Multi-objective Pareto Optimal Solutions Research Articles

Multi-objective process parameters optimization of SLM using the ensemble of metamodels

Selective laser melting (SLM) is one of the most common additive manufacturing (AM) technologies that shows great potential for intelligent and clean manufacturing. The process parameters involved in the SLM process have a significant impact on the part quality and energy consumption during the printing process. Since the relationships between the process parameters and various part quality characteristics cannot be expressed explicitly, it is impractical to decide the optimal process parameters intuitively. In this work, a hybrid multi-objective optimization approach by combining the ensemble of metamodels (EM) and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to generate optimal process parameters to improve the energy consumption, the tensile strength, and the surface roughness of the as-built parts. First, the Taguchi experiment design is adopted and the corresponding SLM experiments are conducted to obtain the experimental results. Second, the correlations between the process parameters (i.e., laser power, layer thickness, scanning speed) and the three responses are fitted using the proposed EM. The comparative results show that the prediction ability of the EM outperforms the stand-alone metamodels. Then, the NSGA-II is used to search for multi-objective Pareto optimal solutions based on the constructed EM. Finally, the verification experiments were conducted to verify the optimal results obtained by the proposed multi-objective optimization approach. Results indicate that the optimal process parameters are effective and reliable. Besides, the main effects of process parameters on the responses are analyzed. Overall, the proposed hybrid multi-objective optimization method exhibits great ability to improve the effectiveness of SLM.

Multi-objective optimization in the vibration characteristics of a hydraulic steering system using a conservative and feasible response surface method

ABSTRACTThis article addresses the approximate multi-objective optimum design of an automotive hydraulic steering system based on a multi-body dynamics analysis. The design problem of a hydraulic steering system was formulated to determine the design dimensions of a steering mechanism that is able to estimate the multi-objective Pareto-optimal solutions of weight and vibration frequencies that are subject to the dynamic response constraints of the main steering components. The multi-objective Pareto-optimal solutions were calculated using the non-dominated sorting genetic algorithm-II (NSGA-II) based on various approximate models, and reviewed in terms of exploration performance and constraint feasibility. The multi-objective Pareto-optimal solution characteristics according to the approximate model were reviewed to identify a proper approximate model for the engineering design of a hydraulic steering system. The results of the Pareto solution from the proposed optimization methods could improve the vibration performance as well as the weight reduction of hydraulic steering systems.

Genetically optimized diamond-like carbon thin film coatings

ABSTRACTDiamond-like carbon (DLC) thin films find extensive applications in manufacturing, aerospace, and medical sector and thus, a huge need exists to optimize its deposition process. However, the experimental complexity and high costs involved limits the conduction of exhaustive experiments to determine the best process combinations. Consequently, in this research, a predictive modeling approach is coupled with global optimization procedures to find the optimum combination of deposition parameters. The prediction model is based on response surface methodology modeling of 20 LPCVD deposition experiments carried out as per central composite design. Scanning electron microscopy is used for morphology characterization of the DLCs and nanohardness is measured by nanoindentation technique. Raman spectroscopy and X-ray diffraction is used for characterizing the structural properties. Using a genetic algorithm, single- and multiobjective Pareto optimal solutions are reported which are validated experimentally. It is seen that for single-objective optimization, the best-predicted solutions for maximized hardness and maximized Young’s modulus are only 2% and 12% away from their true experimental values. Similarly, the most-desirable solution selected by TOPSIS from a Pareto optimal solution of 96 nondominated solutions (simultaneously maximized Young’s modulus and hardness) is only 2% away from their respective true values.

