Sorting Genetic Algorithm Research Articles

Genetic Algorithm-Based Fatigue Data Editing Technique

Durability testing is an essential process node in automotive component design analysis. The test associated with loading history can be accelerated if the fatigue data editing approach is considered for simplifying the given history. Even though they have been proven, unfortunately, the existing editing techniques involve complex mechanisms (e.g. abrupt detection, Fourier transformation and wavelet analysis), which are complicated in nature and which demand high computational costs. Therefore, this paper is a proposal of a simple technique that makes use of the rule-based fatigue segment classifier when deciding which parts of the history need to be removed. Rules representing the new labelling practice have been generated based on the classification data mining framework. In the context of this study, a rule set represents a group of undiscovered relationship between time domain statistical parameters and damage level. A dataset consisting of an equal length of fatigue segments trained using a multi-objective approach called the Elitist Non-dominated Sorting in Genetic Algorithm (NSGA-II) for seeking several optimal sets of rules (i.e., classifiers) by maximizing predictive accuracy and comprehensibility. The number of attributes underlying the rule set is referred to for final classifier selection where the fitter solution serves as the proposed editing technique. Comparison results on strain-stress cycle properties for the edited history and the full-length version shows that the proposed technique is suitable for fatigue data editing. Moreover, it has an additional benefit that no prior requirement on the frequency or time-frequency analysis is needed, providing the damage level of fatigue segments rapidly and the discovering of linguistic knowledge as a novelty.

Application of a Multi-Objective Approach and Sequential Covering Algorithm to the Fatigue Segment Classification Problem

In this paper, a multi-objective rule discovery approach is introduced to address the problem related to fatigue data editing. A set of rules are introduced to simplify the editing process, with which users can easily predict an appropriate level of damage for fatigue data segments subject to SAE1045 steel without need for a cycle-counting algorithm or stress analysis. A multi-objective approach called the elitist non-dominated sorting in genetic algorithm (NSGA-II) is modified and applied to find high-level knowledge representation IF-THEN rules in the eight-dimensional search space. Three possible outcomes represented with the labels very low, low and high are chosen for the rule consequent. Two conflicting classification objectives, the predictive accuracy and comprehensibility, are considered as the rule optimisation criteria. To accelerate the searching process, a sequential covering algorithm is applied in advance of the training session, which positively reduces data size and provides several simple rules. A set of seven high-accuracy and high-interpretability rules is discovered, and their uncomplicated implementation provides an alternative to the task of estimating the fatigue damage value and could be a part of a fatigue data editing process.

Using NSGA‐II and TOPSIS Methods for Interior Ballistic Optimization Based on One‐Dimensional Two‐Phase Flow Model

AbstractIn order to meet the design demands of new gun systems or new types of projectiles, the interior ballistic charge design seems especially important. In this paper, a one‐dimensional two‐phase flow model is presented. The model describes the transient combustion of granular propellants in a gun, and pressure waves are considered as an objective. This study adopts a hybrid method to solve the problem. In the first stage, the non‐dominated sorting genetic algorithm (NSGA‐II) with “a “filter” is employed to approximate a set of Pareto‐optimal solutions. In the subsequent stage, a multi‐attribute decision‐making (MADM) approach is adopted to rank these solutions from the best to the worst. The ranking of Pareto‐optimal solutions is based on the technique ordered preference by similarity to ideal solution (TOPSIS) method. In TOPSIS method each objective needs a corresponding weight coefficient, and a practical problem is introduced. Both the entropy method and linear analysis method are adopted to get two sets of weights for the objectives, respectively. The two pairs of final, best compromise solutions are compared for satisfying the designer’s aim. For the analysis of the results, a two‐phase flow interior ballistic model for design optimization is established, and the hybrid approach could get a reasonable design scenario.

Feature Selection for Fatigue Segment Classification System Using Elitist Non-Dominated Sorting in Genetic Algorithm

Having relevant features for representing dataset would motivate such algorithms to provide a highly accurate classification system in less-consuming time. Unfortunately, one good set of features is sometimes not fit to all learning algorithms. To confirm that learning algorithm selection does not weights system accuracy user has to validate that the given dataset is a feature-oriented dataset. Thus, in this study we propose a simple verification procedure based on multi objective approach by means of elitist Non-dominated Sorting in Genetic Algorithm (NSGA-II). The way NSGA-II performs in this work is quite similar to the feature selection procedure except on interpretation of the results i.e. set of optimal solutions. Two conflicting minimization elements namely classification error and number of used features are taken as objective functions. A case study of fatigue segment classification was chosen for the purpose of this study where simulations were repeated using four single classifiers such as Naive-Bayes, k nearest neighbours, decision tree and radial basis function. The proposed procedure demonstrates that only two features are needed for classifying a fatigue segment task without having to place concern on learning algorithm

