Bi-objective Genetic Programming Research Articles

Machine learning-assisted design of high-entropy alloys for optimal strength and ductility

High Entropy Alloys (HEAs) are a novel class of multi-component alloys with compositional flexibility, presenting a promising alternative to traditional alloys. This research aims to enhance the strength of HEAs while achieving adequate ductility, a challenging objective due to their conflicting nature. We applied evolutionary data-driven models and Bi-Objective Genetic Programming (BioGP) with genetic algorithms (GA) to accurately predict and optimize yield strength and ductility. The predictions were validated through experimental methods, including casting by vacuum arc melting and comprehensive mechanical and microstructural characterization. Our integrated approach successfully developed an HEA exhibiting a strength of 1795 ± 21 MPa and a ductility of 31.45 %. This study highlights the effectiveness of combining data-driven models with experimental validation to advance the development of high-performance materials.

Hybrid approach of using bi-objective genetic programming in well control optimization of waterflood management

A new hybrid optimization approach is proposed by applying bi-objective genetic programming (BioGP) algorithm along with NSGA-II algorithm to expand the diversity of the Pareto solutions and speed up the convergence. The novel methodology is used in two distinct cases: the benchmark model for the Brugge field and a Middle Eastern oil-field sector model. The Brugge field includes twenty producing wells and ten injecting wells, but the real sector model has three injectors and four producers. The two primary objectives applied are to optimize the total volume of produced oil and reduce cumulative produced water. In the optimization process, the injection rate (qwi) and the bottom-hole pressure (BHP) are the control parameters for injection and producing wells, respectively. The hybrid technique of applying BioGP guided NSGA-II in the Brugge field model demonstrated a 50% acceleration in the convergence speed when compared to the NSGA-II solution. The calculated Pareto solutions for the Middle-Eastern sector model by the proposed methodology at various generations exhibited better diversity and convergence in comparison to the NSGA-II solutions. The highest cumulative produced oil of 550.45 × 103 m3 is obtained by the proposed hybrid methodology in comparison to the NSGA-II's highest cumulative of 522 × 103 m3. The two solution points A′ and B′ achieved using the BioGP guided NSGA-II have lower WOR by 17% and 15%, respectively, than A and B solutions established by NSGA-II alone. Pareto solution ranking is performed using the net flow method (NFM) and the best optimum solution determined for BioGP guided NSGA-II is 532.38 × 103 m3 oil using equal-based weight compared to 505.44 × 103 m3 using the entropy-based weights of 41% oil & 59% water. Overall, the optimal Pareto solutions achieved by the proposed methodology of using BioGP guided NSGA-II algorithm has better diversity with improvement in convergence speed in comparison to the NSGA-II.

Optimization of dome shape for filament wound pressure vessels using data-driven evolutionary algorithms

ABSTRACT Filament wound glass/epoxy and carbon/epoxy pressure vessels were designed using a data-driven evolutionary approach along with a classical mechanics-based analysis. Analytical solutions for three known end domes (a spherical shell, a geodesic-isotensoid shell and a shell based on minimizing of the Tsai-Hill’s criterion) and end dome based on Hoffman’s criterion were used to create surrogate models through two different evolutionary optimization algorithms: Evolutionary Neural Net (EvoNN) and Bi-objective Genetic Programming (BioGP) and bi-objective evolutionary optimization studies were carried out using them. Composite pressure vessels are manufactured by means of filament (helical) winding. The stresses in the end domes were evaluated analytically and compared with each other. Hoffman strength criterion was chosen for the evaluation of the critical areas of the shells. Moreover, the best dome shape for given material and polar hole/equator ratio was selected for various types of failure.

Evolutionary data driven modeling and tri-objective optimization for noisy BOF steel making data

Evolutionary data-driven modeling and optimization play a major role in generating meta models from real-time data. These surrogate models are applied effectively in various industrial operations and processes to predict a more accurate model from the nonlinear and noisy data. In this work, the data collected from a basic oxygen furnace of TATA steel are utilized in the modeling process by using evolutionary algorithms like evolutionary neural network (EvoNN), bi-objective genetic programming (BioGP), and evolutionary deep neural network (EvoDN2) to generate the meta models. For creating surrogates out In the current scenario of the Indian plants, reduction of phosphorus to an acceptable level, limiting the carbon and controlling the temperature are the basic needs in a basic oxygen furnace (BOF) to produce steels with a suitable composition. This work focused on three essential process parameters, temperature, carbon and phosphorus contents, and created intelligent models using 91 process variables of the operational process. The analysis began with a total of around 17000 operational observations and creating surrogate models out of them is a mammoth task, for which the data-driven evolutionary algorithms were some apt choices. Even there deep learning turned out to be essential and only the EvoDN2 algorithm performed at the expected level. Once the trained models are generated, optimization work was carried on three objectives simultaneously by using a constraint-based reference vector evolutionary algorithm (cRVEA). The optimized results were analyzed in multi-dimensional hyperspace, and their effectiveness in BOF steel making is presented in this work.

