Automatic control systems (5th ed.)
Automatic control systems (5th ed.)
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Modelling genetic algorithm dynamics
Theoretical aspects of evolutionary computing
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
On The Dynamics Of Evolutionary Multi-objective Optimization
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Two improved differential evolution schemes for faster global search
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Adaptive computational chemotaxis in bacterial foraging optimization: an analysis
IEEE Transactions on Evolutionary Computation
Self-adaptive differential evolution
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
Stability analysis of the particle dynamics in particle swarm optimizer
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
On stability of the chemotactic dynamics in bacterial-foraging optimization algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
The Effects of Different Kinds of Move in Differential Evolution Searches
ACAL '09 Proceedings of the 4th Australian Conference on Artificial Life: Borrowing from Biology
Disturbed Exploitation compact Differential Evolution for limited memory optimization problems
Information Sciences: an International Journal
An effective memetic differential evolution algorithm based on chaotic local search
Information Sciences: an International Journal
Information Sciences: an International Journal
A Differential Covariance Matrix Adaptation Evolutionary Algorithm for real parameter optimization
Information Sciences: an International Journal
A population dynamics model to describe gene frequencies in evolutionary algorithms
Applied Soft Computing
Advances in Engineering Software
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Theoretical analysis of the dynamics of evolutionary algorithms is believed to be very important to understand the search behavior of evolutionary algorithms and to develop more efficient algorithms. In this paper we investigate the dynamics of a canonical Differential Evolution (DE) algorithm with DE/rand/1 type mutation and binomial crossover. Differential Evolution (DE) is well known as a simple and efficient algorithm for global optimization over continuous spaces. Since its inception in 1995, DE has been finding many important applications in real-world optimization problems from diverse domains of science and engineering. The paper proposes a simple mathematical model of the underlying evolutionary dynamics of a one-dimensional DE-population. The model shows that the fundamental dynamics of each search-agent (parameter vector) in DE employs the gradient-descent type search strategy (although it uses no analytical expression for the gradient itself), with a learning rate parameter that depends on control parameters like scale factor F and crossover rate CR of DE. The stability and convergence-behavior of the proposed dynamics is analyzed in the light of Lyapunov's stability theorems very near to the isolated equilibrium points during the final stages of the search. Empirical studies over simple objective functions are conducted in order to validate the theoretical analysis.