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

Abstract

Identification of a region in biological sequences, motif extraction problem (MEP) is solved in bioinformatics. However, the MEP is an N P-hard problem. Therefore, it is almost impossible to obtain an optimal solution within a reasonable time frame. To find near optimal solutions for N P-hard combinatorial optimization problems such as traveling salesman problems, quadratic assignment problems, and vehicle routing problems, chaotic search, which is one of the deterministic approaches, has been proposed and exhibits better performance than stochastic approaches. In this paper, we propose a new alignment method that employs chaotic dynamics to solve the MEPs. It is called the Chaotic Motif Sampler. We show that the performance of the Chaotic Motif Sampler is considerably better than that of the conventional methods such as the Gibbs Site Sampler and the Neighborhood Optimization for Multiple Alignment Discovery.

Solving the Steiner tree problem in graphs by chaotic search

“…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.…”

Searching characteristics of chaotic neurodynamics for combinatorial optimization

“…To find approximate solutions for combinatorial optimization problems, many heuristic algorithms have already been proposed. An effective algorithm that introduces chaotic neurodynamics for exploring solution spaces has also been proposed [1][2][3][4][5][6][7]. The algorithm is primarily based on the concept that the execution of a heuristic algorithm or a local search algorithm, such as the 2-opt algorithm for solving TSP, is controlled by chaotic neurodynamics.…”

“…Further, it has already been shown that if the concept is introduced, good near-optimal solutions can be found, because the chaotic dynamics effectively avoids undesirable traps of the local search algorithm into local minima. Then, the local search algorithm controlled by the chaotic dynamics is very effective not only for TSP [1,2] but also for other NP-hard problems such as the quadratic assignment problem (QAP) [3], the vehicle routing problem (VRP) [4,5], and the motif extraction problem (MEP) [6,7].…”

“…In this algorithm [1][2][3][4][5][6][7], a chaotic neural network model is used for realizing a chaotic search; the model qualitatively realizes an important biological feature of a real neuron-the refractory effect [8]. Because of this effect, a neuron hardly fires again for a certain period of time after it has fired or emitted a spike.…”

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

“…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. Salient features of the exponential chaotic tabu search are an exponential decaying continuous tabu (exponential tabu) effect, and an efficient dynamical search in the state-space through chaotic itinerancy [36].…”