Multi‐Objective Evolutionary Algorithm Based on Decomposition With Orthogonal Experimental Design

This paper firstly analyzes the limitations of the traditional ergonomic experimentation, and for the limitations, put forward orthogonal regression experiment by the combination of the advantages and disadvantages of each two commonly portion experimentation: orthogonal experimental design and regression experimental design. Finally, use an interface design experiment example to illustrate the application of the orthogonal regression experiment design in the interface design, and also provide reference for the application of this field.

In multi-objective optimization problems (MOPs), set-based performance indicators are commonly used to assess the convergence and diversity of Pareto front approximation. Performance indicators can be used as the selection strategies. The selection strategy of indicator based evolutionary multi-objective algorithms (EMOAs) is guided by a general preference information, which maps objectives into a single contribution value by means of a set of utility functions. R2-EMOA is one of the most important indicator-based algorithms to solve MOPs. We use fast R2-ranking to rank the individuals of EMOAs. This paper suggests a new weight generator strategy, which is based on direction angles, for MOPs. Our main purpose is to explore the relationship among direction angles, weight vectors and direction vectors. Our proposed weight generator scheme is incorporated to two different search engines, resulting in two new EMOAs, named IR2-MOGA and IR2-MODE. The performance of our proposed method is validated and compared with other R2-EMOAs on a number of unconstraint benchmark problems. Experimental results demonstrate that our algorithms can significantly improve the convergence and diversity of R2-EMOA.

Orthogonal simulated annealing for multiobjective optimization

In order to improve the machining precision, the carriage of the gantry machine tool must have high anti-vibration performance, and its mass should be as light as possible. Based on the finite element modal analysis, a precision gantry machine tool's carriage was taken as the study object, and a multi-objective optimization mathematical model of the carriage was built by taking the mass and the first four order natural frequencies of the carriage as the objective functions, and the thickness of stiffener plates as the design variables. The second-order response surface model for carriage's multi-objective optimization was established through orthogonal experimental design. The accuracy of the response surface model was verified by comparing the response surface model with finite element model. The optimal solution of carriage multi-objective optimization was obtained by solving the response surface optimization model, which made carriage's mass decreasing 9.63%, the first four natural frequencies increasing 6.48%, 7.41%, 8.36% and 10.32% respectively. Finally, the correctness of carriage's optimization design method proposed in this paper was verified by the static and dynamic experiments.

With the aim of enhancing both reliability and fatigue life of gasket, this study combines finite element analysis, orthogonal experimental design, dynamically-guided multi-objective optimization, and the non-dominated sorting genetic algorithm with elitist strategy to optimize the geometric parameters of the cylinder gasket. The finite element method was used to analyze the temperature field, thermal-mechanical coupling stress field, and deformation of cylinder gasket. The calculation results were experimentally validated by measured temperature data, and comparison results show that the maximum error between calculated value and experiment value is 7.1%, which is acceptable in engineering problems. Based on above results and orthogonal experiment design method, the effects of five factors, including diameter of combustion chamber circle, diameter of coolant flow hole, length of the insulation zone between third and fourth cylinders, thickness of gasket, and bolt preload, on three indexes: temperature, stress, and deformation of gasket, were examined in depth. Through the variance analysis of the results, three important factors were identified to proceed later calculation. The dynamically guided multi-objective optimization strategy and the non-dominated sorting genetic algorithm were effectively used and combined to determine the optimal geometric parameters of cylinder gasket. Furthermore, calculation results suggest that temperature, stress, and deformation of the optimized cylinder gasket have been improved by 27.88 K, 16.84 MPa, and 0.0542 mm, respectively when compared with the origin object, which shows the excellent performance of gasket optimization and effectiveness of the proposed optimization strategy.

A kind of low cost, high breakage resistance ceramic proppant special for exploitation of the coal‐bed methane is successfully produced. The producing conditions are optimized through orthogonal experimental design method. The breakage resistance results of the orthogonal analyses show the best condition of this kind of ceramic proppant is A4B3C3D2, which means sintering temperature of 1350 °C, manganese mineral powder content of 5 wt.%, weight ratio of 75/25 (second grade bauxite to mujie clay), and holding time of 3 h. The ceramic proppants under this very condition of A4B3C3D2 are then prepared and their phase structure and microstructure are characterized subsequently. X‐ray diffraction pattern exhibits that mullite and corundum are the main crystallographic phases. Scanning electron microscopy illustrates the A4B3C3D2 sample is with non‐porous morphology and small amount of corundum grains and liquid phase, which play the role of improving strength. It reveals the orthogonal experimental design is a feasible optimization method and the ceramic proppant made under the condition of A4B3C3D2 is a promising material for exploiting the coal‐bed methane resources.