EBM3GP: A novel evolutionary bi-objective genetic programming for dimensionality reduction in classification of hyperspectral data

Dimensionality reduction (DR) is vital in hyperspectral image (HSI) classification, and feature extraction and band selection methods have been demonstrated to be effective at accomplishing it. However, both types of methods can only obtain single-level features from HSI spectra, which suffers from insufficient useful information and makes accurate classification of the high dimensionality of HSI pixels challenging. To overcome the shortcomings, this study proposes a novel Evolutionary Bi-objective Genetic Programming-based unsupervised DR approach named EBM3GP for obtaining low-level features (bands) and high-level features from raw HSI spectra simultaneously. In EBM3GP, multi-dimensional trees are used to encode the raw spectrum to low- and high-level features; two mutually restrictive measures are applied to evaluate the amount of information and the redundancy contained in trees (evaluation does not utilize the HSI pixel’s label); multiple trees are optimized through population evolution by combining three types of crossover operators, two types of mutation operators and nondominated sorting method; a Pareto optimal individual is finally output and decoded as a DR strategy. Then, this study applies Random Forest, least squares Support Vector Machine, and Extreme Learning Machine for classification to evaluate the efficacy of the DR strategy. Based on three HSIs (including Indian Pines, Salinas, and Pavia University datasets), EBM3GP is demonstrated to outperform five popular DR methods for HSI classification. Moreover, the EBM3GP is not sensitive to data size and thus is available for DR of small-size HSI datasets.

Mechanical properties of micro-alloyed steels studied using a evolutionary deep neural network

ABSTRACT The existing Evolutionary Neural Net Algorithm (EvoNN) for data-driven modeling has been augmented during this study using an evolutionary deep neural net strategy to give rise to a novel algorithm named EvoDN, which has been further upgraded to an improved version named EvoDN2. This study reports an application of EvoDN2 to study vanadium and niobium based micro-alloyed steels. For this purpose, a dataset for ultimate tensile strength, elongation and Charpy impact energy at −40°C is collected and trained using aforementioned EvoNN, EvoDN2, and another in house algorithm named Bi-objective genetic programming (BioGP). This trained models are then optimized to get optimized properties using a constrained version Reference Vector Evolutionary Algorithm (cRVEA). The results are thoroughly compared with the existing correlations and prior work and found to be well within the acceptable range.

Application of bi-objective genetic programming for optimizing irrigation rules using two reservoir performance criteria

ABSTRACT A bi-objective genetic programming (BO-GP) algorithm is developed and applied to optimize the operating rules of the Aidoghmoush reservoir (East Azerbaijan in northeastern Iran). The two-objective optimization problem maximizes reservoir reliability and minimizes the vulnerability index associated with the supply of agricultural water. The developed BO-GP algorithm calculates Pareto possibility frontiers representing loci of optimal operating policies. Any operation policy is calculated by the BO-GP based on the inflow volume to reservoir, the storage volume, and the water demand volume that minimize vulnerability and maximize reliability. The application results show a successful performance of the BO-GP algorithm in solving the bi-objective water supply problem with reservoir operation. This paper’s results establish that the system vulnerability and its reliability range between 16–41% and 46–78%, respectively.

Evolutionary Data Driven Modeling and Multi Objective Optimization of Noisy Data Set in Blast Furnace Iron Making Process

Data driven models are constructed for the tuyere cooling heat loss, total blast furnace gas flow, tuyere velocity, productivity, and coke rate for an operational blast furnace of an integrated steel plant by using evolutionary computation methods like bi objective genetic programming (BioGP) and evolutionary neural network (EvoNN), which serve as the objectives for their optimization. The models are used to compute the Pareto tradeoff between these conflicting objectives with the help of predator prey genetic algorithm well tasted for computing the Pareto optimality earlier. The results of optimization and the performances of these models are thoroughly analyzed and accessed and a discussion regarding these data driven models and their influence in the ironmaking process are presented. The results are also compared against a similar calculation performed with the commercial software KIMEME.