Fast artificial bee colony algorithm with complex network and naive bayes classifier for supply chain network management

In supply chain network (SCN) management, multi-objective Pareto optimization means the network can meet the demand for both minimal cost and minimal lead-time in SCN. Due to the compromise between cost and lead-time, it is a non-trivial issue to search for multi-objective Pareto optimal solutions (POS) in SCN. Furthermore, with the wide application of the internet, an increasing number of SCN applications have been based on the internet. As a result, the complexity of SCN increases exponentially with the number of suppliers increasing. It is really a big challenge to find the global multi-objective POS within a limited time in SCN management. In order to solve this problem, first, this paper proposes an artificial bee colony (ABC) optimization algorithm with two improvements: (1) a novel solution framework designed to extend the application field of the SCN based on complex network; (2) the acceleration of search speed by adopting naive Bayes classifier. Second, the paper provides a case example of optimizing a three-echelon SCN with the objective of minimizing both cost and lead-time. After the simulation with this example, it turns out that the enhanced ABC algorithm can satisfy the requirements of: (1) finding the global multi-objective POS; (2) improving the speed of finding optimal solutions in SCN management.

Identifying optimal process parameters in deep penetration laser welding by adopting Hierarchical-Kriging model

The quality of welding joints is largely dependent on the laser welding process parameters. In this work, an integrated optimization methodology by combining the Hierarchical-Kriging model and non-dominated sorting genetic algorithm II (NSGA-II) is developed for identifying the optimal process parameters in deep penetration laser welding. Firstly, a three-dimensional thermo-mechanical finite element model is developed as a low-fidelity (LF) model, while the laser welding experiment is taken as a high-fidelity (HF) model. Then, the data sets from these two different levels fidelity models are integrated by Hierarchical-Kriging model to build the relationships between welding process parameters and bead profile and angular distortion. Secondly, the NSGA-II algorithm is employed to obtain the multi-objective Pareto optimal solutions based on the constructed Hierarchical-Kriging model. Finally, the effectiveness and reliability of the obtained optimum are verified by laser welding experiments. Results illustrate that the developed integrated optimal method provides a promising way to identify favorable process parameters for generating a desirable bead profile and reducing the angular distortion in deep penetration laser welding.

Multi-objective process parameters optimization of hot-wire laser welding using ensemble of metamodels and NSGA-II

Abstract Hot-wire laser welding (HLW) can reduce the dispersion of laser energy and improve deposition efficiency by preheating filler wire during laser welding process. In order to obtain sound welding results, it is crucial to select appropriate process parameters. In this study, an optimization methodology based on ensemble metamodels (EM) which take the advantages of the prediction ability of stand-alone metamodels (Kriging, RBF and SVR), and Non-dominated sorting genetic algorithm (NSGA-II) are presented to obtain optimum process parameters during stainless steel 316L hot-wire laser welding. Firstly, EMs are developed through minimizing the generalized mean square Leave-one-out (LOO) errors to find the optimum weight factors of the used stand-alone Kriging, RBF and SVR metamodels. And then the EMs are applied to establish the relationships between process parameters (i,e., laser power (LP), welding speed (WS) and hot-wire current (I)) and welding results (i,e., welding depth-to-width ratio (DW), welding reinforcement (BR) and tensile strength (TS)). During optimization process, NSGA-II is employed to search for multi-objective Pareto optimal solutions based on EMs. In addition, the main effects of multiple process parameters on welding results are analyzed. The verification tests indicate that the obtained optimal process parameters are effective and reliable for producing expected welding results (maximized DW, maximized TS and desired BR value). In general, the proposed optimization method can provide a reliable guidance for HLW in engineering practice.

