Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II

In this paper, we propose to add Grey prediction model GM(1,2) into the self-tuning Neuro-PID controller based on radial basis function (RBF) algorithm to improve the performance of the controller. Initially, the prediction of system output by the simple GM(1,2) model is added to the RBF algorithm as one of the inputs to enhance the performance of RBF neural network system identifier. The output of this GM(1,2)-RBF on-line learning system model is subsequently used to establish a set of updating algorithms for the gains of self-tuning PID controller. The detailed description of the proposed system structure and the design algorithm is given in this paper. The proposed auto-tuning PID controller via GM(1,2)-RBF algorithm is put into tests by Matlab simulations and motor speed control experiments by using Lab VIEW. The system responses of self-tuning PID controller based on GM(1,2)-RBF and RBF are compared. Both simulations and motor test results confirm that the proposed self-tuning PID controller based on GM(1,2)-RBF performs better than the one based on RBF.

This paper presents a new multi-objective optimization method, which is inspired from the idea of non-dominated sorting genetic algorithm (NSGA) and genetic quantum algorithm (GQA). The GQA has been tested on well known test beds in single objective optimization and compared with the genetic algorithm (GA) in the lead author’s previous work [22]. This paper aims to apply the idea of GQA to multi-objective optimization (MOO). The developed method is called non-dominated sorting genetic quantum algorithm (NSGQA). The developed method is tested with benchmark problems collected from literature, which have characteristics representing various aspects of a MOO problem. Test results show that NSGQA has better performance on most benchmark problems than currently popular MOO methods such as the NSGA. The integration of GQA with MOO, and the systematic comparison with other MOO methods on benchmark problems, should be of general interest to researchers on MOO and to practitioners using MOO methods in design.

The large-scale high-intensity homogeneous magnetic field is an important resource to perform magnetic immunity tests for large scientific facilities. Generally, a multi-coil system with large cross-sectional area is used to generate the required test field, which has high power loss and conductor mass. In this article, we propose a novel method that introduces magnetically shielded room (MSR) to enhance the coil magnetic field and reduce power loss. The analytical model of the coil system based on MSR is established through the multi-reflection image method. In addition, the multi-objective optimization model is brought forward based on the non-dominated sorting genetic algorithm (NSGA-II). Theoretical results indicate that the magnetic field can be significantly enhanced under the presence of MSR. Consequently, prominent reductions in total current by about 61.4% and in total power loss by 75.5%–81.7% are achieved. Finally, the effectiveness of the theoretical result is numerically verified by the finite-element analysis (FEA). The proposed method provides a novel and promising way to reduce the power loss and conductor mass of such high-intensity magnet systems and other similar applications.

When large-scale electric vehicles are connected to the grid for unordered charging, it will seriously affect the stability and security of the power system. To solve this problem, this paper proposes a regional power network optimization scheduling method considering vehicle network interaction. Initially, based on the user behavior characteristics and charging and discharging characteristics of electric vehicles, a charging and discharging behavior model of electric vehicles was established. Based on the Monte Carlo sampling algorithm, the scheduling upper and lower limits of each scheduling cycle of electric vehicles were described, and the scheduling potential of each scheduling cycle of electric vehicles was obtained. Then, the electricity price is then used as an incentive parameter to guide EV users to charge during periods of low electricity prices and participate in discharge during periods of peak electricity prices. Aiming at the highest economic efficiency, the best consumption effect of new energy and the smoothest demand-side power curve of regional power grid, a three-objective optimal dispatching model was established. In the later stage, uncertainty factors are taken into consideration by introducing the concept of interval numbers, and an interval multi-objective optimization dispatching model is established. The two dispatching models are solved by NSGA-II algorithm and improved NSGA-II algorithm, and the Pareto solution set is obtained. Finally, based on the analytic Hierarchy Process (AHP), the optimal scheduling scheme is determined. The Monte Carlo sampling method is used to simulate the user side charging demand, and the effectiveness of this method is verified. In addition, the results of the interval multi-objective optimization model and the deterministic multi-objective optimization model are compared, and it is proved that the solution results of the interval multi-objective model are more adaptive, practical and robust to the uncertain factors.

