Adaptive Evolutionary Programming Research Articles

Average convergence rate of evolutionary algorithms in continuous optimization

The average convergence rate (ACR) measures how fast the approximation error of an evolutionary algorithm converges to zero per generation. It is defined as the geometric average of the reduction rate of the approximation error over consecutive generations. This paper makes a theoretical analysis of the ACR in continuous optimization. The obtained results are summarized as follows. According to the limit property, the ACR is classified into two categories: (1) linear ACR whose limit inferior value is larger than a positive and (2) sublinear ACR whose value converges to zero. Then, it is proven that the ACR is linear for evolutionary programming using positive landscape-adaptive mutation, but sublinear for that using landscape-invariant or zero landscape-adaptive mutation. The relationship between the ACR and the decision space dimension is also classified into two categories: (1) polynomial ACR whose value is larger than the reciprocal of a polynomial function of the dimension for any generation, and (2) exponential ACR whose value is less than the reciprocal of an exponential function of the dimension for an exponential long period. It is proven that for easy problems such as linear functions, the ACR of the (1 + 1) adaptive random univariate search is polynomial. But for hard functions such as the deceptive function, the ACR of both the (1 + 1) adaptive random univariate search and evolutionary programming is exponential.

Embedded adaptive mutation evolutionary programming for distributed generation management

<span>Distribution generation (DG) is a widely used term to describe additional supply to a power system network. Normally, DG is installed in distribution network because of its small capacity of power. Number of DGs connected to distribution system has been increasing rapidly as the world heading to increase their dependency on renewable energy sources. In order to handle this high penetration of DGs into distribution network, it is crucial to place the DGs at optimal location with optimal size of output. This paper presents the implementation of Embedded Adaptive Mutation Evolutionary Programming technique to find optimal location and sizing of DGs in distribution network with the objective of minimizing real power loss. 69-Bus distribution system is used as the test system for this implementation. From the presented case studies, it is found that the proposed embedded optimization technique successfully determined the optimal location and size of DG units to be installed in the distribution network so that the real power loss is reduced.</span>

A New Under-Frequency Load Shedding Scheme Based on Adaptive Neuro-Fuzzy Inference System and Evolutionary Programming Shedding Priority

Frequency stability of islanded distribution system is a topic of interest, due to the significant penetration of distributed generation (DG). This paper proposes a new under frequency load shedding technique, which address the over-shedding issue caused by fixed priority. The proposed scheme consists of two units; first, the power imbalance estimation unit (PIEU), which use adaptive neuro-fuzzy inference system (ANFIS) to estimates the power imbalance. Second, the load shed unit (LSU), which is based on binary evolutionary programming (BEP) technique to shed the optimal loads. To validate the performance of the proposed UFLS scheme, different simulation studies have been conducted using PSCAD software. Moreover, the response of the proposed scheme is compared with another UFLS scheme having fixed priority loads. From the simulation results, the proposed scheme can shed the optimal loads, which is not achieved in the existing load shedding schemes.

Spectral Quantitative Analysis Model with Combining Wavelength Selection and Topology Structure Optimization

Spectroscopy is an efficient and widely used quantitative analysis method. In this paper, a spectral quantitative analysis model with combining wavelength selection and topology structure optimization is proposed. For the proposed method, backpropagation neural network is adopted for building the component prediction model, and the simultaneousness optimization of the wavelength selection and the topology structure of neural network is realized by nonlinear adaptive evolutionary programming (NAEP). The hybrid chromosome in binary scheme of NAEP has three parts. The first part represents the topology structure of neural network, the second part represents the selection of wavelengths in the spectral data, and the third part represents the parameters of mutation of NAEP. Two real flue gas datasets are used in the experiments. In order to present the effectiveness of the methods, the partial least squares with full spectrum, the partial least squares combined with genetic algorithm, the uninformative variable elimination method, the backpropagation neural network with full spectrum, the backpropagation neural network combined with genetic algorithm, and the proposed method are performed for building the component prediction model. Experimental results verify that the proposed method has the ability to predict more accurately and robustly as a practical spectral analysis tool.

Adaptive Evolutionary Programming

Abstract Previous work has shown that evolutionary programming is an effective method for constructing skillful forecast ensembles. Here, two prototype adaptive methods are developed and tested, using minimum temperature forecast data for Chicago, Illinois, to determine whether they are capable of incorporating improvements to forecast inputs (as might occur with changes to operational forecast models and data assimilation methods) and to account for short-term changes in predictability (as might occur for particular flow regimes). Of the two methods, the mixed-mode approach, which uses a slow mode to evolve the overall ensemble structure and a fast mode to adjust coefficients, produces the best results. When presented with better operational guidance, the mixed-mode method shows a reduction of 0.57°F in root-mean-square error relative to a fixed evolutionary program ensemble. Several future investigations are needed, including the optimization of training intervals based on flow regime and improvements to the adjustment of fast-mode coefficients. Some remarks on the appropriateness of this method for other ensemble forecast problems are also provided.

