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PubMed1969

Chemical evolution.

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Biological Evolution↗
PubMedDate not supplied

[Memory and evolution].

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Biological Evolution↗
PubMed2005

Maximum likelihood of evolutionary trees: hardness and approximation.

MOTIVATION: Maximum likelihood (ML) is an increasingly popular optimality criterion for selecting evolutionary trees. Yet the computational complexity of ML was open for over 20 years, and only recently resolved by the authors for the Jukes-Cantor model of substitution and its generalizations. It was proved that reconstructing the ML tree is computationally intractable (NP-hard). In this work we explore three directions, which extend that result. RESULTS: (1) We show that ML under the assumption of molecular clock is still computationally intractable (NP-hard). (2) We show that not only is it computationally intractable to find the exact ML tree, even approximating the logarithm of the ML for any multiplicative factor smaller than 1.00175 is computationally intractable. (3) We develop an algorithm for approximating log-likelihood under the condition that the input sequences are sparse. It employs any approximation algorithm for parsimony, and asymptotically achieves the same approximation ratio. We note that ML reconstruction for sparse inputs is still hard under this condition, and furthermore many real datasets satisfy it.

Algorithms↗
PubMed2005

The hierarchical fair competition (HFC) framework for sustainable evolutionary algorithms.

Many current Evolutionary Algorithms (EAs) suffer from a tendency to converge prematurely or stagnate without progress for complex problems. This may be due to the loss of or failure to discover certain valuable genetic material or the loss of the capability to discover new genetic material before convergence has limited the algorithm's ability to search widely. In this paper, the Hierarchical Fair Competition (HFC) model, including several variants, is proposed as a generic framework for sustainable evolutionary search by transforming the convergent nature of the current EA framework into a non-convergent search process. That is, the structure of HFC does not allow the convergence of the population to the vicinity of any set of optimal or locally optimal solutions. The sustainable search capability of HFC is achieved by ensuring a continuous supply and the incorporation of genetic material in a hierarchical manner, and by culturing and maintaining, but continually renewing, populations of individuals of intermediate fitness levels. HFC employs an assembly-line structure in which subpopulations are hierarchically organized into different fitness levels, reducing the selection pressure within each subpopulation while maintaining the global selection pressure to help ensure the exploitation of the good genetic material found. Three EAs based on the HFC principle are tested - two on the even-10-parity genetic programming benchmark problem and a real-world analog circuit synthesis problem, and another on the HIFF genetic algorithm (GA) benchmark problem. The significant gain in robustness, scalability and efficiency by HFC, with little additional computing effort, and its tolerance of small population sizes, demonstrates its effectiveness on these problems and shows promise of its potential for improving other existing EAs for difficult problems. A paradigm shift from that of most EAs is proposed: rather than trying to escape from local optima or delay convergence at a local optimum, HFC allows the emergence of new optima continually in a bottom-up manner, maintaining low local selection pressure at all fitness levels, while fostering exploitation of high-fitness individuals through promotion to higher levels.

Algorithms↗