A Comparison of Metamodel-Assisted Pre-Screening Criteria for Multi-Objective Genetic Algorithms

2009 ◽  
Author(s):  
Vero´nica E. Mari´n ◽  
Jose´ A. Rinco´n ◽  
David A. Romero
Keyword(s):  
Genetic Algorithms ◽  
Performance Metrics ◽  
Potential Effect ◽  
Expected Improvement ◽  
Research Activity ◽  
Screening Criteria ◽  
Design And Optimization ◽  
Multi Objective ◽  
Effectiveness And Efficiency ◽  
Current Approximation

Over the last few years, research activity in approximation (e.g. metamodels) and optimization (e.g. genetic algorithms) methods has improved upon current practices in engineering design and optimization of complex systems with respect to multiple performance metrics, by reducing the number of evaluations of the system’s model that are needed to obtain the set of non-dominated solutions to a given multi-objetive optimal design problem. To this end, several authors have proposed to enhance Multi-Objective Genetic Algorithms (MOGAs) with metamodel-based pre-screening criteria (PSC), so that only those solutions that have the most potential to improve the current approximation of the Pareto Front are evaluated with the (costly) system model. The main goals of this work are to compare the performance of several PSC with an array of test functions taken from the literature, and to study the potential effect on their effectiveness and efficiency of using multi-response metamodels, instead of building independent, individual metamodels for each objective function, as has been done in previous work. Our preliminary results show that no single PSC is observed to be superior overall, though the Minimum of Minimum Distances and Expected Improvement criteria outperformed other PSC in most cases. Results also show that the use of multi-response metamodels improved both the effectiveness and efficiency of PSC and the quality of solution at the end of the optimization in 50% to 60% of test cases.

Expected-Improvement-Based Methods for Adaptive Sampling in Multi-Objective Optimization Problems

2016 ◽  
Author(s):  
Jesper Kristensen ◽  
You Ling ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Convex Hull ◽  
Design Optimization ◽  
Adaptive Sampling ◽  
Pareto Front ◽  
Performance Metrics ◽  
Sampling Methods ◽  
Optimization Problems ◽  
Expected Improvement ◽  
Multi Objective Optimization ◽  
Multi Objective

Adaptive sampling methods have been used to build accurate meta-models across large design spaces from which engineers can explore data trends, investigate optimal designs, study the sensitivity of objectives on the modeling design features, etc. For global design optimization applications, adaptive sampling methods need to be extended to sample more efficiently near the optimal domains of the design space (i.e., the Pareto front/frontier in multi-objective optimization). Expected Improvement (EI) methods have been shown to be efficient to solve design optimization problems using meta-models by incorporating prediction uncertainty. In this paper, a set of state-of-the-art methods (hypervolume EI method and centroid EI method) are presented and implemented for selecting sampling points for multi-objective optimizations. The classical hypervolume EI method uses hyperrectangles to represent the Pareto front, which shows undesirable behavior at the tails of the Pareto front. This issue is addressed utilizing the concepts from physical programming to shape the Pareto front. The modified hypervolume EI method can be extended to increase local Pareto front accuracy in any area identified by an engineer, and this method can be applied to Pareto frontiers of any shape. A novel hypervolume EI method is also developed that does not rely on the assumption of hyperrectangles, but instead assumes the Pareto frontier can be represented by a convex hull. The method exploits fast methods for convex hull construction and numerical integration, and results in a Pareto front shape that is desired in many practical applications. Various performance metrics are defined in order to quantitatively compare and discuss all methods applied to a particular 2D optimization problem from the literature. The modified hypervolume EI methods lead to dramatic resource savings while improving the predictive capabilities near the optimal objective values.

Multi-objective seismic design of BRBs-reinforced concrete buildings using genetic algorithms

2021 ◽  
Author(s):  
Herian Leyva ◽  
Juan Bojórquez ◽  
Edén Bojórquez ◽  
Alfredo Reyes-Salazar ◽  
Julián Carrillo ◽  
...  
Keyword(s):  
Genetic Algorithms ◽  
Reinforced Concrete ◽  
Seismic Design ◽  
Reinforced Concrete Buildings ◽  
Concrete Buildings ◽  
Multi Objective

scholarly journals A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 543
Author(s):  
Alejandra Ríos ◽  
Eusebio E. Hernández ◽  
S. Ivvan Valdez
Keyword(s):  
Genetic Algorithm ◽  
Performance Metrics ◽  
Tracking Error ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Statistical Hypothesis ◽  
Two Stage ◽  
Multi Objective ◽  
Second Stage ◽  
Conflicting Objectives

This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.

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