Evolian: Evolutionary optimization based on lagrangian with constraint scaling

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 work proposed an evolutionary building facility control optimization method that re-utilized a promising solution set archived during the optimization process. Evolutionary optimization was suited to solve multi-objective optimization problems. Evolutionary algorithms especially for addressing real-world optimization problems often employed an archive solution set to increase the approximation quality of the Pareto front, the optimal trade-off among objective functions. The proposed method not only employed the archive solution set but also reutilized it for the search. The proposed method updated the searching solution set by the archive solution set at regular intervals. Experimental results showed the re-use of the archived solutions contributed to obtaining solutions that could not be obtained by the conventional method without re-utilization of the archive solution set.

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.

In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.

The control of multi-fingered robot hands has been the subject of interest. To manipulate some object with regrasping motion, there are many parameters to be determined; the grasping points, grasping forces, regrasping phases, finger allocation and so on. It is difficult to optimize such manipulation parameters for achieving effective manipulation. We propose a generation method of regrasping motion for a four-fingered robot hand using evolutionary programming (EP). In this case, EP determines not only finger motions, but also rotation of the target object in order to increase its manipulability. In manipulating an object like a rectangular solid, it is very important to change the object directions and to grasp another face according to the task progress because the grasping faces tend to be limited to only two. The evolutionary optimization method is generally able to find optimal solutions without a supervisor after much iteration, which makes it almost impractical to apply a real robot directly. Therefore we control the real robot hand with an optimal controller that has been generated in computer simulations. We show the effectiveness of the proposed acquisition method for the regrasping motion with experimental results.

A major limitation of the widely used evolutionary optimization (EO) methods is their inability to handle constraints directly. To address this issue, penalty function methods have been used in most EO applications involving constrained problems such as those of the water distributions networks (WDNs). However, the disadvantage of penalty function methods is that the parameters involved require great expertise in calibration with numerous time consuming trial runs. In addition, penalty parameters are case sensitive and do not necessarily steer the EO search toward the best solutions in every situation. This paper presents a penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution networks. The basis behind this approach is to involve the pressure dependent analysis (PDA) in developing a multi-objective evolutionary search. PDA is capable of simulating both normal and pressure deficient networks and provides a quick and precise means to identify the feasible region of the solution space. The proposed PFMOEA couples the renowned NSGA II with an enhanced seamless version of EPANET 2 which is capable of PDA. The PFMOEA has been applied to several WDN benchmarks. Excellent results in terms of the initial network cost and number of hydraulic simulations required were obtained. Comprehensive discussions along with comparisons of solutions from previous studies are presented herein.

A hybrid evolutionary programming (EP) method is presented for global optimization of complex circuits. The conventional EP is integrated with a clustering algorithm to improve the robustness of the algorithm for complex multimodal circuit optimization problems. The EP generates populations around the regions of the search space which can potentially contain a minimum but may be overlooked. The clustering algorithm is used to identify these regions dynamically. In order to improve the speed of optimization, the EP is combined with a gradient-based search method in an efficient fashion. The local search is performed from the center of each identified cluster in order to find the minimum in the region very fast. The hybrid algorithm can also reduce the search space by avoiding the search in the areas that were previously investigated. This feature greatly improves the speed of optimization and prevents the premature convergence as well. The algorithm performed very well in several benchmark problems including a test function minimization and global optimization of a complex RF diplexer circuit.

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.

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.

Structural topology optimization is a crucial approach for achieving lightweight design. An effective topology optimization algorithm must strike a balance between the objective functions, constraints, and design variables, which essentially reflects the symmetry and tradeoff between the objective and constraints. In this study, a topology optimization method grounded in load path theory is proposed. Element bearing capacity is quantified using the element birth and death method, with an explicit formulation derived via finite element theory. The effectiveness in evaluating structural performance is assessed through comparisons with stress distributions and topology optimization density maps. In addition, a novel evaluation index for element bearing capacity is proposed as the objective function in the topology optimization model, which is validated through thin plate optimization. Subsequently, sensitivity redistribution mitigates checkerboard patterns, while mesh filtering suppresses multi-branch structures and prevents local optima. The method is applied for the lightweight design of a triangular arm, with results benchmarked against the variable density method, demonstrating the feasibility and effectiveness of the proposed method. The element bearing capacity seeks to homogenize the load distribution of each element; the technique in this study can be extended to the optimization of symmetric structures.

