Multiobjective Optimization for High Dimensional Expensively Constrained Black-Box Problems

2021 ◽  
pp. 1-59
Author(s):  
George Cheng ◽  
G. Gary Wang ◽  
Yeong-Maw Hwang
Keyword(s):  
Multiobjective Optimization ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Black Box ◽  
Superior Performance ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Semiconductor Substrate ◽  
Multi Objective ◽  
Computationally Expensive

Abstract Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the Situational Adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.

An Adaptive Aggregation-Based Approach for Expensively Constrained Black-Box Optimization Problems

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
George H. Cheng ◽  
Timothy Gjernes ◽  
G. Gary Wang
Keyword(s):  
Design Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Black Box ◽  
Superior Performance ◽  
Adaptive Aggregation ◽  
Novel Approach ◽  
Single Objective

Expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches often assume inexpensive constraints. In this work, the situational adaptive Kreisselmeier and Steinhauser (SAKS) method was employed in the development of a hybrid adaptive aggregation-based constraint handling strategy for expensive black-box constraint functions. The SAKS method is a novel approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The SAKS strategy was integrated with a modified trust region-based mode pursuing sampling (TRMPS) algorithm to form the SAKS-trust region optimizer (SAKS-TRO) for single-objective design optimization problems with expensive black-box objective and constraint functions. SAKS-TRO was benchmarked against five popular constrained optimizers and demonstrated superior performance on average. SAKS-TRO was also applied to optimize the design of an industrial recessed impeller.

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

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.

Interactive Multiobjective Optimization Design Strategy for Decision Based Design

1999 ◽  
Author(s):  
Ravindra V. Tappeta ◽  
John E. Renaud
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Design ◽  
Optimization Procedure ◽  
Design Strategy ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Original Algorithm ◽  
Multi Objective ◽  
Local Preference ◽  
Preference Functions

Abstract This research focuses on multi-objective system design and optimization. The primary goal is to develop and test a mathematically rigorous and efficient interactive multi-objective optimization algorithm that takes into account the Decision Maker’s (DM’s) preferences during the design process. An Interactive Multi-Objective Optimization Procedure (IMOOP) developed in [12] has been modified in this research to include the DM’s local preference functions in an Iterative Decision Making Strategy (IDMS). This enhanced multiobjective optimization procedure called the interactive MultiObjective Optimization Design Strategy (iMOODS) provides the DM with a formal means for efficient design exploration around a given Pareto point. The use of local preference functions allows the original algorithm [12] to be modified such that the second order Pareto surface approximation is more accurate in the preferred region of the Pareto surface. The iMOODS has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for the objectives and constraints. The second problem is the design and sizing of a high-performance and low-cost ten bar structure that has multiple objectives. The results indicate that the class functions are effective in capturing the local preferences of the DM. The Pareto designs that reflect the DM’s preferences can be efficiently generated within IDMS.

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

2019 ◽  
Vol 33 (08) ◽  
pp. 1959025
Author(s):  
Lan Zhang
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Nearest Neighbor ◽  
Superior Performance ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Evolution Algebra ◽  
Neighbor List

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.

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