Multi-objective optimization of cascade reservoirs using NSGA-II: A case study of the Three Gorges-Gezhouba cascade reservoirs in the middle Yangtze River, China

ABSTRACTA multi-objective optimization model of cascade reservoirs was developed to maximize the power generation and minimizie the appropriate ecological flow shortage index (AEFSI) downstream from the reservoir. Additionally, the non-dominated sorting genetic algorithm (NSGA-II) was used to search for multi-objective Pareto optimal solutions. The paper took the Three Gorges-Gezhouba cascade reservoirs as a case study. After validating the model, data from three typical years were used in the optimization. The results indicated that maximizing power generation by adjusting the optimal rules increased power generation by 1.07%, 0.91%, and 1.03% in normal, wet, and dry hydrological years, respectively, while increasing the AEFSI by 22.12%, 11.78%, and 14.67% (compared to real operations). The AEFSI was improved (decreased) by 21.90%, 10.27%, and 18.52% when the optimal rules favored the downstream ecology, but power generation decreased by 1.61%, 1.06%, and 2.29%, respectively, in the different hydrological years. Moreover, the results provide a set of well-distributed optimal solutions along the Pareto front that allow decision-makers to easily determine the best compromised solutions based on the trade-offs between the economic and ecological benefits. The results of this study provide guidance for decision-makers to improve the comprehensive benefits of the Three Gorges-Gezhouba cascade reservoirs.

Laser Welding Process Parameters Optimization Using Variable-Fidelity Metamodel and NSGA-II

An optimization methodology based on variable-fidelity (VF) metamodels and nondominated sorting genetic algorithm II (NSGA-II) for laser bead-on-plate welding of stainless steel 316L is presented. The relationships between input process parameters (laser power, welding speed and laser focal position) and output responses (weld width and weld depth) are constructed by VF metamodels. In VF metamodels, the information from two levels fidelity models are integrated, in which the low-fidelity model (LF) is finite element simulation model that is used to capture the general trend of the metamodels, and high-fidelity (HF) model which from physical experiments is used to ensure the accuracy of metamodels. The accuracy of the VF metamodel is verified by actual experiments. To slove the optimization problem, NSGA-II is used to search for multi-objective Pareto optimal solutions. The results of verification experiments show that the obtained optimal parameters are effective and reliable.

Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II

Laser welding process parameters have significant effects on the welding bead profile and quality of the welding joint. This paper proposes an integration method of process parameters optimization using finite element method (FEM), Kriging metamodels and nondominated sorting genetic algorithm II (NSGA-II) in laser welding for stainless steel 316L. The process parameters in this study are laser power (LP), welding speed (WS) and laser focal position (LF). Firstly, a three-dimensional thermal finite element model is developed to obtain the simulated results of bead width (BW) and depth of penetration (DP). Then, Kriging metamodels are constructed to reflect the relationship between input process parameters and output responses. Finally, NSGA-II is used to search for multi-objective Pareto optimal solutions. In addition, the main effects and contribution rates of multiple process parameters on welding bead profile are analyzed. The results of verification experiments indicate that the optimal process parameters are effective and reliable for producing expected welding bead profile.

Optimization design of a gating system for sand casting aluminium A356 using a Taguchi method and multi-objective culture-based QPSO algorithm

This article combined Taguchi method and analysis of variance with the culture-based quantum-behaved particle swarm optimization to determine the optimal models of gating system for aluminium (Al) A356 sand casting part. First, the Taguchi method and analysis of variance were, respectively, applied to establish an L27(38) orthogonal array and determine significant process parameters, including riser diameter, pouring temperature, pouring speed, riser position and gating diameter. Subsequently, a response surface methodology was used to construct a second-order regression model, including filling time, solidification time and oxide ratio. Finally, the culture-based quantum-behaved particle swarm optimization was used to determine the multi-objective Pareto optimal solutions and identify corresponding process conditions. The results showed that the proposed method, compared with initial casting model, enabled reducing the filling time, solidification time and oxide ratio by 68.14%, 50.56% and 20.20%, respectively. A confirmation experiment was verified to be able to effectively reduce the defect of casting and improve the casting quality.

