Non-dominated Sorting Genetic Algorithm II Method Research Articles

Optimal Temperature Calculation for Multicriteria Optimization of the Hydrogenation of Polycyclic Aromatic Hydrocarbons by NSGA-II Method

Introduction. Multicriteria optimization, taking into account contradicting criteria, is used to improve production efficiency, reduce costs, improve product quality and environmental safety of processes. The literature describes the application of multicriteria optimization for production purposes, including the selection of reaction conditions and improvement of technological processes. In the presented paper, the object of research is the process of hydrogenation of polycyclic aromatic hydrocarbons (PAH) in the production of high-density fuels. To determine the optimal conditions of the process, the problem of multicriteria optimization based on the kinetic model is solved. The criteria include maximizing the yield of targeted naphthenes and conversion of feedstock. The research objective is to create a program implementing the multicriteria optimization non-dominated sorting genetic algorithm-II (NSGA-II). Due to this, it is possible to calculate the optimal temperature for the PAH hydrogenation process on the basis of the kinetic model.Materials and Methods. The NSGA-II genetic algorithm was used to solve the multicriteria optimization problem. Modified parental and survival selection within the Pareto front was also used. If it was necessary to divide the front, solutions based on the Manhattan distance between them were selected. The program was implemented in Python.Results. In the system of ordinary nonlinear differential equations of chemical kinetics, the concentration was designated yi, the conditional contact time of the reaction mixture with the catalyst — τ. The system was solved for the hydrogenation reaction of polycyclic aromatic hydrocarbons. The calculations showed that at τ = 0 y1(0) = 0.025; y2(0) = 0.9; y6(0) = 0.067; y9(0) = 0.008; yi(0) = 0, i = 3–5, 7, 8, 10–20; Q(0) = 1. The process temperature was considered as a control parameter according to two optimality criteria: maximizing the yield of target naphthenes (f1) at the end of the reaction, and maximizing the conversion of feedstock (f2). Values f1 were in the range of 0.43–0.79; conversion — 0.01–0.03; temperature — 200–300 K. The growth of temperature was accompanied by an increase in the yield of target naphthenes and a decrease in the conversion of feedstock. Each solution obtained was not an unimprovable one. When modeling the process of hydrogenation of PAH, an algorithm was launched with a population size of 100 and a number of generations of 100. A program implementing the NSGA-II algorithm was developed. The optimal set of values of the PAH hydrogenation reaction temperature was calculated, which made it possible to obtain unimprovable values of the optimality criteria — maximizing the yield of target naphthenes and conversion of feedstock.Discussion and Conclusion. The NSGA-II algorithm is effective for solving the problem of non-dominance, and deriving the optimal solution for all criteria. Future research should be devoted to the selection of optimal algorithm parameters to increase the speed of the solution. Based on the obtained theoretical optimal conditions of the PAH hydrogenation reaction, it is possible to implement the process in industry

Design Optimization of Null-Flux Superconducting Electrodynamic Suspension for Cost-Saving and Performance Improvement

The onboard superconducting magnets and null-flux coils (NFCs) on the track side are the crucial components for realizing the null-flux superconducting electrodynamic suspension (EDS). In this article, the multiobjective optimization of a null-flux EDS system was investigated to improve the performance using the nondominated sorting genetic algorithm-II (NSGA-II) method. First, a precise mathematical model of the superconducting EDS was established by adopting mutual inductance calculation method we proposed before. Then, the comprehensive sensitive analysis was carried out to analyze the influence of variables on different objectives. The ratio of levitation force to drag force (drag ratio), the ratio of levitation force to mass of NFCs (mass ratio) as well as the fluctuation of levitation force, were defined to be the optimization objectives. Third, an optimization scheme employing NSGA-II method was built, and the Pareto front was obtained. Afterward, the effectiveness of optimized results was verified by the finite element analysis. Finally, an equivalent experimental method was used to characterize the performance of a down-scale EDS system to confirm the proposed optimization methodology. To conclude, the optimal method can greatly improve the performance of EDS, and provide diverse design scheme choices.

