Solution Archive and Its Re-use in Evolutionary Many-objective Facility Control Optimization

Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.

Запропоновано метод оптимізації неперервних функції багатьох змінних, який втілює підходи методів рою часток та моделювання штучної імунної системи. Проведено дослідження з метою визначення оптимальних налаштувань алгоритму, що реалізує запропонований метод. Показано, що запропонований метод може бути застосований як складова інформаційної технології супроводу підтримки управлінських рішень та розв’язання задач оптимізації технологічних процесів у металургійному виробництві. Метою роботи є розробка оригінального гібридного методу глобальної оптимізації на основі методу штучної імунної системи та методу рою частинок, а також формулювання рекомендацій щодо налаштування його параметрів. Запропонований метод має прискорити прийняття рішень при керуванні технологічними процесами у металургійному виробництві та підвищити їх точність. Методологія забезпечення рішення полягає у поєднанні основних пошукових операторів еволюційних методів оптимізації на основі рою часток і моделювання штучної імунної системи людини. Використовуються традиційні для ройового пошуку кроки з пошуку рішення та обміну інформацією про знайдені локальні оптимуми. Такий пошук доповнюється принципом змагальності, запозиченим у методі штучної імунної системи, для чого популяція поділяється на менші рої або пошукові команди. Також запропоновані кроки контролю різноманіття в рої та радіусу розсіювання часток. Останнє дозволяє вирішувати задачі як безумовної, так і умовної оптимізації у неперервному просторі високої розмірності. Наукова новизна отриманих у роботі результатів полягає в формулюванні нового еволюційного методу оптимізації в неперервному просторі на основі ройового інтелекту, який на відміну від відомих раніше ройових методів використовує принцип змагання підгруп рою та оператор стиснення популяції, властивих методу моделювання штучних імунних систем. Емпірично встановленні параметри методу, що визначають його ефективність. Висновки. Застосування запропонованого еволюційного методу пошукової оптимізації до мінімізації тестових функцій у неперервному просторі розмірністю до 20 показало його ефективність у порівнянні з відомими раніше. В подальшому актуальним бачиться застосування викладеного алгоритму для розв’язання задач оптимізації технологічних процесів у металургійному виробництві. Зокрема, даний алгоритм вбачається ефективним для задач шихтування, оптимізації використання феросплавів у ливарному виробництві, а також при прогнозуванні механічних властивостей готової продукції.

This paper provides a new evolutionary multiobjective optimization method for automatically optimizing the network topology of recurrent neural networks (NNs). To obtain NNs with higher prediction capability for time-series data, the proposed method is constructed by focusing on the intensively exploration of a feasible region including solutions with small training errors on the Pareto frontier, unlike existing evolutionary multiobjective optimization methods, which aim to find a whole set of the Pareto optimal solutions. Our method is characterized by the ideas of self-adaptive mutation probability setting, elite preservation strategies and archive for the preservation of local optimal solutions. Through the comparison with the performances of the most promising existing method by Delgado et al. using benchmark time-series data instances, it is shown that the proposed method is superior to the existing effective algorithm with respect to the capability of time-series prediction.

Challenging multi-modal optimization problems have been very successfully solved by evolutionary computation (EC) techniques. To date, many methods have been proposed on evolutionary optimization for both single and multiobjective large scale problems. In the age of Big Data, there is an urge to take evolutionary optimization techniques to the next level for solving problems with even larger scales: thousands and millions of variables. These problems arise in many domains ranging from bioinformatics, to neuroscience and social simulations. In this paper, we investigate the use of EC to solve Big electroencephalography (EEG) data optimization problems with thousands of variables. The optimization problem attempts to identify maximum information that should be kept from a signal while minimizing the artifact. The high level of epistasis inherent in a signal can slow down the evolution. Therefore, we investigate the advantages of optimizing the problem in the frequency domain with different thresholds as opposed to the time domain. We propose synthetic EEG data sets of various scale and noise level. These data sets were the basis for the Optimization of Big Data 2015 Competition (BigOpt), CEC 2015. Two state-of-art multiobjective evolutionary algorithms (MOEAs) were evaluated. The results of this work suggest that frequency representation of the signals facilitates dimensionality reduction for big scale optimization of time series data, and hence provides faster and better quality solutions for EEG data cleaning. Moreover, the results suggest that existing state-of-art multiobjective evolutionary computation methods are extremely slow. Methods that can optimize the problem faster and with high quality are needed.