Approximate multi-objective optimization using conservative and feasible moving least squares method: application to automotive knuckle design

The original version of the moving least squares method (MLSM) does not always ensure solution feasibility for nonlinear and/or non-convex functions in the context of meta-model-based approximate optimization. The paper explores a new implementation of MLSM that ensures the conservative feasibility of Pareto optimal solutions in non-dominated sorting genetic algorithm (NSGA-II)-based approximate multi-objective optimization. We devised a `conservative and feasible MLSM' (CF-MLSM) to realize the conservativeness and feasibility of multi-objective Pareto optimal solutions for both unconstrained and constrained problems. We verified the usefulness of our proposed approach by exploring strength-based sizing optimization of an automotive knuckle component under bump and brake loading constraints.

Integrated Energy and Flux Balance Based Multiobjective Framework for Large-Scale Metabolic Networks

Flux balance analysis (FBA) provides a framework for the estimation of intracellular fluxes and energy balance analysis (EBA) ensures the thermodynamic feasibility of the computed optimal fluxes. Previously, these techniques have been used to obtain optimal fluxes that maximize a single objective. Because mammalian systems perform various functions, a multi-objective approach is needed when seeking optimal flux distributions in such systems. For example, hepatocytes perform several metabolic functions at various levels depending on environmental conditions; furthermore, there is a potential benefit to enhance some of these functions for applications such as bioartificial liver (BAL) support devices. Herein we developed a multi-objective optimization approach that couples the normalized Normal Constraint (NC) with both FBA and EBA to obtain multi-objective Pareto-optimal solutions. We investigated the Pareto frontiers in gluconeogenic and glycolytic hepatocytes for various combinations of liver-specific objectives (albumin synthesis, glutathione synthesis, NADPH synthesis, ATP generation, and urea secretion). Next, we evaluated the impact of experimental flux measurements on the Pareto frontiers. We found that measurements induce dramatic changes in Pareto frontiers and further constrain the network fluxes. This multi-objective optimality analysis may help explain certain features of the metabolic control of hepatocytes, which is relevant to the response to hepatocytes and liver to various physiological stimuli and disease states.

Multiobjective dynamic optimization of a semi-batch epoxy polymerization process

Multiobjective Pareto optimal solutions for epoxy semi-batch polymerization process are obtained by adapting nondominated sorting genetic algorithm II (NSGA II). The objective is to produce polymer of maximum possible number average molecular weight ( M n) with a specified value of polydispersity index (PDI) and number average molecular weight in minimum possible time. The M n and reaction time are, therefore, taken as two objectives where the first one is maximized and the second one is minimized. The decision variables are addition profiles of various reactants and the reaction time itself and PDI is treated as a constraint. In another optimization study, the time intervals are also been changed from hourly addition assumptions to equal interval additions for an optimized time frame. Additionally, similar analysis has been performed with a new addition strategy with total additions of reactants very close to available experimental conditions. Sensitivity analysis for estimated kinetic parameters and analysis for stabilization of products are also studied. A validated model, taking care of required physico-chemical aspects of the proposed reaction mechanism, is a prerequisite for this kind of study.

Multiobjective Optimization of a Semibatch Epoxy Polymerization Process Using the Elitist Genetic Algorithm

Multiobjective Pareto optimal solutions for a semibatch isothermal epoxy polymerization process are obtained by adapting the binary-coded nondominated sorting genetic algorithm II (NSGA II). The nu...

Multiobjective optimization of an industrial nylon‐6 semibatch reactor system using genetic algorithm

Multiobjective Pareto optimal solutions for three different grades of nylon-6 produced in an industrial semibatch reactor are obtained by using the adapted Nondominated Sorting Genetic Algorithm (adapted NSGA). The two objective functions minimized are the total reaction time and the concentration of undesirable cyclic dimer in the product, while simultaneously attaining desired values of the monomer conversion and the number average chain length. The control variables used are the fractional valve opening f(t) and the jacket fluid temperature TJ. The study shows a marked improvement over current industrial operation. It is found that the optimal values of the cyclic dimer concentration in the product are worse (higher) when the reactor-control valve system is studied than when the reactor is considered alone. This is because the control valve leads to additional constraints. The technique used is quite general and can be used to study other reactor systems as well. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 729–739, 1999

