Angeline, P. J. (1997). Tracking extrema in dynamic environments. In Angeline, P. J. et al., editors, Proc. of the Sixth International Conference on Evolutionary Programming --- EP'97, pages 335-- 345. Springer Verlag, Heidelberg.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on empirical observations. An extensive survey of the literature of the field along with a collection of benchmark functions and a discussion of methods that have been proposed to improve the performance of evolutionary algorithms in dynamic environments has been compiled by Branke [7] Angeline [1] compares empirically the tracking performance of an evolutionary algorithm employing a form of mutative self adaptation with that of a strategy using a simple heuristic for mutation strength adaptation. The J.J. Merelo Guervos et al. Eds. PPSN VII, LNCS 2439, pp. 3 12, 2002. c ....

....as a model for fitness landscapes at a stage where the population of candidate solutions is in relatively close proximity to the target and is most often studied in the limit of very high search space dimensionality. So as to study the tracking behavior of evolutionary algorithms, several authors ([1, 4, 13]) have added a dynamic component to the sphere model by stipulating that the target x varies with time. Several modes of motion of the target are conceivable and have been explored empirically. Examples include random motion, linear motion, and circular motion in search space. For the present ....

[Article contains additional citation context not shown here]

P. J. Angeline. Tracking extrema in dynamic environments. In Proc. of the Sixth International Conference on Evolutionary Programming, pages 335--345. Springer Verlag, Heidelberg, 1997.

....on empirical observations. An extensive survey of the literature of the field along with a collection of benchmark functions and a discussion of methods that have been proposed to improve the performance of evolutionary algorithms in dynamic environments has been compiled by Branke [7] Angeline [1] compares empirically the tracking performance of an evolutionary algorithm employing a form of muratlye self adaptation with that of a strategy using a simple heuristic for mutation strength adaptation. The fitness environment considered is a three dimensional, spherically symmetric objective ....

....a model for fitness landscapes at a stage where the population of candidate solutions is in relatively close proximity to the target and is most often studied in the limit of very high search space dimensionality. So as to study the track ing behavior of evolutionary algorithms, several authors ([1,4, 12]) have added a dynamic component to the sphere model by stipulating that the target : varies with time. Several modes of motion of the target are conceivable and have been explored empirically. Examples include random motion, linear motion, and circular motion in search space. For the present ....

[Article contains additional citation context not shown here]

P. J. Angeline. Tracking extrema in dynamic environments. In Proc, of the Sixth International Conference on Evolutionary Programming, pages 335 345. Springer Verlag, Heidelberg, 1997.

....the desired accuracy to 10 ;6 ,we observe that the swarm moves closely to the global minimizer of each test function but it cannot find it with the desired accuracy. This is more clear if we add an offset to the original global minimizer s position, at each iteration, as performed by Angeline [1]. The mean function values of the swarm for each iteration, after 100 runs, for the aforementioned test problems, are exhibited in Figs. 1, 2 and 3. Different line styles in the figures correspond to different values of the offset. For all runs, a value of the noise variance equal to 0:01 was ....

P. Angeline, Tracking extrema in dynamic environments, Proc. Int. Conf. Evol. Progr., Indianapolis, Indiana, USA, 1997.

.... optimum of a dynamically changing pattern based error measure. This approach coincides with the way adaptation on the evolutionary time scale is considered [10] and allows us to explore and expand further research on the tracking performance of evolution strategies and genetic algorithms [10] [11], 12] However, the reader should keep in mind that in this paper we do not seek global minimisers of the error function, but we are interested in developing an on line evolution strategy that will converge to an approximation of the optimum solution (the interesting topic of finding global ....

....adaptive stochastic search methods that mimic the metaphor of natural biological evolution. The main differences between ESs and Genetic Algorithms lie in that the self adaptation of the mutation operator is a key feature of the ESs, and in that GAs prefer smaller mutation probability (rate) 10] [11]. Here we use the Differential Evolution strategies, which have been designed as stochastic parallel direct search methods that can handle non differentiable, non linear and multimodal objective functions efficiently, and require few easily chosen control parameters [21] Experimental results have ....

Angeline, P., 1997, "Tracking extrema in dynamic environments", 6th Annual Conference on Evolutionary Programming VI, 335-345, Springer.

