Efficient Parametric Optimization for Expensive Single Objective Problems

2021 ◽  
pp. 1-12
Author(s):  
Jonathan Weaver-Rosen ◽  
Richard Malak
Keyword(s):  
Adaptive Sampling ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Test Problems ◽  
Surface Model ◽  
High Fidelity ◽  
Unknown Parameters ◽  
Element Analysis ◽  
Better Than

Abstract Parametric optimization solves optimization problems as a function of uncontrollable or unknown parameters. Such an approach allows an engineer to gather more information than traditional optimization procedures during design. Existing methods for parametric optimization of computationally or monetarily expensive functions can be too time-consuming or impractical to solve. Therefore, new methods for the parametric optimization of expensive functions need to be explored. This work proposes a novel algorithm that leverages the advantages of two existing optimization algorithms. This new algorithm is called the efficient parametric optimization (EPO) algorithm. EPO enables adaptive sampling of a high-fidelity design space using an inexpensive low-fidelity response surface model. Such an approach largely reduces the required number of expensive high-fidelity computations. The proposed method is benchmarked using analytic test problems and used to evaluate a case study requiring finite element analysis. Results show that EPO performs as well as or better than the existing alternative, P3GA, for these problems given an allowable number of function evaluations.

Efficient Parametric Optimization for Expensive Single Objective Problems

2020 ◽  
Author(s):  
Jonathan M. Weaver-Rosen ◽  
Richard J. Malak
Keyword(s):  
Adaptive Sampling ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Test Problems ◽  
Surface Model ◽  
High Fidelity ◽  
Unknown Parameters ◽  
Element Analysis ◽  
Better Than

Abstract Parametric optimization solves optimization problems as a function of uncontrollable or unknown parameters. Such an approach allows an engineer to gather more information than traditional optimization procedures during design. Existing methods for parametric optimization of computationally or monetarily expensive functions can be too time-consuming or impractical to solve. Therefore, new methods for the parametric optimization of expensive functions need to be explored. This work proposes a novel algorithm that leverages the advantages of two existing optimization algorithms. This new algorithm is called the efficient parametric optimization (EPO) algorithm. EPO enables adaptive sampling of a high-fidelity design space using an inexpensive low-fidelity response surface model. Such an approach largely reduces the required number of expensive high-fidelity computations. The proposed method is benchmarked using analytic test problems and used to evaluate a case study requiring finite element analysis. Results show that EPO performs as well as or better than the existing alternative, P3GA, for these problems given an allowable number of function evaluations.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

Multiple Surrogate-Assisted Many-Objective Optimization for Computationally Expensive Engineering Design

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Kalyan Shankar Bhattacharjee ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Engineering Design ◽  
Optimization Problems ◽  
State Of The Art ◽  
Performance Criteria ◽  
Vehicle Design ◽  
Multi Objective Optimization ◽  
Element Analysis ◽  
Research Gap ◽  
Computationally Expensive

Engineering design often involves problems with multiple conflicting performance criteria, commonly referred to as multi-objective optimization problems (MOP). MOPs are known to be particularly challenging if the number of objectives is more than three. This has motivated recent attempts to solve MOPs with more than three objectives, which are now more specifically referred to as “many-objective” optimization problems (MaOPs). Evolutionary algorithms (EAs) used to solve such problems require numerous design evaluations prior to convergence. This is not practical for engineering applications involving computationally expensive evaluations such as computational fluid dynamics and finite element analysis. While the use of surrogates has been commonly studied for single-objective optimization, there is scarce literature on its use for MOPs/MaOPs. This paper attempts to bridge this research gap by introducing a surrogate-assisted optimization algorithm for solving MOP/MaOP within a limited computing budget. The algorithm relies on principles of decomposition and adaptation of reference vectors for effective search. The flexibility of function representation is offered through the use of multiple types of surrogate models. Furthermore, to efficiently deal with constrained MaOPs, marginally infeasible solutions are promoted during initial phases of the search. The performance of the proposed algorithm is benchmarked with the state-of-the-art approaches using a range of problems with up to ten objective problems. Thereafter, a case study involving vehicle design is presented to demonstrate the utility of the approach.