An integrated decision support framework for resilient vaccine supply chain network design

Designing resilient supply chain networks for vaccine development and distribution requires reliable and robust infrastructure. This stud develops a novel two-stage decision support framework for configuring multi-echelon Supply Chain Networks (SCNs), resilient supplier selection, and order allocation under uncertainty. Resilient supplier selection is done using a hybrid Multi-Criteria Decision-Making (MCDM) approach based on Best-Worst Method (BWM), Weighted Aggregated Sum Product Assessment (WASPAS), and Type-2 Neutrosophic Fuzzy Numbers (T2NN). A robust multi-objective optimization model is then built for order allocation considering resiliency scores, reliability of facilities, and uncertain supply and demand. The objectives are to minimize the total cost of SCN design, maximize the resiliency score, and maximize the reliability of SC, respectively. A Non-dominated Sorting Genetic Algorithm II (NSGA-II) is developed to tackle the problem on large scales, tuned by the Taguchi design technique. The NSGA-II solution is compared to the ε-constraint and Multi-objective Particle Swarm Optimization (MOPSO) solutions using test problems. We demonstrate the superiority of the suggested NSGA-II method over the two competing methods according to five performance metrics. A case study is then investigated to illustrate the applicability and effectiveness of the offered methodology for COVID-19 vaccine distribution in a developing country. It is revealed that the models and algorithms can treat the problem optimally, such that Germany is the main source (approximately 25.61%) while India does not contribute to the supply of vaccines.

A multi-objective optimization method for hydraulically interconnected suspension system

To enhance the ride comfort and roll stability of the special vehicle, this study concentrates on the inherent parameters optimization of the hydraulically interconnected suspension (HIS) system. A road-tire-HIS-body model of a special vehicle is established based on the AMESim/Simulink co-simulation platform. Then the sensitivity of the HIS system is analyzed to determine the design variables to be optimized through the AMESim/Simulink/Isight co-simulation. Two objectives including improving the ride comfort and roll stability of the vehicle are proposed. In order to enhance the population diversity and accelerate the convergence velocity, the improved non-dominated sorting genetic algorithm II (NSGA-II) based on orthogonal experimental design method is used for multi-objective optimization problem of the HIS system. The numerical simulations indicate that the improved NSGA-II (INSGA-II) can generate better distributed Pareto solutions than traditional NSGA-II. Furthermore, simulation results indicate that both of the ride comfort and roll stability of the vehicle are improved based on the HIS system optimized by INSGA-II than NSGA-II. Compared with the NSGA-II method, the vehicle ride comfort and roll stability of HIS system optimized by INSGA-II are increased by 17.62% and 8.56% in sinusoidal conditions, respectively.

A Novel Multi-Objective Optimal Design Method for Dry Iron Core Reactor by Incorporating NSGA-II, TOPSIS and Entropy Weight Method

Dry iron core reactors are widely used in various power quality applications. Manufacturers want to optimize the cost and loss simultaneously, which is normally achieved by the designers’ experience. This approach is highly subjective and can lead to a non-ideal product. Thus, an objective dry iron core reactor design approach to balance the cost and loss with a scientific basis is desired. In this paper, a multi-objective optimal design method is proposed to optimize both the cost and loss of the reactor, which provides an automatic and scientific design method. Specifically, a three-dimensional finite element model of dry iron core reactor is established, based on which the dependency of cost and loss upon the wire size of the reactor’s winding is studied by using joint Matlab-finite element method (FEM) simulation. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to search for the Pareto optimal solution set, out of which the optimal wire size of the reactor is determined by using the fusion of the technique for order preference by similarity to ideal solution (TOPSIS) method and the entropy weight method. TOPSIS helps the designer to balance the concern between cost and loss, while the entropy weight method can determine the weight information through the dispersion degree of cost and loss. This methodology can avoid personal random subjective opinion when selecting the design solution out of the Pareto set. The calculation shows that the cost and loss can be reduced by up to 17.85% and 19.45%, respectively, with the proposed method. Furthermore, the obtained optimal design is approved by experimental tests.

