Chaotic simulated annealing by a neural network model with transient chaos

Chen, Luonan; Aihara, Kazuyuki

doi:10.1016/0893-6080(95)00033-v

Cited by 610 publications

(260 citation statements)

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“…From Fig. 4F we find that the construction of the optimal path for the whole ant colony is similar to that of chaotic annealing, which is an effective optimization mechanism (24,25). Fig.…”

Section: Resultsmentioning

confidence: 97%

“…A larger y means a higher degree of chaotic crawling. Based on the mechanism of chaotic annealing (24), the continual decrement dynamics of y i (t) is represented by y i ðtÞ = y i ðt − 1Þ ð1+riÞ , which depends on the self-organization factor r i (see Methods for details on r i ). The movement adjustment of each ant is executed as follows:…”

Section: Resultsmentioning

confidence: 99%

“…As time evolves, the pheromone intensity increases and the chaotic crawling of ants is gradually reduced. Based on the annealing mechanism (24,25), the adjustment of the chaotic behavior of individual ant i is achieved by introducing a successively decreasing dynamical equation represented by y i ðtÞ = y i ðt − 1Þ ð1+ri Þ . The self-organization factor r i is used to control the time of the chaotic search.…”

Section: Methodsmentioning

confidence: 99%

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Chaos–order transition in foraging behavior of ants

Peng

Kurths

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit lowdimensional deterministic-chaotic activities. However, the influences of the nest, ants' physical abilities, and ants' knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal.foraging dynamics | learning process | low-dimensional chaos | mathematical modeling | synchronization B oth experimental data analysis and mathematical modeling on the foraging behavior of group animals (especially ant colonies) have recently captured much attention due to the high level of self-organizing structures that emerge at the collective level (1-5). Random walking is a widely discussed strategy in the research literature on the foraging behavior of group animals (2, 6-8). Some ecologists maintain that especially Lévy flight schemes can appropriately be used to describe the foraging behavior (6, 7). However, some recent studies have raised doubts whether this is a valid conjecture (2,8,9). It is even argued that the rules of locomotion for a walker are always consistent with a purely deterministic model, rather than with a stochastic scheme (9, 10).On the other hand, in the studies on the foraging behavior of animals, the existence of homes has so far received relatively little attention. Here we argue that the existence of a home or nest influences the foraging process to a large extent. Animals are due to return to their homes because of increasing exhaustion of energy. Moreover each foraging process of an animal is also a learning process. With foraging repetition, long-term memory continues to accumulate, an animal's knowledge about the environment of its nest gets richer, and the region that the animal is familiar with continues to enlarge. Moreover, animals' physical ability and knowledge as determined by the...

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“…From Fig. 4F we find that the construction of the optimal path for the whole ant colony is similar to that of chaotic annealing, which is an effective optimization mechanism (24,25). Fig.…”

Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Chaos–order transition in foraging behavior of ants

Peng

Kurths

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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“…The first methods applying chaos to combinatorial optimization [4]- [6] was for the Hopfield-Tank neural networks [14]. Reference [4] transformed each neuron in the Hopfield-Tank neural networks to the form having chaotic dynamics, and showed the effectiveness of the chaotic dynamics for solution search.…”

Section: Chaos Applied To Combinatorial Optimizationmentioning

confidence: 99%

Improving Performance of Heuristic Algorithms by Lebesgue Spectrum Filter

Hasegawa

2016

IEICE Trans. Commun.

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SUMMARYThe previous researches on the chaotic CDMA have theoretically derived the chaotic sequences having the minimum asynchronous cross-correlation. To minimize the asynchronous cross-correlation, autocorrelation of each sequence have to be C (τ) ≈ C × r τ , r = −2 + √ 3, dumped oscillation with increase of the lag τ. There are several methods to generate such sequences, using a chaotic map, using the Lebesgue spectrum filter (LSF) and so on. In this paper, such lowest cross-correlation found in the chaotic CDMA researches is applied to solution search algorithms for combinatorial optimization problems. In combinatorial optimization, effectiveness of the chaotic search has already been clarified. First, an importance of chaos and autocorrelation with dumped oscillation for combinatorial optimization is shown. Next, in order to realize ideal solution search, the LSF is applied to the Hopfield-Tank neural network, the 2-opt method and the 2-exchange method. Effectiveness of the LSF is clarified even for the large problems for the traveling salesman problems and the quadratic assignment problems.

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“…Cooper [5] developed the method of higher order neural networks (HONN) for mapping TSP and studied the stability conditions of valid solutions. A number of approaches based upon chaotic neural networks have also been proposed to solve the TSP, and excellent results with less local minima have been obtained due to the global search capability of the chaotic networks [6]- [10]. Manuscript It has been widely recognized that the Hopfield-Tank (H-T) formulation [1] of energy function often causes infeasible solutions in solving the TSP [11].…”

Section: Introductionmentioning

confidence: 99%

Parameter Settings of Hopfield Networks Applied to Traveling Salesman Problems

Tang¹,

Tan²,

Yi³

2007

Neural Networks: Computational Models and Applications

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Abstract-Parameter setting is a critical step in the Hopfield networks solution of the traveling salesman problem (TSP), which is often prone to extraneous solutions. This paper presents some stability criteria that ensure the convergence of valid solutions and suppression of infeasible solutions. Our theory is based on an enhanced parametric formulation that maps TSP onto a continuoustime Hopfield network (CHN), which is more advantageous than the Hopfield-Tank (H-T) formulation. A set of analytical conditions for optimal parameter settings of the CHN is then derived, and the resulting performance is validated by simulations.Index Terms-Hopfield neural networks, traveling salesman problem (TSP), parameter setting, stability.

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Chaotic simulated annealing by a neural network model with transient chaos

Cited by 610 publications

References 50 publications

Chaos–order transition in foraging behavior of ants

Chaos–order transition in foraging behavior of ants

Improving Performance of Heuristic Algorithms by Lebesgue Spectrum Filter

Parameter Settings of Hopfield Networks Applied to Traveling Salesman Problems

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