Engineering Critical Assessment of Embedded Flaws in a Pipeline Using a Probabilistic Approach: A Case Study

2011 ◽  
Author(s):  
Daowu Zhou ◽  
Ali Mirzaee-Sisan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Limit State ◽  
Critical Assessment ◽  
Surface Model ◽  
State Function ◽  
Limit State Function ◽  
Element Analysis ◽  
Reliability Method

A probabilistic engineering critical assessment of embedded flaws in a pipeline was carried out as a case study using the limit state function based on both finite element analysis and the failure assessment diagram. The response surface model was used in determining the finite element analysis based limit state function in order to reduce the number of finite element analysis runs. The first order reliability method and second order reliability method were used to determine the probability of failure. This research work highlights the advantage of using specific limit state function for engineering critical assessment of embedded flaws.

scholarly journals Comparison between genetic algorithm and prey-predator algorithm

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Surafel Luleseged Tilahun ◽  
Hong Choon Ong
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Metaheuristic Algorithms ◽  
Benchmark Problems ◽  
Test Problems ◽  
Search Mechanism ◽  
Complex Optimization ◽  
Better Than

Metaheuristic algorithms are useful in solving complex optimization problems. Genetic algorithm (GA) is one of the well known and oldest metaheuristic algorithms. It was introduced in 1975 and has been used in many applications varying from engineering to management and many other fields as well. However, Prey-Predator algorithm (PPA) is one of recently introduced algorithm, in 2012, inspired by the interaction between preys and their predator. The motivation and the search mechanism for these two algorithms are different. In this paper the comparison of these two algorithms both from theoretical aspects and using simulation on selected benchmark problems is presented. According to the results, PPA performs better than GA in the selected test problems.

Vom Gegenstand zur Gegenständlichkeit des Sozialen Georg Simmels »Soziologie der Sinne« und das Hören im Zeitalter der technischen Reproduzierbarkeit von Musik

2015 ◽  
Vol 2015 (1-2) ◽  
pp. 107-120
Author(s):  
Uwe C. Steiner
Keyword(s):  
High Fidelity ◽  
Elementary Processes ◽  
The Senses

Simmel’s Sociology explores elementary processes of socialization or collectivization. Thus, the sociology of the senses examines how sight, hearing, feeling, smelling and tasting contributes to constituting societies. Though Simmel observes that modern refined civilization diminishes the depths of the senses but increases its emphasis or enhancement with lust or aversion, the conclusion cannot be avoided that the artifacts and technologies of hearing have to be examined. Accordingly, this article can be regarded as a case study in the wake of Simmel: How do modern aural technologies at the threshold between high fidelity and postfidelity inform contemporary hearing?

Municipal wastewater treatment with pond–constructed wetland system: a case study

2005 ◽  
Vol 51 (12) ◽  
pp. 325-329 ◽  
Author(s):  
X. Wang ◽  
X. Bai ◽  
J. Qiu ◽  
B. Wang
Keyword(s):  
Constructed Wetland ◽  
Municipal Wastewater ◽  
Municipal Wastewater Treatment ◽  
Oxidation Pond ◽  
System A ◽  
Treated Effluent ◽  
Wetland System ◽  
Oxidation Ponds ◽  
Better Than

The performance of a pond–constructed wetland system in the treatment of municipal wastewater in Kiaochow city was studied; and comparison with oxidation ponds system was conducted. In the post-constructed wetland, the removal of COD, TN and TP is 24%, 58.5% and 24.8% respectively. The treated effluent from the constructed wetland can meet the Chinese National Agricultural and Irrigation Standard. The comparison between pond–constructed wetland system and oxidation pond system shows that total nitrogen removal in a constructed wetland is better than that in an oxidation pond and the TP removal is inferior. A possible reason is the low dissolved oxygen concentration in the wetland. Constructed wetlands can restrain the growth of algae effectively, and can produce obvious ecological and economical benefits.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

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