This research aims to address the practical difficulties of computational heuristics for symbolic regression, which models data with algebraic expressions. In particular we are motivated by cases in which the target u...
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ISBN:
(纸本)9781728121536
This research aims to address the practical difficulties of computational heuristics for symbolic regression, which models data with algebraic expressions. In particular we are motivated by cases in which the target unknown function may be best represented as the ratio of functions. We propose an alternative general approach based on a different representation of mathematical models with an analytic continued fraction representation, from which rational function models can be extracted. A memetic algorithm, which is a paradigm of meta-heuristic optimization based on the evolution of solutions by a set of computational agents, is implemented to generate solutions in this representation. A population of computational agents with problem domain knowledge improves feasible solutions using local search heuristics and produces models that fit the data better. In addition, the agents compete in searching for function models with fewer number of variables. Agent interactions are constrained by a population structure which has been previously used in several successful MAs for other combinatorial optimization problems. We utilize a tree-based population structure to improve the algorithm's consistency and performance. Data from real-world applications are used to measure the potential of our approach and benchmark its performance against other approaches in symbolic regression.
As a straightforward continuation of our previous work in this paper new memetic (combined evolutionary and gradient based) methods are proposed for constructing hierarchical-interpolative fuzzy rule bases in the fram...
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ISBN:
(纸本)9781467315067
As a straightforward continuation of our previous work in this paper new memetic (combined evolutionary and gradient based) methods are proposed for constructing hierarchical-interpolative fuzzy rule bases in the frame of a supervised machine learning system modeling black box systems defined by input-output pairs. In this work the resulting hierarchical rule bases are constructed by using structure building Genetic and Bacterial memetic programming Algorithms, thus stochastic evolutionary optimization methods containing deterministic local search steps. Applying hierarchical-interpolative fuzzy rule bases has proved an efficient way of reducing the complexity of knowledge bases, whereas memetic techniques often ensure a relatively fast convergence in the learning process. The literature has highlighted the advantages of memetic methods against pure evolutionary algorithms, thus the combination of hierarchical-interpolative fuzzy rule bases with memetic techniques may form promising hierarchical-interpolative machine learning systems.
As a straightforward continuation of our previous work in this paper new memetic (combined evolutionary and gradient based) methods are proposed for constructing hierarchical-interpolative fuzzy rule bases in the fram...
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ISBN:
(纸本)9781467315074
As a straightforward continuation of our previous work in this paper new memetic (combined evolutionary and gradient based) methods are proposed for constructing hierarchical-interpolative fuzzy rule bases in the frame of a supervised machine learning system modeling black box systems defined by input-output pairs. In this work the resulting hierarchical rule bases are constructed by using structure building Genetic and Bacterial memetic programming Algorithms, thus stochastic evolutionary optimization methods containing deterministic local search steps. Applying hierarchical-interpolative fuzzy rule bases has proved an efficient way of reducing the complexity of knowledge bases, whereas memetic techniques often ensure a relatively fast convergence in the learning process. The literature has highlighted the advantages of memetic methods against pure evolutionary algorithms, thus the combination of hierarchical-interpolative fuzzy rule bases with memetic techniques may form promising hierarchical-interpolative machine learning systems.
For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers has increased rapidly, especially in...
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For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers has increased rapidly, especially in information technology, e.g., public key cryptography algorithms, hash tables, and pseudo-random number generators. One of the most popular topics to attract attention is to find a formula that maps the set of natural numbers into the set of prime numbers. However, to date there is no known formula that produces all primes. In this article, we use a hybrid evolutionary algorithm, called the memetic programming (MP) algorithm, to generate mathematical formulas that produce distinct primes. Using the MP algorithm, we succeeded in discovering an interesting set of formulas that produce sets of distinct primes.
For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers increased rapidly especially in info...
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ISBN:
(纸本)9784990288051
For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers increased rapidly especially in information technology, e.g., public key cryptography algorithms, hash tables, and pseudorandom number generators. One of the most popular topics that attract attention is to find a formula that maps the set of integers into the set of prime numbers. However, up to now there is no known formula that produces all primes. In this paper, we use a hybrid evolutionary algorithm, called the memetic programming (MP) algorithm, to generate mathematical formulas that produce distinct primes. Using the MP algorithm, we succeeded to discover an interesting set of formulas that produce sets of distinct primes.
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