Computing an expected hitting time for the 3-urn Ehrenfest model via electric networks

The Study on Convergence and Convergence Rate of Genetic Algorithm Based on an Absorbing Markov Chain

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.239-240.1511 ◽

2012 ◽

Vol 239-240 ◽

pp. 1511-1515 ◽

Cited By ~ 1

Author(s):

Jing Jiang ◽

Li Dong Meng ◽

Xiu Mei Xu

Keyword(s):

Genetic Algorithm ◽

Markov Chain ◽

Convergence Rate ◽

Hitting Time ◽

Sufficient Condition ◽

First Hitting Time ◽

Absorbing Markov Chain ◽

Expected Hitting Time ◽

Optimization Efficiency ◽

Theoretical Issues

The study on convergence of GA is always one of the most important theoretical issues. This paper analyses the sufficient condition which guarantees the convergence of GA. Via analyzing the convergence rate of GA, the average computational complexity can be implied and the optimization efficiency of GA can be judged. This paper proposes the approach to calculating the first expected hitting time and analyzes the bounds of the first hitting time of concrete GA using the proposed approach.

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Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

Advances in Applied Probability ◽

10.1239/aap/1231340160 ◽

2008 ◽

Vol 40 (4) ◽

pp. 966-978

Author(s):

Archis Ghate

Keyword(s):

Markov Chains ◽

Structural Properties ◽

Long Range ◽

World Literature ◽

Relative Size ◽

Small World ◽

Hitting Time ◽

Hitting Times ◽

Message Delivery ◽

Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

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A defender-attacker model and algorithm for maximizing weighted expected hitting time with application to conservation planning

IISE Transactions ◽

10.1080/24725854.2017.1360533 ◽

2017 ◽

Vol 49 (12) ◽

pp. 1112-1128 ◽

Cited By ~ 3

Author(s):

Jorge A. Sefair ◽

J. Cole Smith ◽

Miguel A. Acevedo ◽

Robert J. Fletcher

Keyword(s):

Conservation Planning ◽

Hitting Time ◽

Expected Hitting Time

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Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

Advances in Applied Probability ◽

10.1017/s0001867800002925 ◽

2008 ◽

Vol 40 (04) ◽

pp. 966-978

Author(s):

Archis Ghate

Keyword(s):

Markov Chains ◽

Structural Properties ◽

Long Range ◽

World Literature ◽

Relative Size ◽

Small World ◽

Hitting Time ◽

Hitting Times ◽

Message Delivery ◽

Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

Download Full-text