Fast self-heating battery with anti-aging awareness for freezing climates application

Lithium-ion batteries (LIBs) need to be heated before use at low temperatures to avoid poor electric vehicle performance. In this study, a self-heating method for LIBs at low temperatures is proposed, where the influence of various heating parameters on heating performance is explored experimentally. To make the balance between heating speed and capacity degradation while achieving efficient preheating, a lumped parameter thermal model and an empirical capacity fade model are established to determine appropriate duty ratio and external resistance, which can predict the corresponding time required for LIBs to be heated to the target temperature and reveal the capacity loss of LIBs quantitatively after repeated heating. A multi-objective optimization method based on non-dominated sorting genetic algorithm II (NSGA-II) is employed to obtain the Pareto optimal front between heating speed and capacity degradation, which leads to the selection of the optimal electrical parameters with the help of K-means clustering algorithm and three newly defined heating performance indicators. Finally, the duty ratio and external resistance are preferably 80% and 203.98 mΩ through the NSGA-II method, respectively. The experimental results verify the optimal heating strategy which can heat the LIB quickly from – 20.56 °C to 0 °C within 70 s. This optimal heating strategy is applied to heat the LIB for 200 times, the battery capacity degradation is only about 7.72%.

A multi-objective evolutionary scheme for control points deployment in intelligent transportation systems

One of the problems that hinder emergency in developing countries is the problem of monitoring a number of activities on inter-urban roadway networks. In the literature, the use of control points is proposed in the context of these countries in order to ensure efficient monitoring, by ensuring a good coverage while minimizing the installation costs as well as the number of accidents across these road networks. In this work, we propose an optimal deployment of these control points from several optimization methods based on some evolutionary multi-objective algorithms: the non-dominated sorting genetic algorithm-II (NSGA-II); the multi-objective particle swarm optimization (MOPSO); the strength Pareto evolutionary algorithm -II (SPEA-II); and the Pareto envelope based selection algorithm-II (PESA-II). We performed the tests and compared these deployments using Pareto front and performance indicators like the spread and hypervolume and the inverted generational distance (IGD). The results obtained show that the NSGA-II method is the most adequate in the deployment of these control points.

Optimization of supply chain operation cost and gas usage quantity using non-dominated sorting genetic algorithm II (NSGA-II) Method

ABC plant is one of seven plants in XYZ industry which produce Cold Rolling Coil (CRC) and Cold Rolling Sheet (CRS). The problems faced by ABC plant in its supply chain network are the high overall costs of supply chain operations and the quantity of gas usage. The characteristics of this problem consist of more than one objective, the best method for solving this problem called multi-objective optimization. This research is aim to identify the decision variables that will be optimized and determine the optimal quantity of each decision variable using NSGA-II method. The parameters used in this research are the population size of 50, crossover probability with range 0.1-0.9, mutation probability 0.1 and 0.2 also the number of generation 50 and 100. The result shows that the selected parameters for this research are the crossover probability of 0.7, mutation probability of 0.1, number of generation 100. Four decision variables that are optimized, namely CRC produced (Lite, Medium, and Heavy) and CRC stored with the quantities simultaneously are 40,918, 112,479, 173,758, and 43,209 tons. This result will assist the ABC plant in minimizing the overall cost of supply chain (124,532,272 USD) and the quantity of gas usage (39,634,749,440 Kcal).