Under intense industry competition, decision makers must ensure that products demanded by consumers can be quickly produced with minimum production cost. However, because uncertainties are unavoidable and inevitably affect decision makers, numerous studies have discussed how to control uncertainties or minimize their effects. Multiple uncertainties that interact simultaneously may cause a combined effect in actual systems. Therefore, this study presents a robust optimization model with two uncertainties, extending the method of robust optimization with one uncertainty. To demonstrate the applicability of the proposed model with two uncertainties, this study uses the supplier selection problem with component purchase quantity allocation in supply chain management as an analysis case. This considers the reliability of production and transportation and develops a multi-objective robust optimization model with two uncertainties. In addition, a nondominated sorting genetic algorithm is proposed for solving the proposed multi-objective robust optimization model. The relationship between price of robustness and budget parameters is explored by considering the robust optimization model with production and transportation uncertainties proposed in this study. Finally, there is a comparative analysis between the results for price of robustness in the proposed two-uncertainty model and in the one-uncertainty model.

Batch scheduling is a well-known topic that has been studied widely with various objectives, methods, and circumstances. Unfortunately, batch scheduling in a collaborative flow shop system is still unexplored. All studies about batch scheduling that are found were in a single flow shop system where all arriving jobs come from single door. In a collaborative flow shop system, every flow shop handles its own customers although joint production among flow shops to improve efficiency is possible. This work aims to develop a novel batch scheduling model for a collaborative multi-product flow shop system. Its objective is to minimize make-span and total production cost. This model is developed by using non-dominated sorting genetic algorithm (NSGA II) which is proven in many multi objective optimization models. This model is then compared with the non-collaborative models which use NSGA II and adjacent pairwise interchange algorithm. Due to the simulation result, the proposed model performs better than the existing models in minimizing the make-span and total production cost. The make-span of the proposed model is 10 to 17 percent lower than the existing non-collaborative models. The total production cost of the proposed model is 0.3 to 3.5 percent lower than the existing non-collaborative models.

With the development of excellent software in optimization, there is more and more wishes to use these techniques and make epoch developments in their products. However, most of us know that it costs a lot of time and costs to carry out optimization, because it needs to repeat simulations for the number of times. Therefore, most engineers would like to make mathematical models of design problems just enough to express their needs priori to optimization. Let us call these models as light models, in this paper. However, it is very difficult to make a proper light model in the first trial. Recent optimization will find the global solution, so that it will find some modeling miss and lead light model to some strange results. Such phenomenon is not a fault of optimization, but of the light model. We have to revise the light model but it is way difficult to make it rationally with the information we have had from the light model. We have to think of appropriate values of existed constraints, we have to think of new functions for constraints, and so on. It is almost hopeless to revise the light model at one time. The best thing that we can hope for is to give up the light model and make models complex to express the situation of the products. If we do not know proper values for constraints, treat them as objective functions and just go through trade-off analysis to have their relationships information, so that we can give appropriate values. In this sense, it is very important to make models in multi-objective optimization. In multi-objective optimization, it is quite important to carry out trade-off analysis and which might be a key to find epoch design. We had developed approximate multi-objective optimization method, which is composed by satisficing method, convolute radial basis function network and recommendation of new design variables. In satisficing method, we can handle trade-off analysis much easier than weighting methods. However, scalar function composed by satisficing method is not smooth when it gets close to Pareto solution that is indicated by designer’s requirement. Therefore, it is difficult even for convolute RBF to compose better approximate function although we have better approximation for each objective function. In weighting method, it is quite difficult to give proper weights for designer’s requirement. In approximate optimization, fortunately we have a number of data sets. Thus, it is possible to optimize weights which meet for aspiration level in satisficing method. Then, we can have smooth and better approximation for scalar function. In this paper, we are going to show effectiveness of the proposed method through demonstration of numerical examples.