In this paper, the orthogonal experimental design method is used to study the influences of various factors on unstable water flooding development effects aiming at the seven geological reservoir factors and five engineering factors that influence the unstable water flooding development effects of anisotropic reservoirs. Twenty seven (27) experimental programs are proposed in this paper. Compared with conventional water flooding, most of them can increase the recovery efficiency in a certain degree and the best one can increase it by 2.73%. The visual analyses of range and variance on the experimental results indicate that the key factors affecting the recovery efficiency increase of unstable water flooding are working system, amplitude of fluctuation, relative waterflood frequency and waterflood timing; the moderate factors are reservoir rhythmicity, capillary pressure, water injection cycle and the wettability; and the minor factors are permeability ratio, rock compressibility, viscosity of crude oil and the coefficient of variation. The development engineering factors have the highest influence, followed by the geological factors. An optimum program is achieved after optimizing the development engineering parameters.The average EOR efficiency it achives is 3.83%,which is higher than the preferred plan in the orthogonal experimental design,the parameter optimization effect is scientific and rreasonable.

Shale oil is mainly extracted by fracturing. However, it is difficult to determine the optimum construction parameters to obtain maximum productivity. In this paper, a fuzzy comprehensive production evaluation model for fractured shale oil horizontal wells based on random forest algorithm and coordinated principal component analysis is proposed. The fracturing parameters of the target wells are optimized by combining this model with an orthogonal experimental design. The random forest algorithm was used to calculate the importance of data sample factors. The main controlling factors of the production of fractured horizontal wells in shale oil were obtained. To reduce the noise of the sample data, principal component analysis was used to reduce the dimensions of the main control factors. Furthermore, the random forest algorithm was used to determine the weight of the principal components after reducing the dimensionality. The membership function of the main control factors after reducing dimensionality was established by combining the fuzzy statistics and assignment methods. In addition, the membership matrix of the effect prediction of fractured horizontal wells in shale oil was determined. The fuzzy comprehensive evaluation method is used to score and evaluate the effect of fractured horizontal wells. Combined with the orthogonal experimental design method, the optimized parameter design of a fractured horizontal well considering the comprehensive action of multiple parameters is realized. After construction according to the optimized parameters, production following fracturing increases significantly. This verifies the rationality of the optimization method that is proposed in this paper.

Orthogonal chemical reaction optimization algorithm for global numerical optimization problems

An adaptive decomposition-based evolutionary algorithm for many-objective optimization

Reference sets generated with uniformly distributed weight vectors on a unit simplex are widely used by several multi-objective evolutionary algorithms (MOEAs). They have been employed to tackle multi-objective optimization problems (MOPs) with four or more objective functions, i.e., the so-called many-objective optimization problems. These MOEAs have shown a good performance on MOPs with regular Pareto front shapes, i.e., simplex-like shapes. However, it has been observed that in many cases, their performance degrades on MOPs with irregular Pareto front shapes. In this paper, we designed a new selection mechanism that aims to promote a Pareto front shape invariant performance of MOEAs that use weight vector-based reference sets. The newly proposed selection mechanism takes advantage of weight vector-based reference sets and seven pair-potential functions. It was embedded into the non-dominated sorting genetic algorithm III (NSGA-III) to increase its performance on MOPs with different Pareto front geometries. We use the DTLZ and DTLZ\(^{-1}\) test problems to perform an empirical study about the usage of these pair-potential functions for this selection mechanism. Our experimental results show that the pair-potential functions can enhance the distribution of solutions obtained by weight vector-based MOEAs on MOPs with irregular Pareto front shapes. Also, the proposed selection mechanism permits maintaining the good performance of these MOEAs on MOPs with regular Pareto front shapes.

Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

Clustering-based genetic offspring generation for solving multi-objective optimization problems with intricate Pareto sets

Runtime analysis of a multi-objective evolutionary algorithm for obtaining finite approximations of Pareto fronts

Aluminum rectangular tube is the key component in the field of microwave transmission whose service condition requests strict dimensional accuracy and internal surface quality. To meet these requirements, a newly developed plug featuring a tiny boss club structure in the sizing zone has been proposed in the plug drawing process. The optimal combination of the dimensions in the boss club has been obtained using the method of 3D finite element simulation and orthogonal experimental design. The plastic strain distribution, the contact status between the tube inner surface and the plug, the dimensional accuracy of the formed part, and the forming load have been compared between conditions where the traditional linear-type plug and this new type of plug have been used, respectively. It can be seen clearly that when the plug with a tiny boss club structure is adopted, the contact quality is better and the larger plastic strain exists on the inner surface of the tube, which is very crucial in improving the surface finish of the formed part. Meanwhile, the deviation of wall thickness and the axial length in the formed part is smaller based on the new type of plug. The experiment of the drawing process with two types of plugs has been carried out in which the surface finish of the inner tube surface and the wall thickness have been measured and compared. Experiment result shows that the dimensional accuracy and inner surface quality meet the requirements of the service condition when the plug with a tiny boss club structure is employed.