Model-based water-flooding optimization using multi-objective approach for efficient reservoir management

The efficient development of an oil field mostly depends on a comprehensive optimization of subsurface flow. To account for several discrete or even contradicting objectives, multi-objective optimization (MOO) approach presents multiple optimum solutions for decision-making processes. There are excessive degrees of freedom in any optimization problem of the life-cycle of water-flooding to optimize the short-term performance during the process. Choosing each strategy has a different impact on the long-term reservoir performance. Thus, in this study, we have utilized two different model-based algorithms based on multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II) methods with some modifications to plan the short- and long-term production strategies simultaneously in water-flooded reservoirs. These algorithms are both population-based techniques, in which the Pareto-ranking approach is combined with the inherent search towards the optimal solution for a multi-criterion optimization problem. Maximizing the long-term Net Present Value (LNPV) and short-term (discounted) NPV (SNPV) are the objectives to be met in the investigated MOO problems. To address the imperfect Pareto front obtained in MOO problems, some modifications have been added to the utilized algorithms, including using a modified comparison operator in the NSGA-II method and employing the crowding distance parameter in the leader selection process together with a revised archive controller as well as a dynamic boundary search to MOPSO algorithm. By these means, the entire Pareto fronts are actively generated, which covers the complete solutions area through both algorithms. To validate the developed approaches, two benchmark water-flooded reservoir models have been employed. In the first case, the optimization parameters are the wells injection rates in the Egg benchmark reservoir model. In the second one, we have adjusted the opening values of the inflow control valves (ICV) of smart wells in the water-flooding process of a layered reservoir with a five-spot pattern. The effect of the trading-off between Pareto elitism and diversity on the final results is investigated for both algorithms. Results illustrate that the competitive values of the NPV functions, LNPV and SNPV pairs, lying on the obtained Pareto front, provide a promising criterion to improve the decision-making process. A comparison of various methods shows that for both case-studies, MOPSO can strongly propose a production strategy that more appropriately optimizes SNPV and LNPV compared to the NSGA-II as well as compared to some previous efforts published in the literature. A high rate of convergence, together with the logical Pareto front having enough diversity and uniformity, and also the independency of the final solution on the initial guess, are the main advantages of MOPSO in comparison with other approaches.

Mathematical modeling for green supply chain considering product recovery capacity and uncertainty for demand.

Competition in today's market is the most important concern of companies and producers in free markets. Buyers are also looking for higher quality and lower prices. Manufacturers should, therefore, reduce production costs and increase budgets for research and product development. On the other hand, the limitation of mineral resources in each country and in the world in general is a very important factor for increasing the price of raw materials which increases the cost of production of a product. In this study, a green aspect of decision-making, concurrent modeling for inventory-routing, and application of maximum entropy (ME) method for overcoming uncertainties of demands are applied to optimize the usage of raw materials and returning of defective products to the production cycle in a closed-looped supply chain under multi-period planning horizon. Also, dynamic modeling is used to balance the inventory level in all stages of the network that leads to optimum usage of the raw materials. For this purpose, the first objective function reduces production, transportation-routing, and inventory costs, and the second objective reduces greenhouse gas emissions through all levels of the network. Finally, this model is solved by using the exact solution method with the help of Gams software as well as the non-dominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO) algorithm. Sensitivity analysis has been performed on failure rates, greenhouse gas emissions during recycling and production, and the optimistic-pessimistic coefficient of the ME solution method. Solution methods have been compared using several criteria, and the NSGAII method has finally obtained the best result. The results show that the manager should pay more costs in order to prevent backorder demands. Also, collecting the more defective products leads to increasing production amount since the collective products can return to the production line. Finally, it is required for the managers to control products' failure rate to optimize capacity usage in the model.