This paper proposes a bio-inspired evolutionary computational algorithm for structure topology optimization. It integrates the merits of evolutionary structure optimization and level set method for structure topology optimization. Traditional Level Set Method algorithm depends on the initial topology to some extent. New holes cannot be evolved within the updated topology during the optimization iteration. The algorithm proposed in this paper combines the merits of ESO techniques with that of LSM scheme, allowing new holes to be automatically inserted in regions with low deformation energy at prescribed iterations of the optimization. The nodal neighboring region is adopted in the proposed algorithm. Numerical example shows that good result can be gotten through less optimization iteration. The approach can solve complex structures easily, in which holes cannot be properly layed out in advance. The proposed method considerably improves the ability of LSM to find the optimal topology. The validity and efficiency of the proposed algorithm are supported by some benchmark examples in this paper.

This study presents the time-divided forecasting model to integrate evolutionary optimization algorithm and change point detection based on artificial neural networks (ANN) for the prediction of (Korea) stock price index. The genetic algorithm(GA) is introduced as an evolutionary optimization method in this study. The basic concept of the proposed model is to obtain intervals divided by change points, to identify them as optimal or near-optimal change point groups, and to use them in the forecasting of the stock price index. The proposed model consists of three phases. The first phase detects successive change points. The second phase detects the change-point groups with the GA. Finally, the third phase forecasts the output with ANN using the GA. This study examines the predictability of the proposed model for the prediction of stock price index.

In this paper, an evolutionary optimization method, Evolian, is proposed for the general constrained optimization problem, which incorporates the concept of (1) a multi-phase optimization process and (2) constraint scaling techniques to resolve problem of ill-conditioning. In each phase of Evolian, the typical evolutionary programming (EP) is performed using an augmented Lagrangian objective function with a penalty parameter fixed. If there is no improvement in the best objective function in one phase, another phase of Evolian is performed after scaling the constraints and then updating the Lagrange multipliers and penalty parameter. This procedure is repeated until a satisfactory solution is obtained. Computer simulation results indicate that Evolian gives outperforming or at least reasonable results for multivariable heavily constrained function optimization as compared to other evolutionary computation-based methods.

Conventional evolutionary algorithms operate in a fixed search space with limiting parameter range, which is often predefined via a priori knowledge or trial and error in order to `guess' a suitable region comprising the global optimal solution. This requirement is hard, if not impossible, to fulfil in many real-world optimization problems since there is often no clue of where the desired solutions are located in these problems. Thus, this paper proposes an inductive---deductive learning approach for single- and multi-objective evolutionary optimization. The method is capable of directing evolution towards more promising search regions even if these regions are outside the initial predefined space. For problems where the global optimum is included in the initial search space, it is capable of shrinking the search space dynamically for better resolution in genetic representation to facilitate the evolutionary search towards more accurate optimal solutions. Validation results based on benchmark optimization problems show that the proposed inductive---deductive learning is capable of handling different fitness landscapes as well as distributing nondominated solutions uniformly along the final trade-offs in multi-objective optimization, even if there exist many local optima in a high-dimensional search space or the global optimum is outside the predefined search region.

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time.

Evolutionary multi-task optimization (EMTO) studies on how to simultaneously solve multiple optimization problems, so-called component problems, via evolutionary algorithms, which has drawn much attention in the field of evolutionary computation. Knowledge transfer across multiple optimization problems (being solved) is the key to make EMTO to outperform traditional optimization paradigms. In this work, we propose a simple and effective knowledge transfer strategy which utilizes the best solution found so far for one problem to assist in solving the other problems during the optimization process. This strategy is based on random replacement. It does not introduce extra computational cost in terms of objective function evaluations for solving each component problem. However, it helps to improve optimization effectiveness and efficiency, compared to solving each component problem in a standalone way. This light-weight knowledge transfer strategy is implemented via differential evolution within a multi-population based EMTO paradigm, leading to a differential evolutionary multi-task optimization (DEMTO) algorithm. Experiments are conducted on the CEC’2017 competition test bed to compare the proposed DEMTO algorithm with five state-of-the-art EMTO algorithms, which demonstrate the superiority of DEMTO.