....of a pattern based, and, thus, dynamically changing, error function. This approach coincides with the way adaptation in the evolutionary time scale is considered [20] and allows us to explore and expand further research on the tracking performance of evolution strategies and genetic algorithms [1, 20, 26]. 3 The Hybrid Evolutionary Algorithm In this section, we present a Lamarck inspired combination of Di#erential Evolution strategy and Stochastic Gradient Descent (SGD) The DE strategy works on the termination point of the SGD. Thus, the method consists of a SGD based on line training stage ....

....randomly chosen weight vectors, di#erent from w p i . To increase further the diversity of the mutant weight vector, the crossover operator is applied. Specifically, for each component j, j = 1, 2, n) of the mutant weight vector, we randomly choose a real number r from the interval [0, 1]. Then, we compare this number with # 0 (crossover constant) and if r # # we select, as the j th component of the trial vector, the corresponding component j of the mutant vector. Otherwise, we pick the j th component of the target vector. 4 Experiments and Results We have tested the proposed ....

P. Angeline, "Tracking extrema in dynamic environments ". In: Proc. of the Sixth Annual conference on Evolutionary Programming VI, 335-345, Springer, (1997).

.... In such environments often it is necessary to modify the current solution due to various changes in the environment (e.g. machine breakdowns, sickness of employees, 17 etc) The capabilities of evolutionary algorithm to consider such changes and to track the optimum eciently have been studied [4], 15] 134] 135] A few mechanisms were considered, including (self )adaptation of various parameters of the algorithm, while other mechanisms were based on maintenance of genetic diversity and on redundancy of genetic material. These mechanisms often involved their own adaptive schemes, e.g. ....

P.J. Angeline. Tracking extrema in dynamic environments. In Angeline et al. [6], pages 335-345.

....current locations [32] ffi Adaptation and self adaptation mechanism. Dynamical adjustment of the algorithm to the non stationary environment is the next feature of the efficient optimization. So adaptive and self adaptive techniques are the next significant extension of evolutionary algorithm [1, 3, 8]. In adaptation the parameters of the algorithm are updated using statistic or heuristic rules to determine how to update. Update of the parameters in the genetic process in parallel with searching of the optimum is called a self adaptation. Both these techniques of parameters update were applied ....

.... for static environments, were employed in experiments with non stationary ones [2, 16, 32, 33] In other publications authors visually compared graphs of the best objective function value measured during the entire search process (or graphs of the mean value obtained from series of experiments) [1, 3, 5, 4, 6, 10, 14, 16, 22, 25, 26, 27, 33]. In some papers graphs of average values of all individuals or of the worst individual in the population were also analyzed [5, 14, 6, 25, 26] Both these methods were based on the measures of off line and on line performance. An interesting measure based on the off line performance was an ....

Angeline, P., "Tracking Extrema in Dynamic Environments", Proc. of the Sixth Int. Conf. on Evolutionary Programming - EP'97, vol. 1213 in LNCS, Springer, 1997, pp 335-346.

....the advantage that they can be fully understood and controlled. The experimental setup, including the used algorithms, test functions, and all parameter settings, is summarized in Section 3. Section 4 then presents the results of these basic experiments. Then Section 5 discusses related research [1], and finally, Section 6 provides a conclusion including a short discussion. 2 Adaptation: A Working Hypothesis Adaptation has a long tradition in biology. In nature, each individual is forced to adapt to its environment. These adaptation forces originate from climate changes, limited food ....

....of a moving optima, however, recombination cannot be beneficially exploited, since the combination of existing good solutions will not help in subsequent generations where the optimum is moving further. 5 Related Research Similar research was independently done and has already been presented in [1]. Even though both papers ( 1] and this paper) aim at a similar goal, the following three significant differences can be identified. First, the research presented in [1] aims at investigating the behavior of different adaptation schemes for the mutation strength in evolutionary programming. ....

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Angeline, P., 1997, Tracking Extrema in Dynamic Environments, in: Proceedings of the Sixth Annual Conference on Evolutionary Programming VI , P.J. Angeline, R.G. Reynolds, J.R. McDonnell, and R. Eberhart (eds.) (Springer-Verlag), pp. 335-345.

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Angeline, P. J. (1997). Tracking extrema in dynamic environments. In Angeline, P. J. et al., editors, Proc. of the Sixth International Conference on Evolutionary Programming --- EP'97, pages 335-- 345. Springer Verlag, Heidelberg.

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P.J. Angeline. Tracking extrema in dynamic environments. In Angeline et al. [6], pages 335--345.

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