Hybrid evolutionary programming using adaptive Lévy mutation and modified Nelder–Mead method

Evolutionary programming has been widely applied to solve global optimization problems. Its performance is related to both mutation operators and fitness landscapes. In order to make evolutionary programming more efficient, its mutation operator should adapt to fitness landscapes. The paper presents novel hybrid evolutionary programming with adaptive Lévy mutation, in which the shape parameter of Lévy probability distribution adapts to the roughness of local fitness landscapes. Furthermore, a modified Nelder-Mead method is added to evolutionary programming for enhancing its exploitation ability. The proposed algorithm is tested on 39 selected benchmark functions and also benchmark functions in CEC2005 and CEC2017. The experimental results demonstrate that the overall performance of the proposed algorithm is better than other algorithms in terms of the solution accuracy

Um Algoritmo Híbrido entre Evolução Diferencial e Neder - Mead Usando Entropia para Problemas de Otimização Não - Linear Inteiro Misto.

Vários problemas em engenharia são formulados como problemas de otimização não-lineares inteiros mistos. Métodos estocásticos vem sendo utilizados devido ao seu desempenho, flexibilidade, adaptabilidade e robustez. Evolução Diferencial pode ser utilizado em funções de qualquer natureza e possui habilidades em busca global, porém, tais habilidades não são refletidas na busca local. Este trabalho propõe uma abordagem híbrida entre os algoritmos Evolução Diferencial e Nelder-Mead para problemas de otimização não-linear inteira misto, onde o chaveamento é realizado através da entropia da população. O algoritmo Nelder-Mead foi estendido para manipular variáveis inteiras. O primeiro protótipo foi desenvolvido para solucionar problemas de otimização não-linear inteira sem restrições. O método Alfa Constrained foi incorporado para tratar problemas de otimização não-linear inteira com restrições e o algoritmo demonstrou sua eficácia. Por último, a abordagem foi testada utilizando problemas de otimização não-linear inteira mista com restrições e superou alguns resultados reportados na literatura. A principal vantagem deste método é a habilidade de realizar o chaveamento de acordo com a entropia da população durante a busca