Effect of Carbon Distribution During the Microstructure Evolution of Dual-Phase Steels Studied Using Cellular Automata, Genetic Algorithms, and Experimental Strategies

The development of ferrite-martensite dual-phase microstructures by cold-rolling and intercritical annealing of 0.06 wt pct carbon steel was systematically studied using a dilatometer for two different heating rates (1 and 10 K/s). A step quenching treatment has been designed to develop dual-phase structures having a similar martensite fraction for two different heating rates. An increase in heating rate seemed to refine the ferrite grain size, but it increased the size and spacing of the martensitic regions. As a result, the strength of the steel increased with heating rate; however, the formability was affected. It has been concluded that the distribution of C during the annealing treatment of cold-rolled steel determines the size, distribution, and morphology of martensite, which ultimately influences the mechanical properties. Experimental detection of carbon distribution in austenite is difficult during annealing of the cold-rolled steel as the phase transformation occurs at a high temperature and C is an interstitial solute, which diffuses fast at that temperature. Therefore, a cellular automata (CA)-based phase transformation model is proposed in the present study for the prediction of C distribution in austenite during annealing of steel as the function of C content and heating rate. The CA model predicts that the carbon distribution in austenite becomes more inhomogeneous when the heating rate increases. In the CA model, the extent of carbon inhomogeneity is measured using a kernel averaging method for different orders of neighbors, which accounts for the different physical space during calculation. The obtained results reveal that the 10th order (covering 10-µm physical spaces around the cell of interest) is showing the maximum inhomogeneity of carbon and the same effect has been investigated and confirmed using auger electron spectroscopy (AES) for 0.06 wt pct carbon steel. Furthermore, the optimization of carbon homogeneity with respect to heating rate has been performed using a bi-objective genetic programming (BioGP) strategy for the steel composition varying from 0.06 to 0.12 wt pct carbon along with other parameters like average austenite grain size and time of heating as the input variables. The analysis of the results obtained from BioGP suggests that the homogeneity of carbon increases with the increasing carbon concentration of steel. This is corroborated by analyzing the AES results obtained for 0.28 wt pct carbon steel using the same technique as that used for 0.06 wt pct carbon steel.

Optimization of Cellular Automata Model for the Heating of Dual-Phase Steel by Genetic Algorithm and Genetic Programming

This study considers a common metallurgical problem associated with the phase transformation of steel during heating where austenite grain tends to grow in size with time and results in poor mechanical properties in the final stages. This investigation was performed using a Cellular Automata model for dual-phase steel developed in house. Data-driven metamodels for a biobjective optimization problem involving minimizing average austenite grain size along with the maximizing of time of heating were constructed using Evolutionary Neural Network (EvoNN) and Biobjective Genetic Programming (BioGP). The input variables selected for this task were (i) heating rate, (ii) pearlite percentage, (iii) nucleation density of austenite, and (iv) the finish temperature of austenite formation. The analyses of the results led to the fact that heating rate is the most influencing factor and it needs to be large during transformation to obtain a refined microstructure. The comparison of Pareto front between EvoNN and BioGP reveals a better performance of the latter. Limited experimental confirmation was also carried out.

Genetic Programming Evolved through Bi-Objective Genetic Algorithms Applied to a Blast Furnace

In this study, a new Bi-objective Genetic Programming (BioGP) technique was developed that initially attempts to minimize training error through a single objective procedure and subsequently switches to bi-objective evolution to work out a Pareto-tradeoff between model complexity and accuracy. For a set of highly noisy industrial data from an operational ironmaking blast furnace (BF) this method was pitted against an Evolutionary Neural Network (EvoNN) developed earlier by the authors. The BioGP procedure was found to produce very competitive results for this complex modeling problem and because of its generic nature, opens a new avenue for data-driven modeling in many other domains.

Genetic programming through bi-objective genetic algorithms with a study of a simulated moving bed process involving multiple objectives

A new bi-objective genetic programming (BioGP) technique has been developed for meta-modeling and applied in a chromatographic separation process using a simulated moving bed (SMB) process. The BioGP technique initially minimizes training error through a single objective optimization procedure and then a trade-off between complexity and accuracy is worked out through a genetic algorithm based bi-objective optimization strategy. A benefit of the BioGP approach is that an expert user or a decision maker (DM) can flexibly select the mathematical operations involved to construct a meta-model of desired complexity or accuracy. It is also designed to combat bloat – a perennial problem in genetic programming along with over fitting and under fitting problems. In this study the meta-models constructed for SMB reactors were compared with those obtained from an evolutionary neural network (EvoNN) developed earlier and also with a polynomial regression model. Both BioGP and EvoNN were compared for subsequent constrained bi-objective optimization studies for the SMB reactor involving four objectives. The results were also compared with the previous work in the literature. The BioGP technique produced acceptable results and is now ready for data-driven modeling and optimization studies at large.