tamaki [28], and Walshaw [30].…”