Sequential Cooperative Robust Optimization (SCRO) for Multi-Objective Design Under Uncertainty

2015 ◽  
Author(s):  
J. M. Hamel
Keyword(s):  
Robust Optimization ◽  
Uncertainty Analysis ◽  
Computational Efficiency ◽  
System Optimization ◽  
Surrogate Models ◽  
Optimization Techniques ◽  
Robust Design Optimization ◽  
Optimization Approach ◽  
Deterministic System ◽  
Multi Objective

The optimal design of systems under uncertainty is a critical challenge faced by design engineers. Robust optimization is a well-studied and widely used technique for the design of engineering systems that possess uncertainty, and numerous robust optimization techniques have been presented in recent years. The majority of the robust optimization techniques presented in the literature suffer from a computational efficiency challenge, either due to the expense of obtaining objective or constraint function uncertainty information, or due to the fact that many robust optimization approaches (with a few notable exceptions) require that a potentially expensive uncertainty analysis calculation (e.g. Monte-Carlo simulation) be nested within an already potentially expensive optimization solver (e.g. a genetic algorithm). Additionally, many robust optimization approaches focus solely on design problems that possess a single design objective, and the robust techniques that do consider problems with multiple design objectives often require various simplifying assumptions or are even more computationally expensive to implement. Clearly there are opportunities for improvement in the area of robust optimization, and this paper presents a new robust design Optimization approach called Sequential Cooperative Robust Optimization (SCRO), which uses both a sequential approach and multi-objective optimization techniques in an effort to decouple the deterministic system optimization problem from the associated uncertainty analysis problem. The SCRO approach first fits surrogate models to the system objective and constraint functions, in addition to system sensitivity functions, using as few function calls as possible in order to improve computational efficiency. The approach then performs a series of sequential multi-objective optimizations using the developed surrogate models. These optimizations work to find points in the design space that are optimal with respect to deterministic performance and both objective and feasibility robustness metrics based on predicted system sensitivities. The SCRO approach has the potential to find solutions not available to other robust optimization approaches, and can be more efficient than other more traditional robust optimization techniques due to its use of surrogate approximation and a sequential framework.

Multi-Objective Robust Design Optimization and Knowledge Mining of a Centrifugal Fan That Takes Dimensional Uncertainty Into Account

2008 ◽  
Author(s):  
Kazuyuki Sugimura ◽  
Shinkyu Jeong ◽  
Shigeru Obayashi ◽  
Takeshi Kimura
Keyword(s):  
Data Mining ◽  
Robust Optimization ◽  
Robust Design ◽  
Rough Set Theory ◽  
Optimization Techniques ◽  
Robust Design Optimization ◽  
Centrifugal Fan ◽  
Data Mining Techniques ◽  
Multi Objective ◽  
Design Variables

A new design approach named MORDE (multi-objective robust design exploration), in which multi-objective robust optimization techniques and data mining techniques are combined, is proposed in this paper. We first developed a widely applicable design framework for multi-objective robust optimization. In this framework, probabilistic representation of design variables are introduced and Kriging models are used to approximate relations between design variables with uncertainty and multiple design objectives. A multi-objective genetic algorithm optimizes the mean and standard deviation of the responses. We then applied the framework to the real-world design problem of a centrifugal fan used in a washer-dryer. Taking dimensional uncertainty into account, we optimized the means and standard deviations of the resulting distributions of fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations were used to build Kriging models that approximate these objective functions. With the obtained non-dominated solutions, we demonstrated how to analyze features of solutions and select design candidates. We also attempted to acquire design knowledge by applying several data mining techniques. Self-organizing map was used to visualize and reuse the high dimensional design data. Decision tree analysis and rough set theory were used to extract design rules to improve the product’s performance. We also discussed differences in types of rules, which were extracted by both methods.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

2018 ◽  
Vol 18 (4) ◽  
Author(s):  
Tingli Xie ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Leshi Shu ◽  
Yahui Zhang ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Engineering Design ◽  
Kriging Model ◽  
Support Vector ◽  
Svm Classifier ◽  
Optimization Approach ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

Robust optimization approach to production system with failure in rework and breakdown under uncertainty: evolutionary methods

2015 ◽  
Vol 35 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Masoud Rabbani ◽  
Neda Manavizadeh ◽  
Niloofar Sadat Hosseini Aghozi
Keyword(s):  
Mathematical Model ◽  
Robust Optimization ◽  
Production Planning ◽  
Production System ◽  
Demand Uncertainty ◽  
Optimization Techniques ◽  
Planning Problem ◽  
Optimization Approach ◽  
Content Type ◽  
Evolutionary Methods

Purpose – This paper aims to consider a multi-site production planning problem with failure in rework and breakdown subject to demand uncertainty. Design/methodology/approach – In this new mathematical model, at first, a feasible range for production time is found, and then the model is rewritten considering the demand uncertainty and robust optimization techniques. Here, three evolutionary methods are presented: robust particle swarm optimization, robust genetic algorithm (RGA) and robust simulated annealing with the ability of handling uncertainties. Firstly, the proposed mathematical model is validated by solving a problem in the LINGO environment. Afterwards, to compare and find the efficiency of the proposed evolutionary methods, some large-size test problems are solved. Findings – The results show that the proposed models can prepare a promising approach to fulfill an efficient production planning in multi-site production planning. Results obtained by comparing the three proposed algorithms demonstrate that the presented RGA has better and more efficient solutions. Originality/value – Considering the robust optimization approach to production system with failure in rework and breakdown under uncertainty.