Synergetic trajectory planning of flights is one of the important goals of trajectory-based operation (TBO), and it is also a method to further improve the utilization of airspace resources with the increasing number of flights in recent years. In order to plan the four-dimensional trajectory (4DT) pre-tactically and comprehensively, match the flight traffic with airspace capacity, reduce congestion, potential conflicts, and fuel consumption thus improving the efficiency of flights, this paper conducts a method for synergetic trajectory planning in the en-route phase from the perspective of airlines. Firstly, the aircraft performance model, aircraft fuel consumption model, and atmospheric model are constructed according to the base of aircraft data (BADA3.11), and an airspace congestion prediction model is constructed based on the historical flow data of airspace. Secondly, a multi-objective synergetic trajectory planning model is established, and a solution method based on the non-dominated sorting genetic algorithm and simulated annealing algorithm (NSGA3-SA) for the problem of synergetic trajectory planning is designed. The simulation shows that the optimization model and the solution algorithm of NSGA3-SA can reduce fuel consumption by about 4.5% compared to the original flight plans and has a good effect on reducing congestion and avoiding conflicts. The running time of the NSGA3-SA can meet the operational requirements of the pre-tactical trajectory planning. The multi-objective optimization model and the solution algorithm proposed in this paper have great value for the research of flight plan optimization.

In this paper, a novel model is presented for machines and automated guided vehicles' simultaneous scheduling, which addresses an extension of the blocking job shop scheduling problem, considering the transferring of jobs between different machines using a limited number of multi-mode automated guided vehicles. Since the model is strictly NP-hard, and because objectives contradict each other, a meta-heuristic algorithm called 'multi-objective invasive weeds optimisation algorithm' with a new chromosome structure which guarantees the feasibility of solutions is developed to solve the proposed problem. Two other meta-heuristic algorithms namely 'non-dominated sorting genetic algorithm' and 'multi-objective particle swarm optimisation algorithm' are applied to validate the solutions obtained by the developed multi-objective invasive weeds optimisation algorithm. A certain method was applied to select the algorithm with the best performance. The result of ranking the algorithms indicated that the developed multi-objective invasive weeds optimisation algorithm had the best performance in terms of solving the mentioned problems. [Received: 7 January 2017; Revised: 30 December 2017; Revised: 17 August 2018; Revised: 22 January 2019; Accepted: 26 July 2019]

Background and ObjectiveLarge, uniformly spaced, complex and time varying datasets derived from high resolution medical image velocimetry can provide a wealth of information regarding small-scale transient physiological flow phenomena and pulsation of anatomical boundaries. However, there remains a need for interpolation techniques to effectively reconstruct a fully 4-dimensional functional relationship from this data. This paper presents a preliminary evaluation of a 4-dimensional local radial basis function (RBF) algorithm as a means of addressing this problem for laminar flows. MethodsA 4D interpolation algorithm is proposed based on a Local Hermitian Interpolation (LHI) using a combination of multi-quadric RBF with a partition of unity scheme. The domain is divided into uniform sub-systems with size restricted to immediately neighbouring points. The validity of the algorithm is first established on a known 4D analytical dataset and a CFD based laminar flow phantom. Application is then demonstrated through characterisation of a large 4D laminar flow dataset obtained from magnetic resonance imaging (MRI) measurements of cerebrospinal fluid velocities in the brain. ResultsPerformance of the algorithm is compared to that of a quad-linear interpolation, demonstrating favourable improvement in accuracy. The technique is shown to be robust, computationally efficient and capable of refined interpolation in Euclidean space and time. Application to MR velocimetry data is shown to produce promising results for the 4D reconstruction of the transient flow field and movement of the fluid boundaries at spatial and temporal locations intermediate to the original data. ConclusionThis study has demonstrated feasibility of an accurate, stable and efficient 4-dimensional local RBF interpolation method for large, transient laminar flow velocimetry datasets. The proposed approach does not suffer from ill-conditioning or high computational cost due to domain decomposition into local stencils where the RBF is only ever applied to a limited number of points. This work offers a potential tool to assist medical diagnoses and drug delivery through better understanding of physiological flow fields such as cerebrospinal fluid. Further work will evaluate the technique on a wider range of flow fields and against CFD simulation.