Multiobjective Optimization of Milling Parameters for Ultrahigh-Strength Steel AF1410 Based on the NSGA-II Method

In this paper, ultrahigh-strength steel AF1410 was milled with the carbide tool, and a total of thirty experiments were performed based on central composite design (CCD) of response surface methodology. The prediction models of milling force and surface roughness are established, respectively. The influence of milling parameters (milling speed, each tooth feed, radial depth of cut, and axial depth of cut) on milling force and surface roughness is studied by ANOVA and established prediction model. Multiobjective optimization of milling parameters is accomplished based on nondominated sorting genetic algorithm II (NSGA-II) with milling force, surface roughness, and material removal rate as optimization objectives. The surface roughness, cutting force, and material removal rate are important indexes to measure the energy consumed in the process of product, the surface machining quality, and machining efficiency of processing, respectively. In order to minimize milling force and surface roughness and maximize material removal rate, NSGA-II was used for multiobjective optimization to obtain the optimal fitness value of the objective function. The NSGA-II has been applied to obtain a set of optimal combination of parameters from the Pareto-optimal solution set to enhance the machining conditions.

Integrated framework of system dynamics and meta-heuristic for multi-objective land use planning problem

Land use optimization as a resource allocation problem can be defined as the process of assigning different land uses to a region. Sustainable development also involves the exploitation of environmental resources, investment orientation, technology development, and industrial changes in a coordinated form. This paper studies the multi-objective sustainable land use planning problem and proposes an integrated framework, including simulation, forecasting, and optimization approaches for this problem. Land use optimization, a multifaceted process, requires complex decisions, including selection of land uses, forecasting land use allocation percentage, and assigning locations to land uses. The land use allocation percentage in the selected horizons is simulated and predicted by designing a System Dynamics (SD) model based on socio-economic variables. Furthermore, land use assignment is accomplished with a multi-objective integer programming model that is solved using augmented e-constraint and non-dominated sorting genetic algorithm II (NSGA-II) methods. According to the results of the SD model, land use changes depend on population growth rate and labor productivity variables. Among the possible scenarios, a scenario focusing more on sustainable planning is chosen and the forecasting results of this scenario are used for optimal land use allocation. The computational results show that the augmented e-constraint method cannot solve this problem even for medium sizes. The NSGA-II method not only solves the problem at large sizes over a reasonable time, but also generates good-quality solutions. NSGA-II showed better performance in metrics, including number of non-dominated Pareto solutions (NNPS), mean ideal distance (MID), and dispersion metric (DM). Integrated framework is implemented to allocate four types of land uses consisting of residential, commercial, industrial, and agricultural to a given region with 900 cells.

Simulation and Optimization of Coal Gasification in a Moving-bed Reactor to Produce Synthesis Gas Suitable for Methanol Production Unit

This paper presents process simulation and optimization of coal gasification process<br /> in a moving-bed reactor using Pittsburgh No. 8 coal as feed. The system of differential<br /> equations for the mass and energy balances was solved using 4th-order Runge-Kutta method and optimized by non-dominated sorting genetic algorithm-II (NSGA-II) method.<br /> The simulation was used to predict solid and gas temperature profile and gas composition<br /> along the reactor. The simulation results were compared successfully with experimental<br /> data relevant to Westfield plant in Scotland. In addition, the effect of operating parameters such as coal-to-oxygen molar ratio, steam-to-oxygen molar ratio, inlet gas temperature, reactor pressure, and oxygen mole fraction in inlet air on amount of synthesis gas (syngas) production, hydrogen to carbon monoxide molar ratio (HCMR) in produced syngas, and coal conversion was investigated. Finally, the reactor performance was optimized to produce the highest syngas production with a HCMR of two using NSGA-II method.

Green Supply Chain Management Optimization Based On NSGA II Method

Green Supply Chain Management (GSCM) is the adopted by many companies due to the government policies of various countries. The optimization technique can be applied in the GSCM to increase the profit of the company. In this research, Non-dominated Sorting Genetic Algorithm-II (NSGA-II) technique is applied for the optimization of GSCM to increase the performance. The NSGA-II method has the advantage of choosing the solution closer to the pareto-solution and uses the elitist technique to preserve the best solution in the next generation. Mathematical model of the GSCM system is established and data is provided as input to the mathematical mode. Data is generated in three types, small scale, medium scale and large scale. The proposed NSGA-II method has high performance in the optimization technique compared to existing method. The proposed NSGA-II method has the Number of Pareto Solution (NPS) metrics of 17 for large scale data, while existing method has 14.