Numerical simulation and optimisation of unconventional three‐section simulated countercurrent moving bed chromatographic reactor for oxidative coupling of methane reaction

AbstractThe simulated countercurrent moving‐bed chromatographic reactor (SCMCR) has been reported to significantly enhance methane conversion and C2 product yield for oxidative coupling of methane (OCM) reaction, which is otherwise a low per pass conversion reaction. A mathematical model of an unconventional three‐section SCMCR for OCM was first developed and solved using numerically tuned kinetic and adsorption parameters. The model predictions showed good agreement with available experimental results of SCMCR for OCM. Effects of several process parameters on the performance of SCMCR were investigated. A multi‐objective optimisation problem was solved at the operating stage using state‐of‐the‐art AI‐based non‐dominated sorting genetic algorithm with jumping genes adaptations (NSGA‐II‐JG), which resulted in Pareto Optimal solutions. It was found that the performance of the SCMCR could be significantly improved under optimal operating conditions. © 2011 Canadian Society for Chemical Engineering

Multi‐objective optimisation and multi‐criteria decision making in SLS using evolutionary approaches

PurposeThe goal of this study is to carry out multi‐objective optimization by considering minimization of surface roughness (Ra) and build time (T) in selective laser sintering (SLS) process, which are functions of “build orientation”. Evolutionary algorithms are applied for this purpose. The performance comparison of the optimizers is done based on statistical measures. In order to find truly optimal solutions, local search is proposed. An important task of decision making, i.e. the selection of one solution in the presence of multiple trade‐off solutions, is also addressed. Analysis of optimal solutions is done to gain insight into the problem behavior.Design/methodology/approachThe minimization of Ra and T is done using two popular optimizers – multi‐objective genetic algorithm (non‐dominated sorting genetic algorithm (NSGA‐II)) and multi‐objective particle swarm optimizers (MOPSO). Standard measures from evolutionary computation – “hypervolume measure” and “attainment surface approximator” have been borrowed to compare the optimizers. Decision‐making schemes are proposed in this paper based on decision theory.FindingsThe objects are categorized into groups, which bear similarity in optimal solutions. NSGA‐II outperforms MOPSO. The similarity of spread and convergence patterns of NSGA‐II and MOPSO ensures that obtained solutions are (or are close to) Pareto‐optimal set. This is validated by local search. Based on the analysis of obtained solutions, general trends for optimal orientations (depending on the geometrical features) are found.Research limitations/implicationsA novel and systematic way to address multi‐objective optimization decision‐making post‐optimal analysis is shown. Simulations utilize experimentally derived models for roughness and build time. A further step could be the experimental verification of findings provided in this study.Practical implicationsThis study provides a thorough methodology to find optimal build orientations in SLS process. A route to decipher valuable problem information through post‐optimal analysis is shown. The principles adopted in this study are general and can be extended to other rapid prototyping (RP) processes and expected to find wide applicability.Originality/valueThis paper is a distinct departure from past studies in RP and demonstrates the concepts of multi‐objective optimization, decision‐making and related issues.

Multi-Objective Aerodynamic Optimization Design Method of Compressor Rotor Based on Isight

In order to achieving the multi-objective optimization of the compressor rotor blade, a hybrid optimization design algorithm was proposed. The algorithm included three parts: the design of experiment technology was applied to reduce the dimensions of the design variables; the response surface model was established according to the simulation data of the experiment design; the Non-Dominated Sorting in Genetic Algorithm was applied to acquire the multi-objective optimization solutions. In this study, NASA rotor37 was optimized for the maximization of the pressure ratio and adiabatic efficiency using the hybrid optimization algorithm. The result demonstrates that the optimization design method was effectively feasible.

A multi‐objective analysis of a special switched reluctance motor

PurposeThe design of electrical machines includes the computation of several requirements and, in general, the improvement of one requirement implies in a degradation of another one: this is a typical multi‐objective scenario. The paper focuses on the multi‐optimization analysis of a special switched reluctance motor.Design/methodology/approachTwo design requirements were analyzed: the average torque and the ripple torque. The electromagnetic field computation was performed by the finite element method and the torque was computed by the Coulomb's Virtual Work for several positions. This allows us to calculate the average torque and the ripple torque. Three different methods were used to obtain the Pareto set: a min‐max approach, the non‐dominated sorting genetic algorithm (NSGA) and the strength Pareto evolutionary algorithm (SPEA). In order to save the computation time, the objective functions (the average torque and the ripple torque) were replaced with surrogate functions. Kriging models were used as surrogate functions.FindingsThe evolutionary methods (NSGA and SPEA) have a similar performance. The min‐max has not the same performance. It could have the same performance only if some unconstrained optimization problems are solved before the multi‐objective optimization. The maximum relative deviation between the approximated function (Kriging model) and the same value calculated by the finite element method was equal to 0.8 percent for the average torque and 1.2 percent for the ripple torque. The ripple torque, considered as the difference between the maximum and the minimum values in the 0‐90° region, has reduced while its frequency has doubled. This last characteristic provides a better mechanical stability for the driven load because its inertia softens the ripple effects at the double the frequency. The optimized prototype presents higher torques in the region θ<0° and this allows the electronic drive to switch in a broader range rendering the motor operation more flexible.Originality/valueThe use of surrogate functions save the computation time with high accuracy. This is very important on the design of electrical machines, a typical multi‐objective scenario. Evolutionary methods seem to be well suited to solve this class of problem.

