The Lin-Kernighan Algorithm Driven by Chaotic Neurodynamics for Large Scale Traveling Salesman Problems

Solving the Steiner tree problem in graphs by chaotic search

“…The chaotic search is one of the effective metaheuristics for solving N P-hard combinatorial optimization problems, such as the traveling salesman problems [13][14][15][16], the quadratic assignment problems [17][18][19], and the vehicle routing problems [20,21]. From this viewpoint, we apply a chaotic search for solving the Steiner tree problem in graphs.…”

“…On the other hand, as one of the effective metaheuristics, an algorithm using chaotic dynamics, or the chaotic search, has already been proposed to escape from undesirable local minima. The chaotic search shows good performance for solving various N P-hard combinatorial optimization problems, such as the traveling salesman problems [13][14][15][16], the quadratic assignment problems [17][18][19], the vehicle routing problems [20,21], the packet routing problems [22][23][24][25][26][27][28][29], and the motif extraction problems [30,31]. However, the Steiner tree problem in graphs has a different feature from the abovementioned combinatorial optimization problems; local searches we introduced in this paper produce not only feasible solutions but also infeasible solutions during the search.…”

The double-assignment method for the exponential chaotic tabu search in quadratic assignment problems

“…The exponential chaotic tabu search, then, has been improved by combining chaotic neuro-dynamics with the Or-opt algorithm, k-opt algorithm, LK algorithm, and stem-and-cycle ejection chain algorithm. As a result, TSPs with the size of 10 5 to 10 7 can be efficiently solved through the chaotic search [25][26][27][28][29][30]. In addition to TSPs, the exponential chaotic tabu search with chaotic neuro-dynamics was also applied to QAPs [31,32], motif extraction problems [33], vehicle routing problems with time window [34], and packet routing problems [35]; furthermore, effectiveness of the exponential chaotic tabu searches was demonstrated through these problems.…”

Chaotic motif sampler: detecting motifs from biological sequences by using chaotic neurodynamics

“…In deterministic approaches, such as tabu search [4,5] and chaotic search, the solution space is changed deterministically to avoid the local minima. It has been shown that the most effective algorithm is the one that uses chaotic dynamics to explore the solution spaces [6][7][8][9][10]. The central idea of the algorithm is that the execution of a heuristic algorithm, for instance, the 2-opt algorithm 1 for solving traveling salesman problems (TSPs), is controlled by chaotic dynamics.…”

“…Chaotic search-an approach that combines a heuristic algorithm and chaotic dynamics-is employed to overcome the local minimum problem and to find better near optimal solutions. It has already been shown that the chaotic search method can yield good near optimal solutions not only for TSPs [6][7][8][9][10] but also for other N P-hard problems such as the quadratic assignment problem (QAP) [11] and the vehicle routing problem (VRP) [12,13].…”