An innovative method for the automatic design of optical systems is presented and verified. The proposed method is based on a multi-objective evolutionary memetic optimization algorithm. The multi-objective approach simultaneously, but separately, addresses the image quality, tolerance, and complexity of the system. The memetic technique breaks down the search for optical designs in to three different parts or phases: optical glass selection, exploration, and exploitation. The optical glass selection phase defines the most appropriate set of glasses for the system under design. The glass selection phase limits the available glasses from hundreds to just a few, drastically reducing the design space and significantly increasing the efficiency of the automatic design method. The exploration phase is based on an evolutionary algorithm (EA), more specifically, on a problem-tailored generalized extremal optimization (GEO) algorithm, named Optical GEO (O-GEO). The new EA incorporates many features customized for lens design, such as optical system codification and diversity operators. The trade-off systems found in the exploration phase are refined by a local search, based on the damped least square method in the exploitation phase. As a result, the method returns a set of trade-off solutions, generating a Pareto front. Our method delivers alternative and useful insights for the compromise solutions in a lens design problem. The efficiency of the proposed method is verified through real-world examples, showing excellent results for the tested problems.

The Chapter presents some evolutionary algorithm based methods used for solving global optimization problems. Firstly, the methods, which use proportional selection, are briefly described. Secondly, a bicriterion approach is applied for solving the constrained function minimization problem. This method transforms the constrained function minimization problem to the bicriteria optimization problem in the way that the first objective function is the sum of violated constraints and the second objective function is the one that should be minimized. Thirdly, the constraint tournament selection method is presented. The aim of the method is to reduce the number of function evaluations in the optimization process. The method is very effective while solving highly constrained single criterion optimization problems as well as the problems with the computationally expensive objective function. The method may also reduce the computation time for ordinary nonlinear programming problems as well as produce better results. Finally, the application of evolutionary algorithms to two design optimization problems is presented. The first problem deals with optimum design of concentric springs, whereas the second problem deals with the optimum design of a robot gripper. Both of these problems are considered as discrete programming problems. For problems like these the use of conventional optimization methods is very limited or even impossible. As it is shown in this Chapter evolutionary algorithm based methods can easily handle such problems.

Both evolutionary Bayesian optimization (EBO) and Bayesian evolutionary optimization (BEO) are used to solve time-consuming optimization problems, where in the EBO method, the evolutionary algorithm is adopted to optimize the acquisition function for finding its optimal solution to be evaluated using the time consuming objective functions, while in the BEO approach, surrogates are utilized to replace the expensive objective functions and the acquisition function is used in the model management to choose individuals for evaluations using the expensive objective functions. In this paper, we perform comparisons on these two approaches to see which method is better for solving computationally expensive multi-objective problems. The expected improvement (EI) is used as the acquisition function in both EBO and BEO approaches. Two strategies are proposed to select individuals to be evaluated using the real computationally expensive objectives. The experimental results conducted on ZDT and DTLZ test problems showed that the BEO approach is more efficient than the EBO approach for solving multi-objective problems.

Remote sensing image data clustering is a tough task, which involves classifying the image without any prior information. Remote sensing image clustering, in essence, belongs to a complex optimization problem, due to the high dimensionality and complexity of remote sensing imagery. Therefore, it can be easily affected by the initial values and trapped in locally optimal solutions. Meanwhile, remote sensing images contain complex and diverse spatial-spectral information, which makes them difficult to model with only a single objective function. Although evolutionary multiobjective optimization methods have been presented for the clustering task, the tradeoff between the global and local search abilities is not well adjusted in the evolutionary process. In this article, in order to address these problems, a multiobjective sine cosine algorithm for remote sensing image data spatial-spectral clustering (MOSCA_SSC) is proposed. In the proposed method, the clustering task is converted into a multiobjective optimization problem, and the Xie-Beni (XB) index and Jeffries-Matusita (Jm) distance combined with the spatial information term (SI_Jm measure) are utilized as the objective functions. In addition, for the first time, the sine cosine algorithm (SCA), which can effectively adjust the local and global search capabilities, is introduced into the framework of multiobjective clustering for continuous optimization. Furthermore, the destination solution in the SCA is automatically selected and updated from the current Pareto front through employing the knee-point-based selection approach. The benefits of the proposed method were demonstrated by clustering experiments with ten UCI datasets and four real remote sensing image datasets.