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.

Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

In this paper is described a procedure to synthesize the optimal topology, shape, and size of compliant continua for a given nonlinear output path. The path is prescribed using a finite number of distinct precision points much in accordance with the synthesis for path generation in traditional kinematics. Geometrically nonlinear analysis is employed to model large displacements of the constituent members. It is also essential to employ nonlinear analysis to allow the output port to negotiate the prescribed path accurately. The topology synthesis problem is addressed in its original binary form in that the corresponding design variables are only allowed to assume values of “0” for no material and “1” for the material present at a site in the design region. Shape and size design variables are modeled using continuous functions. Owing to the discrete nature of topology design variables, since gradient based optimization methods cannot be employed, a genetic algorithm is used that utilizes only the objective values to approach an optimum solution. A notable advantage of a genetic algorithm over its gradient based counterparts is the implicit circumvention of nonconvergence in the large displacement analysis, which is another reason why a genetic algorithm is chosen for optimization. The least squared objective is used to compare the design and desired output responses. To allow a user to specify preference for a precision point, individual multiple least squared objectives, same in number as the precision points are used. The multiple objectives are solved using Nondominated Sorting in Genetic Algorithm (NSGA-II) to yield a set of pareto optimal solutions. Thus, multiple solutions for compliant mechanisms can be obtained such that a mechanism can traverse one or some precision points among those specified more precisely. To traverse the entire path, a solution that minimizes the sum of individual least square objectives may be chosen. Synthesis examples are presented to demonstrate the usefulness of the proposed method that is capable of generating a solution that can be manufactured as is without requiring any interpretation.

Multi‐Objective Optimization of Semi‐Batch Copolymerization Reactors Using Adaptations of Genetic Algorithm

AbstractSummary: The polymerization of styrene‐acrylonitrile (SAN) random copolymers in semi‐batch reactors is optimized using multiple objective functions that are often conflicting and non‐commensurate in nature. These include the average composition of the copolymer product, its number‐average molecular weight, its polydispersity index, and the conversion of monomers attained in the reactor. Two decision/control variables are used, namely, the rate of continuous addition of a monomer‐solvent‐initiator mixture (having a specified and fixed composition) and the history of the temperature in the reactor. The elitist non‐dominated sorting genetic algorithm, NSGA‐II, is adapted and used for decision variables that are functions of time (trajectory optimization). This robust, AI (artificial intelligence)‐based technique, enables the solution of far more complex optimization problems than those reported in the literature. A set of several non‐dominating (equally good) Pareto optimal solutions was obtained. These provide insights into the conflicting nature of the objective functions. An engineer (decision maker) can then use his judgment (often intuitive) to choose the preferred solution from among these possibilities.Pareto set of optimal solutions and some corresponding state variables for a Reference Problem.imagePareto set of optimal solutions and some corresponding state variables for a Reference Problem.

Multi‐objective optimization of venturi scrubbers using a three‐dimensional model for collection efficiency

AbstractMulti‐objective optimization of a venturi scrubber was carried out using a three‐dimensional model for collection efficiency and non‐dominated sorting genetic algorithm (NSGA). Two objective functions, namely (a) maximization of the overall collection efficiency, and (b) minimization of the pressure drop were used in this study. Three decision variables including two operating parameters, viz liquid–gas ratio and gas velocity in the throat, and the nozzle configuration, which takes into account the three‐dimensional nature of the problem, were used in the optimization. Optimal design curves (non‐dominated Pareto sets) and the values of the decision variables corresponding to optimum conditions on the Pareto set for a pilot‐scale scrubber were obtained. The liquid to gas (L/G) ratio, which is a key decision variable that determines the uniformity of liquid distribution, and a staggered nozzle configuration can produce uniform liquid distribution in the scrubber. Multiple penetration using nozzles of two different sizes in a triangular staggered arrangement can reduce liquid loading by as much as 50%, consequently reducing the pressure drop in the scrubber.© 2003 Society of Chemical Industry

Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms

In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.