Mixture Surrogate Models for Multi- Objective Optimization

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Shailesh S. Kadre ◽  
Vipin K. Tripathi
Keyword(s):  
Finite Element ◽  
Optimization Problems ◽  
Surrogate Models ◽  
Optimization Techniques ◽  
Optimization Process ◽  
Multiple Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Costly Function ◽  
Selection Of

Multi-objective optimization problems (MOOP) involve minimization of more than one objective functions and all of them are to be simultaneously minimized. The solution of these problems involves a large number of iterations. The multi- objective optimization problems related structural optimization of complex engineering structures is usually solved with finite element analysis (FEA). The solution time required to solve these FEA based solutions are very high. So surrogate models or meta- models are used to approximate the finite element solution during the optimization process. These surrogate assisted multi- objective optimization techniques are very commonly used in the current literature. These optimization techniques use evolutionary algorithm and it is very difficult to guarantee the convergence of the final solution, especially in the cases where the budget of costly function evaluations is low. In such cases, it is required to increase the efficiency of surrogate models in terms of accuracy and total efforts required to find the final solutions.In this paper, an advanced surrogate assisted multi- objective optimization algorithm (ASMO) is developed. This algorithm can handle linear, equality and non- linear constraints and can be applied to both benchmark and engineering application problems. This algorithm does not require any prior knowledge for the selection of surrogate models. During the optimization process, best single and mixture surrogate models are automatically selected. The advanced surrogate models are created by MATSuMoTo, the MATLAB based tool box. These mixture models are built by Dempster- Shafer theory (DST). This theory has a capacity to handle multiple model characteristics for the selection of best models. By adopting this strategy, it is ensured that most accurate surrogate models are selected. There can be different kind of surrogate models for objective and constraint functions. Multi-objective optimization of machine tool spindle is studied as the test problem for this algorithm and it is observed that the proposed strategy is able to find the non- dominated solutions with minimum number of costly function evaluations. The developed method can be applied to other benchmark and engineering applications.

Robust Design Optimization of a Steam Turbine Labyrinth Seal Based on Surrogate Models

2018 ◽  
Author(s):  
Kevin Cremanns ◽  
Dirk Roos ◽  
Simon Hecker ◽  
Andreas Penkner ◽  
Christian Musch
Keyword(s):  
Power Plants ◽  
Fluid Dynamic ◽  
Labyrinth Seal ◽  
Surrogate Models ◽  
Robust Design Optimization ◽  
Optimized Design ◽  
Multi Objective Optimization ◽  
Total Enthalpy ◽  
Multi Objective ◽  
Conflicting Objectives

This work presents a robust multi-objective optimization of a labyrinth seal used in power plants steam turbines. The conflicting objectives of this optimization are to minimize the mass flow and to minimize the total enthalpy increase in order to increase the performance and to reduce the temperature, which results in elevated component utilization. The focus should be the robustness aspect to be involved into the optimization. So that the final design is not only optimized for its deterministic values but also robust under its uncertainties. To achieve a robust and optimized design, surrogate models are trained and used to replace the computational fluid dynamic solver (CFD), so as to speed up the calculations. In contrast to most techniques used in literature, the robustness criteria are directly involved in the multi-objective optimization. This leads to a more robust Pareto front compared to a purely deterministic one. This method needs many design evaluations, which would be not effective, if a CFD solver were used.

A robust policy bootstrapping algorithm for multi-objective reinforcement learning in non-stationary environments

2019 ◽  
Vol 28 (4) ◽  
pp. 273-292 ◽  
Author(s):  
Sherif Abdelfattah ◽  
Kathryn Kasmarik ◽  
Jiankun Hu
Keyword(s):  
Reinforcement Learning ◽  
Learning Algorithm ◽  
Markov Property ◽  
Special Kind ◽  
Optimization Techniques ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Sequential Decision ◽  
Major Drawback ◽  
Multi Objective

Multi-objective Markov decision processes are a special kind of multi-objective optimization problem that involves sequential decision making while satisfying the Markov property of stochastic processes. Multi-objective reinforcement learning methods address this kind of problem by fusing the reinforcement learning paradigm with multi-objective optimization techniques. One major drawback of these methods is the lack of adaptability to non-stationary dynamics in the environment. This is because they adopt optimization procedures that assume stationarity in order to evolve a coverage set of policies that can solve the problem. This article introduces a developmental optimization approach that can evolve the policy coverage set while exploring the preference space over the defined objectives in an online manner. We propose a novel multi-objective reinforcement learning algorithm that can robustly evolve a convex coverage set of policies in an online manner in non-stationary environments. We compare the proposed algorithm with two state-of-the-art multi-objective reinforcement learning algorithms in stationary and non-stationary environments. Results showed that the proposed algorithm significantly outperforms the existing algorithms in non-stationary environments while achieving comparable results in stationary environments.

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