Solar PV parameter estimation using multi-objective optimisation

The estimation of the electrical model parameters of solar PV, such as light-induced current, diode dark saturation current, thermal voltage, series resistance, and shunt resistance, is indispensable to predict the actual electrical performance of solar photovoltaic (PV) under changing environmental conditions. Therefore, this paper first considers the various methods of parameter estimation of solar PV to highlight their shortfalls. Thereafter, a new parameter estimation method, based on multi-objective optimisation, namely, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is proposed. Furthermore, to check the effectiveness and accuracy of the proposed method, conventional methods, such as, ‘Newton-Raphson’, ‘Particle Swarm Optimisation, Search Algorithm, was tested on four solar PV modules of polycrystalline and monocrystalline materials. Finally, a solar PV module photowatt PWP201 has been considered and compared with six different state of art methods. The estimated performance indices such as current absolute error matrics, absolute relative power error, mean absolute error, and P-V characteristics curve were compared. The results depict the close proximity of the characteristic curve obtained with the proposed NSGA-II method to the curve obtained by the manufacturer’s datasheet.

Multi-objective NSGA-II optimization of a compression ignition engine parameters using biodiesel fuel and exhaust gas recirculation

In this study an exhaust gas recirculation system was developed for a small single cylinder 4-stroke engine. Then the mathematical models to correlate responses as the engine emissions and performance characteristics to the factors, include engine load, engine speed, EGR rate and biodiesel fuel percent, were developed. Finally, by using the developed models and NSGA-II (Non-dominated Sorting Genetic Algorithm II) method, the factors were optimized. The highest decrease in NOx emissions while using the biodiesel and EGR is 63.76% with B10 fuel blend (10% biodiesel fuel and 90% diesel fuel blend by volume) and 30% EGR rate. The highest reduction in HC emission levels while using EGR and biodiesel simultaneously, has been 54.05%. The adjusted R2 of the proposed model for the CO, HC, NOx, Power, BSFC and smoke were 0.94, 0.91, 0.88, 0.95, 0.89 and 0.94, respectively. Results of the optimization of the engine factors with NSGA-II method has been satisfactory and the pareto front for different test conditions was proposed. The outcomes of the study revealed that the optimization should be taken into account in the development of the new policy for using of the biofuel in the internal combustion engines.

A multi-objective optimization approach for simultaneously lightweighting and maximizing functional performance of vehicle body structure

This study presents a hybrid approach to integrate the comprehensive sensitivity analysis method, support vector machine technology, modified non-dominated sorting genetic algorithm-II method and the technique for order preference by similarity to ideal solution, which have been applied to multi-objective lightweight optimization of the B-pillar structure of an automobile. First, numerical models of the static–dynamic stiffness and the crashworthiness performance of automobile are established and validated by experimental testing. Then, the comprehensive sensitivity analysis method is used to define the final optimization variables. Experimental design and support vector machine based surrogate model techniques are introduced to establish the approximate model; subsequently, the modified non-dominated sorting genetic algorithm-II algorithm is applied to the multi-objective lightweight optimization design of the B-pillar structure, and the non-dominated solution set is determined. The principal component analysis method is applied to determine the weight of each objective. Finally, the technique for order preference by similarity to ideal solution method is used to rank Pareto front from best to worst to obtain the optimal solution; furthermore, a comparison between the original model and optimized design denotes that the mass of the B-pillar being reduced by 22.55% under the other impacting indicators is well guaranteed. Therefore, the proposed hybrid approach provided promising prospects in the lightweight and crashworthiness optimization application of the B-pillar.