The Evolutionary Structural Optimization (ESO) has been applied to find the optimal structural topology for design and construction purposes. However, its efficiency is low due to the imperfect deletion criteria. This paper presents an improved elimination criterion and the Windowed Evolutionary Structural Optimization (WESO) method. The former considers the structural average strain energy as the elimination criteria in the optimization, with the elimination rate set as a self-adaption state by an adjustable window. Thus, the problems of low optimization efficiency and distorted optimization results in the traditional ESO can be solved to a certain extent. The WESO method can then be extended and applied with a complex finite element model. It is found that the method has better optimal ability in handling discrete elements in vast structures. Compared with the other method, the WESO method has high computational efficiency and offers more stable and reliable topology than the Michell theoretical solution. Lastly, upon developing the optimal topology for a double-deck structure, it is shown that the WESO method has a great potential in civil engineering applications.

Differential evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, nonlinear and multi-modal objective functions. Previous studies have shown that DE is an efficient, effective and robust evolutionary algorithm, but usually it takes large computational time for optimizing the computationally expensive objective function, therefore it is necessary to find a trade-off between convergence speed and robustness. For this purpose, in this paper, a new DE based on uniform design is presented for solving nonlinear constrained optimization problems. Constraints are handled by embodying them in an augmented Lagrangian function, where the penalty parameters and multipliers are adapted as the execution of the algorithm proceeds. The efficiency of the proposed methodology is illustrated by solving numerous constrained optimization problems that can be found in the literature

This paper proposes a new bi-directional evolutionary structural optimization (BESO) method with draw direction constraints. Draw direction constraints, defined by required manufacturing process, are achieved by modifying element removal/addition criteria such that elements are removed from the top surface of the draw direction to the inner design domain. The optimized design with draw direction constraints is free from hollow or closed cavity geometries which are infeasible for manufacturing. A stiffness design of a motor front cover is carried out to show the ability of the proposed method in practical mechanical design problems.

Optimal arrangement of damping materials is an important problem in vibration control of thin walled structure treated with constrained layer damping, which directly affects vibration energy dissipation and global energy flow distribution. In this thesis, an evolutionary topology optimization method is used to establish the optimization model for constrained layer damping processing panel, with the optimization goal of maximizing the modal loss factor and limiting the usage of damping material. Taking into account the sensitivity of modal shapes, based on an improved modal superposition method, the sensitivity of the objective function with respect to the design variables is obtained. The level set function constructed from the node sensitivity determines the implicit smooth structure topology of the restricted damping layer. Numerical examples suggest that the algorithm is feasible, correct and valid. Studies show that this method not only allows the objective function to converge stably to the optimal value, but also obtains smooth and clear boundaries.

To address problems with multiple conflicting objective functions while incorporating preference information from a decision maker (a domain expert), interactive evolutionary multiobjective optimization methods have been proposed and widely adopted. To systematically assess the performance of these methods, it is desirable to have indicators that not only rely on the Pareto dominance relation, where solutions with better objective function values are preferred, but also take the decision maker's preferences into account. In this way, indicator values can meaningfully reflect the decision maker's preferences and the quality of the solutions obtained. In this paper, we propose the first performance indicator that incorporates preference information in the form of two reference points, specifically, an aspiration point, consisting of aspiration levels that represent the decision maker's full satisfaction, and a reservation point, consisting of reservation levels that represent dissatisfaction. The new indicator, termed D-PHI, translates information about reservation and aspiration points into a transformed hypervolume measure that assesses the performance of a solution set. We introduce D-PHI with an extended set of guidelines for preference-based performance evaluation, discuss its theoretical properties, and demonstrate its behavior through empirical examples. Moreover, we define a complementary indicator (CI) based on a so-called achievement scalarizing function. CI offers additional insight into whether aspiration and reservation levels have been achieved, and its usefulness is demonstrated through examples.