Robust Optimization of Planar Constrained Mechanical System with Varying Joint Clearance Size Based on Sensitivity Analysis

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 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.

Multi-Objective Robust Optimization (MORO) can find Pareto solutions to multi-objective engineering problems while keeping the variation of the solutions being within an acceptable range when parameters vary. While the literature reports on many techniques in MORO, few papers focus on the implementation of Multi-Objective Differential Evolution (MODE) for robust optimization and the performance improvement of solutions. In this paper, MODE is first modified and implemented for robust optimization, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid MODE-SQP-RO algorithm is further proposed, where Sequential Quadratic Programming (SQP) is incorporated to enhance the local search. In the hybrid algorithm, two criteria, indicating the convergence speed of MODE-RO and the switch between MODE and SQP are proposed respectively. One numerical and one engineering examples are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving Multi-Objective Robust Optimization problems; while on the average, MODE-SQP-RO significantly improves the quality of robust solutions with comparable numbers of function evaluations.

Robust multi-objective optimization has emerged as an active research. A recent study proposed two different definitions of robust solutions in the context of multi-objective optimization. In this paper, we extend the concepts for finding robust solutions in the presence of active constraints. The meaning of robust solutions for constrained problems is demonstrated by suggesting three test problems and simulating an evolutionary multi-objective optimization method using the two definitions of robustness. The inclusion of constraint handling strategies makes the multi-objective robust optimization procedure more pragmatic and the procedure is now ready to be applied to real-world problems

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

Multi-objective evolutionary optimization is widely utilized in industrial design. Despite the success of multi-objective evolutionary optimization algorithms in addressing complex optimization problems, research focusing on input disturbances remains limited. In many manufacturing processes, design parameters are vulnerable to random input disturbances, resulting in products that often perform less effectively than anticipated. To address this issue, we propose a novel robust multi-objective evolutionary optimization algorithm based on the concept of survival rate. The algorithm comprises two stages: the evolutionary optimization stage and the construction stage of the robust optimal front. In the former stage, we introduce the survival rate as a new optimization objective. Subsequently, we seek a robust optimal front that concurrently addresses convergence and robustness by employing a non-dominated sorting approach. Furthermore, we propose a precise sampling method and a random grouping mechanism to accurately recover solutions resilient to real noise while ensuring population’s diversity. In the latter stage, we introduce a performance measure that integrates both robustness and convergence to guide the construction of the robust optimal front. Experimental results demonstrate the superiority of the proposed algorithm in terms of both convergence and robustness compared to existing approaches under noisy conditions.

Engineering design optimization problems are commonly multi-objective, involve computationally expensive simulations, and have uncertainty. In these problems, consideration of uncertainty can produce feasibly robust optimized design solutions, i.e., optimized and feasible under uncertainty. In general, methods for solving multi-objective robust optimization problems can be computationally expensive. To ease the computational burden and make these methods more accessible, a surrogate-based bi-objective Bayesian feasibility robust optimization method from the literature has been extended in this paper to higher numbers of objectives. A key component of the proposed method is a new acquisition function. The acquisition function proposed in this paper uses a Monte Carlo approach to approximate the expected centroidal improvement of the solution set. The proposed acquisition function is compared against exact (closed form) acquisition function-based approaches and other methods from the literature. The experimental results from this study suggest the multi-objective robust optimization framework is insensitive to the selection of acquisition function.

In order to maximise the impact automotive energy-absorbing capacity considering uncertainties in the parameters of the design, it is desired to perform a robust optimum design process. Moreover, the optimum design of such absorption system is inherently a multi-objective optimisation problem. In this paper, a multi-objective optimisation approach is thus proposed to consider the robustness issue of those objective functions in the presence of parameter uncertainties. First, the axial impact crushing behaviour of the S-shaped box beams, as a highly simplified model of the front member of a vehicle body, is studied by the finite-element method using the software ABAQUS. Two polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are then obtained to simply represent both the absorbed energy (E) and the peak crushing force (F max) with respect to geometrical and material design variables using the training and testing data obtained from the finite-element study. Using such obtained polynomial neural network models and the Monte Carlo simulation, a multi-objective genetic algorithm is then used for the reliability-based robust Pareto design of the S-shaped box beams having probabilistic uncertainties in material and geometrical parameters. In this way, the statistical moments of mean and variances of the important crashworthiness criteria functions, namely the specific energy absorption (SEA) and the peak crushing force (F max), are considered as the conflicting objectives. It is shown that some useful optimal design principles involved in the performance of the S-shaped box beams can be discovered by the reliability-based robust Pareto optimisation.

A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.

The main concern of this research is to control traffic flow and monitor highways by installing wireless sensors. Therefore, a new multi-objective model is proposed to find the optimal location of wireless sensors along highways. The sensors are paired and each pair of sensors communicates and interacts with each other to receive information from passing cars. The speed estimation of the vehicles passing through this pair of sensors must have the minimum deviation from the actual speed that is obtained by an accurate measurement. This deviation is called measurement error, which is minimized in the first objective function. In this research when traffic jams happens, some sensors located in proper distance with enough energy, move into the traffic area to reduce the measurement error which is caused by traffic congestion. In fact, for each traffic area a new location problem should be solved to relocate sensors so that the maximum decrease in error rate happens. The second objective maximizes the error reduction resulted from sensors movement. In this paper, movement of sensors is considered based on the amount of solar energy stored in the sensor at that moment. Finally, the third objective function maximizes the benefits resulted from detecting the bottlenecks in highways. Since some parameters of the objective functions such as error rates, error reduction resulted from movement of sensors and benefits are uncertain, this research employs a multi-objective robust optimization approach which results in a traffic control plan which is less sensitive to the realization of uncertain parameters.

Robust optimization is proving to be a fruitful tool to study problems with uncertain data. In this paper we deal with the minmax aproach to robust multiobjective optimization. We survey the main features of this problem with particular reference to results concerning linear scalarization and sensitivity of optimal values with respect to changes in the uncertainty set. Furthermore we prove results concerning sensitivity of optimal solutions with respect to changes in the uncertainty set. Finally we apply the presented results to mean-variance portfolio optimization.

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.

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

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

In the last decade, multiobjective Particle Swarm Optimization (MOPSO) has been observed as one of the most powerful optimization algorithms in solving Multiobjective Optimization Problems (MOPs). Nowadays, it is becoming increasingly clear that MOPSO can handle complex MOPs based on the competitive-cooperative framework. The goal of this paper is to provide a comprehensive review of MOPSO from the basic principles to hybrid evolutionary strategies. To offer the readers insights on the prominent developments of MOPSO, the key parameters on the convergence and diversity performance of MOPSO were analyzed to reflect the influence on the searching performance of particles. Then, the main advanced MOPSO methods were discussed, as well as the theoretical analysis of multiobjective optimization performance metrics. Even though some hybrid MOPSO methods show promising multiobjective optimization performance, there is much room left for researchers to improve further, in particular in terms of engineering applications. As a result, further in-depth studies are required. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.