Multiobjective optimization of an industrial nylon-6 semibatch reactor system using genetic algorithm

Multiobjective Pareto optimal solutions for three different grades of nylon-6 produced in an industrial semibatch reactor are obtained by using the adapted Nondominated Sorting Genetic Algorithm (adapted NSGA). The two objective functions minimized are the total reaction time and the concentration of undesirable cyclic dimer in the product, while simultaneously attaining desired values of the monomer conversion and the number average chain length. The control variables used are the fractional valve opening f(t) and the jacket fluid temperature TJ. The study shows a marked improvement over current industrial operation. It is found that the optimal values of the cyclic dimer concentration in the product are worse (higher) when the reactor-control valve system is studied than when the reactor is considered alone. This is because the control valve leads to additional constraints. The technique used is quite general and can be used to study other reactor systems as well. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 729–739, 1999

Multiobjective dynamic optimization of an industrial nylon 6 semibatch reactor using genetic algorithm

The nondominated sorting genetic algorithm (NSGA) is adapted and used to obtain multiobjective Pareto optimal solutions for three grades of nylon 6 being produced in an industrial semibatch reactor. The total reaction time and the concentration of an undesirable cyclic dimer in the product are taken as two individual objectives for minimization, while simultaneously requiring the attainment of design values of the final monomer conversion and for the number-average chain length. Substantial improvements in the operation of the nylon 6 reactor are indicated by this study. The technique used is very general in nature and can be used for multiobjective optimization of other reactors. Good mathematical models accounting for all the physicochemical aspects operative in a reactor (and which have been preferably tested on industrial data) are a prerequisite for such optimization studies. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 69–87, 1998

Simulation and Optimization of an Industrial Nylon 6 Reactor: A Review

An industrial semibatch Nylon 6 reactor has been modeled and then optimized. The model developed accounts for most of the important physicochemical phenomena present, like heat transfer, vaporization, polymerization, and so forth. Five parameters are present in the model, which are “tuned” using data from the industrial reactor under one set of operating conditions, producing one grade of the polymer (using initial water concentration, [W]0, of 3.45 wt%). The tuned model is found to predict the behavior of the reactor for two other operating conditions ([W]0 = 2.52% and 4.43%), giving confidence in the model. The optimization involves the minimization of two objective functions, namely the reaction time, tf. and the concentration of the undesirable cyclic dimer in the product, [C2] f , The final monomer conversion, conv f , and the degree of polymerization of the final product, μ nf, are constrained to lie at values currently obtained for the three different cases. The (constant value of the) jacket fluid temperature, Tj , is one of the control variables, whose optimal value is to be ascertained. The pressure history, p(t), in the reactor, which can be manipulated through the vapor release rate, V T (t), is the other optimizing variable. Initially, the shapeof the pressure history is selected to be similar to that used currently, and p(t) is described in terms of four constants, Pmax, t f , S, and tf (tf is decided by the attainment of the desired value of μ nf ). Optimal values of Pmax, t f , S, and T f are obtained using the sequential quadratic programming (SQP) method to give the Pareto set (set of equally optimal or noninferior points). An adapted Nondominated Sorting Genetic Algorithm (NSGA) is then used with the optimal results from the SQP study to obtain improved multiobjective Pareto optimal solutions for the three grades of Nylon 6, using the continuous variable, VT (t), and the value Tj as the optimizing variables. The solutions obtained are better than those obtained using the SQP technique with the shape of p(t) fixed a priori. A decision-maker can select the best operating condition from among these equivalent optimal points on the Pareto set, based on considerations which are usually nonquantifiable. The methodology used here can be used for studying other industrial reactors as well. Good mathematical models accounting for all the physicochemical aspects operative in a reactor (and which have been preferably tested on industrial data) are a prerequisite for such optimization studies. * Mahila Mahavidyalaya, BHU, Varanasi, 221-005, India