Adaptive evolutionary programming with p-best mutation strategy

Although initially conceived for evolving finite state machines, Evolutionary Programming (EP), in its present form, is largely used as a powerful real parameter optimizer. For function optimization, EP mainly relies on its mutation operators. Over past few years several mutation operators have been proposed to improve the performance of EP on a wide variety of numerical benchmarks. However, unlike real-coded GAs, there has been no fitness-induced bias in parent selection for mutation in EP. That means the i-th population member is selected deterministically for mutation and creation of the i-th offspring in each generation. In this article we propose a p-best mutation scheme for EP where any one from the p (p∈[1,2,…,μ], where μ denotes population size) top-ranked population-members (according to fitness values) is selected randomly for mutation. The scheme is invoked with 50% probability with each index in the current population, i.e. the i-th offspring can now be obtained either by mutating the i-th parent or by mutating a randomly selected individual from the p top-ranked vectors. The percentage of best members is made dynamic by decreasing p in from μ/2 to 1 with generations to favor explorative behavior at the early stages of search and exploitation during the later stages. We investigate the effectiveness of introducing controlled bias in parent selection in conjunction with an Adaptive Fast EP (AFEP), where the value of a strategy parameter is updated based on the previous records of successful mutations by the same parameter. Comparison with the recent and best-known versions of EP over 25 benchmark functions from the CEC (Congress on Evolutionary Computation) 2005 test-suite for real-parameter optimization and two other engineering optimization problems reflects the statistically validated superiority of the new scheme in terms of final accuracy, speed, and robustness. Comparison with AFEP without p-best mutation demonstrates the improvement of performance due to the proposed mutation scheme alone.

Ensemble strategies with adaptive evolutionary programming

Mutation operators such as Gaussian, Lévy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests.

Adaptive Evolutionary Programming Incorporating Neural Network for Transient Stability Constrained Optimal Power Flow

This paper presents an adaptive evolutionary programming incorporating neural network for solving transient stability constrained optimal power flow (TSCOPF). The proposed AEP method is an evolutionary programming (EP)-based algorithm, which adjusts its population size automatically during an optimization process. The artificial neural network, which classifies the AEP individual based on its stability degrees, is embedded into the search template to reduce the computational load caused by transient stability constraints. The fuel cost minimization is selected as the objective function of TSCOPF. The proposed method is tested on the IEEE 30-bus system with two types of the fuel cost functions, i.e. the conventional quadratic function and the quadratic function superimposed by sine component to model the cost curves without and with valve-point loading effect respectively. The numerical examples show that AEP is more effective than conventional EP in terms of computational speed, and when the neural network is incorporated into AEP, it can significantly reduce the computational time of TSCOPF. A study of the architecture of the neural network is also conducted and discussed. In addition, the effectiveness of the proposed method for solving TSCOPF with the consideration of multiple contingencies is manifested.

An Adaptive Evolutionary Programming Algorithm Based on Q Learning

Selection of mutation strategies plays an important role in evolutionary programming,and adaptively selecting a mutation strategy in each evolutionary step can achieve good performance.A mutation strategy is evaluated and selected only based on the one-step performance of mutation operators in clas- sical adaptive evolutionary programming,and the performance of mutation operators in the delayed mutation steps is ignored. This paper proposes a novel adaptive mutation strategy based on Q learning—QEP (Q learning based evolutionary program- ming).In this algorithm,several candidate mutation operators are used and each is considered as an action.The evolutionary performance of delayed mutation steps is considered in calculat- ing the Q values for each mutation operator and the mutation operator that maximizes the learned Q values is the optimal one. Experimental results show that the proposed mutation strategy achieves better performance than the existing algorithms.

Adaptive evolutionary programming based on reinforcement learning

This paper studies evolutionary programming and adopts reinforcement learning theory to learn individual mutation operators. A novel algorithm named RLEP (Evolutionary Programming based on Reinforcement Learning) is proposed. In this algorithm, each individual learns its optimal mutation operator based on the immediate and delayed performance of mutation operators. Mutation operator selection is mapped into a reinforcement learning problem. Reinforcement learning methods are used to learn optimal policies by maximizing the accumulated rewards. According to the calculated Q function value of each candidate mutation operator, an optimal mutation operator can be selected to maximize the learned Q function value. Four different mutation operators have been employed as the basic candidate operators in RLEP and one is selected for each individual in different generations. Our simulation shows the performance of RLEP is the same as or better than the best of the four basic mutation operators.