하천 오염물질 혼합 해석을 위한 저장대 모형의 매개변수 산정법 및 경험식 개발

학위논문(석사)--서울대학교 대학원 :공과대학 건설환경공학부,2019. 8. 서일원.Analyses of solute transport and retention mechanism are essential to manage water quality and river ecosystem. As reported by tracer injection studies that have been conducted to identify solute transport mechanism, concentration curves measured in natural stream have steep rising and long tail parts. This phenomenon is due to solute exchange process between transient storage zones and the main river stream. The transient storage model (TSM) is one of the most widely used models for describing solute transport in natural stream, taking transient storage exchange process into consideration. In order to use this model, calibration of four TSM parameters is necessary. Inverse modelling using measured breakthrough curves (BTCs) from tracer injection test is general method for TSM parameter calibration. However, it is not feasible to carry out performing tracer injection tests, for every parameter calibration. For that reasons, empirical formulae with hydraulic data, which is comparatively easier to obtain, have been proposed for the purpose of parameter estimation. This study presents two methods for TSM parameter estimation. At first, inverse modelling method employing global optimization framework Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL), that incorporating famous evolutionary algorithms in water resource management field, was suggested. Second, TSM parameter empirical equations were derived adopting Multigene Genetic Programming (MGGP) based symbolic regression library GPTIPS and using Principal Components Regression (PCR). In terms of general performance, equations of this study were superior to published empirical equations.하천의 수질을 관리하기 위해서는 자연하천에서 유입된 물질이 이송되고 지체되는 메카니즘을 규명하고 이해하는 것이 필요하다. 하천에서의 물질 혼합을 이해하기 위해 수행된 추적자 실험 연구들에 따르면 자연하천에서 계측되는 농도곡선에서는 가파른 상승부와 긴 꼬리기 관측되는 것으로 알려졌다. 이러한 현상은 주로 물질이 흐르는 본류대와 잠시 물질이 포획되었다가 재방출되는 본류대와 저장대 간의 물질교환 효과 때문에 일어난다고 알려져 있다. 이러한 저장대 물질교환 효과를 모사하는 저장대모형 중 Transient Storage zone Model (TSM)은 가장 광범위하게 이용되는 모형으로, 이를 이용하기 위해선 네 가지의 저장대 매개변수를 보정하여야 한다. 네 가지 저장대 매개변수를 결정하는 방법으로는 일반적으로 현장실험에서 측정된 농도곡선을 이용한 역산모형이 이용된다. 그러나 매개변수가 필요할 때마다 추적자실험을 수행하여 역산모형을 이용하는 것은 현실적으로 불가능한 경우가 있어 이러한 경우에는 비교적 취득하기 쉬운 수리지형학적 인자들을 이용해 매개변수를 산정하는 방법이 이용될 수 있다. 따라서 본 연구에서는 TSM 매개변수를 결정하기 위해 두 가지 방법을 제시하였다. 첫 번째로, 전역 최적화 프레임워크인 Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL)을 이용한 역산모형 기반 TSM 매개변수 산정 프레임워크를 제시하였다. 둘째로는 기호회귀법 라이브러리인 GPTIPS를 이용한 다중유전자 유전 프로그래밍(Multigene Genetic Programming, MGGP) 과 주성분회귀법(Principal Components Regression, PCR)을 통해 네 가지 매개변수 별로 각 두 개씩의 경험식이 개발되었다. 개발된 경험식들의 성능평가 결과, 선행 연구에서 제시된 저장대 매개변수 식에 비해 본 연구에서 제시된 방법이 대체적으로 우수한 것으로 나타났다. 결과적으로 본 연구에서는 분석을 통해 실무적으로 활용 가능한 TSM 매개변수 산정 프레임워크와 경험식들이 제시되었으며, 이 방법들은 추적자 실험 자료의 유무에 따라 TSM의 매개변수 결정에 유용하게 사용될 것으로 기대된다.Chapter 1. Introduction 1 1.1 Necessity and Background of Research 1 1.2 Objectives 12 Chapter 2. Theoretical Background 15 2.1 Transient Storage Model 15 2.1.1. Mechanisms of Transient Storage 15 2.1.2. Models Accounting for Transient Storage 21 2.1.2.1 The one Zone Transient Storage Model (1Z-TSM) 24 2.1.2.2 The two Zone Transient Storage Model (2Z-TSM) 25 2.1.2.3 The Continuous Time Random Walk Approach (CTRW) 26 2.1.2.4 The Modified Advection Dispersion Model (MADE) 27 2.1.2.5 The Fractional Advection Dispersion Equation Model (FADE) 28 2.1.2.6 The Multirate Mass Transfer Model (MRMT) 29 2.1.2.7 The Advective Storage Path Model (ASP) 30 2.1.2.8 The Solute Transport in Rivers Model (STIR) 31 2.1.2.9 The Aggregate Dead Zone Model (ADZ) 34 2.2 Empirical Equations for Predicting Transient Storage Model Parameters 39 2.3 Parameter Estimation 47 2.3.1. The SC-SAHEL Framework 50 2.3.1.1 Modified Competitive Complex Evolution (MCCE) 52 2.3.1.2 Modified Frog Leaping (MFL) 52 2.3.1.3 Modified Grey Wolf Optimizer (GWO) 53 2.3.1.4 Modified Differential Evolution (DE) 53 2.4 Regression Method 54 2.4.1. The Multi-Gene Genetic Programming (MGGP) 56 2.4.1.1 The Simple Genetic Programming 56 2.4.1.2 Scaled Symbolic Regression via Multi-Gene Genetic Programming 57 2.4.2. Evolutionary Polynomial Regression (EPR) 61 2.4.2.1 Main Flow of EPR Procedure 62 Chapter 3. Model Development 66 3.1 Numerical Model 66 3.1.1. Model Validation 69 3.2 Merger of TSM-SC-SAHEL 73 3.3 Further assessments for the parameter estimation framework 76 3.3.1. Tracer Test Description 76 3.3.2. Grid Independency of Estimation 81 3.3.3. Choice of Optimization Setting 85 Chapter 4. Development of Formulae for Predicting TSM Parameter 91 4.1 Dimensional Analysis 91 4.2 Data Collection via Meta Analysis 95 4.3 Formulae Development 106 Chapter 5. Result and Discussion 110 5.1 Model Performances 110 5.2 Sensitivity Analysis 118 5.3 In-stream Application of Empirical Equations 130 Chapter 6. Conclusion 140 References 144 Appendix. I. The mean, minimum, and maximum values of the model fitness value and number of evolution using the SC-SAHEL with single-EA and multi-EA 159 Appendix. II. Used dimensionless datasets for development of empirical equations 161 국문초록 165Maste

A novel hybrid firefly algorithm for global optimization

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A novel hybrid firefly algorithm for global optimization

Global optimization is challenging to solve due to its nonlinearity and multimodality. Traditional algorithms such as the gradient-based methods often struggle to deal with such problems and one of the current trends is to use metaheuristic algorithms. In this paper, a novel hybrid population-based global optimization algorithm, called hybrid firefly algorithm (HFA), is proposed by combining the advantages of both the firefly algorithm (FA) and differential evolution (DE). FA and DE are executed in parallel to promote information sharing among the population and thus enhance searching efficiency. In order to evaluate the performance and efficiency of the proposed algorithm, a diverse set of selected benchmark functions are employed and these functions fall into two groups: unimodal and multimodal. The experimental results show better performance of the proposed algorithm compared to the original version of the firefly algorithm (FA), differential evolution (DE) and particle swarm optimization (PSO) in the sense of avoiding local minima and increasing the convergence rate

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