Multi-objective optimization method for spectrum allocation in cognitive heterogeneous wireless networks

In a multi-heterogeneous network dense deployment and convergence environment, the cognitive radio technology dynamically utilizes the idle spectrum resources of each primary network, which can effectively improve the data transmission rate and system capacity, and is also a key technology of the next generation wireless communication network. However, how to efficiently and reasonably select the network and allocate idle spectrum resources to meet the low cost and large traffic demand of users is a difficult problem in the case of dynamic coupling with multiple heterogeneous primary networks overlapping coverage and diversified user requirements. In this paper, with the goal of maximizing the total bandwidth and minimizing the total cost, a multi-objective optimization mathematical model for network selection and idle spectrum allocation is established in the context of comprehensive consideration of the difference of spectrum resource attributes of different primary networks in the network domain and the diversification of secondary user requirements in the user domain, and the complexity of the problem is analyzed. Based on this, two kinds of technical paths to solve the complex network selection and spectrum allocation problem are applied in this paper. The first is the simplification method. By analyzing the relationship between optimization objectives and constraints, simplification method simplifies the objective function and constraints of the mathematical model and transforms the complex allocation problem into a standard form of the 01 programming problem. The second is the intelligent optimization algorithm. By improving the traditional multi-objective optimization algorithm Non-dominated Sorting Genetic Algorithm II (NSGA-II), an improved NSGA-II(INSGA-II) method is proposed, which combines the interference constraints of the primary network and the service quality requirements of the secondary users into the objective value evaluation of NSGA-II algorithm, while making the decision selection on the optimal solution set to select a compromise solution. Finally, the performance of this two methods is compared and analyzed through experiments. The experimental results show that the simplified method has higher efficiency advantages, and the INSGA-II algorithm can often meet the user’s service requirements at a lower cost, especially the cost priority strategy.

Investigation of power quality disturbances by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms

Abstract The aim of this paper is to investigate the power quality analysis by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms. The fact that PQ signals are one-dimensional (1D) signals due to their nature leads to the search for feature extraction approaches based on 1D signal processing methods. Due to the electric network is getting more and more complicated day by day, it is necessary to determine effectively the disturbances events. In the proposed method, extraction of a new feature based on two-dimensional (2D) signal processing by 2D Fast Discrete Orthonormal Stockwell Transform (2D-FDOST) method and determination of the most suitable feature group by Non-dominated Sorting Genetic Algorithm II (NSGA-II) method are performed. Eleven different PQ events are synthetically produced based on mathematical modelling. 1D signals are transformed into 2D signals with equal row and column numbers. Statistical and image-based features are created on the amplitude and phase matrices obtained by 2D-FDOST method from 2D signals. The NSGA-II method, which is one of the multi-objective evolutionary optimization methods, is used to convert a large number of feature vectors into a small number of useful feature groups. NSGA-II produces the optimal solution for two different fitness functions that calculate the number of features and classifier performance. By using different machine learning classifiers for selected features, a model classifying PQ disturbances with high performance and robust structure against noisy situations is created.

Multi-objective optimization of the environmental-economic dispatch with reinforcement learning based on non-dominated sorting genetic algorithm

This paper presents an improved non-dominated sorting genetic algorithm II (NSGA-II) approach incorporating a parameter-free self-tuning by reinforcement learning technique called learner non-dominated sorting genetic algorithm (NSGA-RL) for the multi-objective optimization of the environmental/economic dispatch (EED) problem. To evaluate the performance features, the proposed NSGA-RL approach is investigated on ten multi-objective benchmark functions. Besides, to evaluate the effectiveness of the proposed approach, the standard IEEE (Institute of Electrical and Electronics Engineers) of 30-bus network with six generating units (with/without considering losses) is adopted, with operating cost (fuel cost) and pollutant emission as two conflicting objectives to be optimized at the same time. In comparison to literature, it was observed that the proposed approach provides a better satisfaction level in conflicting objectives with well distributed Pareto front, in comparison with the classical NSGA-II method, and to other existing methods reported in the literature. The NSGA-RL was found to be comparable to them considering the quality of the solutions obtained, with the advantage of non-time spent for parameters tuning.