— Neural networks are frequently used as a classifier for tasks in many classifications. However there are disadvantages in terms of amount of training data required, and length of training time. This paper, develop an intelligent diagnosis system for zinc oxide (ZnO) surge arrester fault classification. First the features were extracted from 600 ZnO surge arrester thermal images and leakage currents. Then these features were presented to several neural network architectures to investigate the most suitable network model for classifying the ZnO surge arrester fault condition effectively. Three classification models were used namely feed forward back propagation (FFBP), radial basis function (RBF) and learning vector quantization (LVQ) algorithm. The performance of the networks was compared based on resulted of misclassify and correct rate. The method was evaluated using 24 testing datasets. Comparison results showed that LVQ was the best training algorithm for the ZnO surge arrester fault classification compared to the others system. Also the LVQ is faster than FFBP and RBF.

A new multi-objective optimization approach based on layered objective is proposed.Two improvements on the non-dominated sorting genetic algorithm are given which are new layering method and the new selection mechanism.On the basis of the traditional non-dominated sorting genetic algorithm, a new objective layer approach is adapted and cycle copy through the first half layers.Another one is making a restriction mechanism before crossover on the classical non-dominated sorting genetic algorithm with elitist strategy.Through these operations, it can effectively improve the convergence rate of the optimal solution set.At last, the corresponding non-inferior solutions will be maintained.Several classic test functions commonly adopted in evolutionary multi-objective optimization and the network design problem are used.The results indicate that the non-dominated sorting genetic algorithm based on layered objective can effectively speed up the convergence rate.

In the compressed processing of hyperspectral images, orthogonal matching pursuit algorithm (OMP) can be used to obtain sparse decomposition results. Aimed at the time-complex and difficulty in applying real-time processing, an evolutionary multi-objective optimization sparse decomposition algorithm for hyperspectral images is proposed. Instead of using OMP for the matching process to search optimal atoms, the proposed algorithm explores the idea of reference point non-dominated sorting genetic algorithm (NSGA) to optimize the matching process of OMP. Take two objective function to establish the multi-objective sparse decomposition optimization model, including the largest inner product of matching atoms and image residuals, and the smallest correlation between atoms. Utilize NSGA-III with advantage of high accuracy to solve the optimization model, and the implementation process of NSGA-III-OMP is presented. The experimental results and analysis carried on four hyperspectral datasets demonstrate that, compared with the state-of-the-art algorithms, the proposed NSGA-III-OMP algorithm has effectively improved the sparse decomposition performance and efficiency, and can effectively solve the sparse decomposition optimization problem of hyperspectral images.

PurposeThis study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.Design/methodology/approachA robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.FindingsCompared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.Originality/valueThis study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

Three 100-compound spectra libraries have been used to evaluate artificial neural network classifications of functional groups. A near-IR gas-phase library was used to compare neural network classifications with those obtained by two-dimensional principal component analysis (PCA) score plots and by the use of the Mahalanobis distance metric based on multidimensional (score) vectors. The neural network using a radial basis function algorithm was able to correctly classify all aromatic and nonaromatic samples in a test set of 40 samples from the 100-compound library; PCA score plots were successful in separating ∼92% of the 100-compound library into aromatic and nonaromatic classes, whereas the Mahalanobis distance metric could not separate the in-class vs out-of-class aromatics in the library. Using principal component scores as input to the neural network training with 40 randomly selected samples, validating with 20 randomly selected samples, and testing with 40 randomly selected samples were performed in less than 5 s and produced perfect classifications. The neural network algorithm incorporating the radial basis function was then used to compare the information available in a near-IR spectral library of condensed-phase molecules with spectra of identical (or very similar) compounds in a mid-IR library. Results with the radial basis function were very good for both libraries, with classifications >85% in all cases. The near-IR library produced better results for aromatics (95 vs 88%), identical or very similar results for OH's (98%), alkyls (>85%), and halogens (98%), and poorer results for carbonyls (85 vs 98%). Better mid-IR results for carbonyls were anticipated due to the sharp band for carbonyl-containing compounds in the fingerprint region; however, the improved results for aromatics in the near-IR were not anticipated.