Robust multi-objective optimization for sustainable design of distributed energy supply systems

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

This review critically analyzes the design of sustainable energy systems implemented on islands and beyond. It emphasizes the importance of integrating renewable and non-renewable energy sources to enhance energy output in hybrid systems. Due to the Island's unique geographical and environmental characteristics, islands face distinct energy supply and sustainability challenges. The review examines different aspects of sustainable energy system design, such as renewable energy sources, energy storage solutions, grid integration, and policy frameworks. Hence, by synthesizing current research and case studies, this review aims to provide insights into effective strategies for designing sustainable energy systems that are specifically tailored to the needs and constraints of islands. This paper detailed the critical role of renewable energy sources such as solar, wind, hydro, and biomass in driving sustainability in island communities and urges energy stakeholders and policymakers to embrace their potential to effectively energize rural and underprivileged areas

This paper presents a new approach aims to solve robust multidisciplinary design optimization MDO problem called Improved Multi-objective Robust Collaborative Optimization . This method combines the Multi-objective Robust Collaborative Optimization method, the Worst Possible Point constraint cuts and the Genetic algorithm NSGA-II type as an optimizer to solve the robust optimization problem of complex structure named Y-stiffened panel under interval uncertainty . The proposed approach hierarchically decomposes the optimization problem into a structure level considered as an upper level in the Y-stiffened panel and a second level considered as a lower level of the studied panel. A robust multi-objective optimization problem intended to optimize the eigenfrequency, the global mass and the displacement at a fixed point of the Y-stiffened panel at the first level and each structure’s robust optimization problem allows optimizing its eigenfrequency and mass limited by their local constraint functions at the second one. Tor demonstrate our method, an engineering example of Y-stiffened panel is treated. A good performance of proposed method is proved by a comparison between obtained results and Non-Distributed Multi-objective Robust Optimization .

A new multi-criterial methodology is introduced for the combined structural and operational optimization of energy supply systems and production processes. The methodology combines a multi-criterial evolutionary optimizer for structural optimization with a code for the operational optimization and simulation. The genotype of the individuals is interpreted with a superstructure. The methodology is applied to three real world case studies: one communal and one industrial energy supply system, one distillation plant. The resulting Pareto fronts and potentials for cost reduction and ecological savings are discussed.KeywordsCommunal energy supply conceptsDistillation plantsEvolutionary algorithmsIndustrial energy supply systemsMulti-objective optimization

A new approach for multi-objective robust design optimization was proposed and applied to a practical design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relationships between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.

Multi-objective robust optimization of a solar power tower plant under uncertainty

In the present paper, we explore issues in handling equality constraints in multiobjective robust design optimization (RDO) problems. Satisfying an equality constraint exactly under uncertainty can be a challenging task. The challenge of handling equality constraints is compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the performance and the variation of the performance for each design objective in a multiobjective RDO problem is a complex task by itself. Equality constraints add to this complexity because of the additional tradeoffs that are introduced between constraint satisfaction under uncertainty and multiobjective performance. Satisfying equality constraints at their mean values, an approach typically followed, could lead to undesirable results. In this paper, we study the implications of equality constraint satisfaction in a multiobjective RDO problem, and provide a new problem formulation approach to resolve the above discussed tradeoffs. We illustrate that the proposed formulation can be used as an effective multiobjective design space exploration tool, with emphasis on equality constraint satisfaction under uncertainty. We present numerical examples to illustrate our theoretical developments.

ABSTRACTTo reduce the scatter of fatigue life for welded structures, a robust optimization method is presented in this study based on a dual surrogate modelling and multi-objective particle swam optimization algorithm. Considering the perturbations of material parameters and environment variables, the mean and standard deviation of fatigue life are fitted using dual surrogate modelling and selected as the objective function to be minimized. As an example, a welded box girder is presented to reduce the standard deviation of fatigue life. A set of non-dominated solutions is produced through a multi-objective particle swam optimization algorithm. A cognitive approach is used to select the optimum solution from the Pareto sets. As a comparative study, traditional single objective optimizations are also presented in this study. The results reduced the standard deviation of the fatigue life by about 16.5%, which indicated that the procedure improved the robustness of the fatigue life.

<div class="section abstract"><div class="htmlview paragraph">Existing multi-axle steering system designs generally use the deterministic optimization method without considering the uncertainties during the design process; therefore an actual steering movement may deviate from the ideal movement calculated by some mathematical models. In order to make design results have less sensitive to the uncertainties in the design process, some uncertainties need be taken into account at the early design stage. This paper proposes a robust optimization design method for a double front axle steering system (DFASS) of heavy trucks based on Monte Carlo method. The DFASS consists of two trapezoidal steering mechanisms (TSM) and one rocker system, and the optimization objectives of DFASS include the minimum mean value and variance of the maximum turning angle error of the TSM and rocker system. In addition, the robust optimization model includes 13 design variables which are all geometry parameters of DFASS and represented by normal distribution. Through the orthogonal experiment, we obtain the important factors affecting optimization objectives and build the response surface models of optimization objective. Based on the response surfaces, robustness design of DFASS is performed. By simulating analysis, the improved robustness of DFASS based on robust design method is approved.</div></div>

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

This paper is devoted to a general methodological study on sensitivity analysis and robust optimization for a planar crank-slider mechanism in presence of joint clearances and random parameters and investigate the effects of parameter uncertainty on optimization results when joint clearance sizes are constantly changing due to wear. The first-order sensitivity analysis based on the response surface proxy model is performed. Then, a multiobjective robust optimization algorithm based on sensitivity analysis is carried out to reduce the undesirable effects of joint clearances and random parameters. In the algorithm, a multiobjective robust optimization model derived from the mean and variance of the objective function is constructed. Here, the objective function is defined based on the consideration of reducing the contact force generated at all clearance joints. Additionally, in order to balance computational accuracy and efficiency in the multiobjective robust optimization process, high-precision Kriging agent models are established. The optimum values of design variables are determined by combining Monte Carlo sampling and multiobjective particle swarm optimization method. By combining the Baumgarte approach with Lankarani–Nikravesh contact force model and Coulomb friction model, the dynamic equations of the planar multibody system with clearance joints are established. The uniform probability distribution is applied for characterizing random parameters. Simulation results show that the influence of design variable variations on the objective function changes in relation to the joint clearance size, but their relative influence degree on the objective function will not vary with the size of joint clearances. Moreover, the optimal solution selected on the Pareto front will affect the average levels and peak fluctuations of the dynamic responses in multibody systems.

A number of game strategies have been developed in past decades and used in the fields of economics, engineering, computer science, and biology due to their efficiency in solving design optimization problems. In addition, research in multiobjective and multidisciplinary design optimization has focused on developing a robust and efficient optimization method so it can produce a set of high quality solutions with less computational time. In this paper, two optimization techniques are considered; the first optimization method uses multifidelity hierarchical Pareto-optimality. The second optimization method uses the combination of game strategies Nash-equilibrium and Pareto-optimality. This paper shows how game strategies can be coupled to multiobjective evolutionary algorithms and robust design techniques to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid and non-Hybrid-Game strategies are demonstrated.

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model

A new approach for multi-objective robust design optimization has been proposed and applied to a real-world design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, which results in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can realize accurate predictions of robustness measures, and dramatically reduces the computational time for objective function evaluation. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness of design in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relations between optimality and robustness of design, and also the location of sweet-spots in the design space, can be performed in a comprehensive manner.