An intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method

2017 ◽  
Vol 57 (3) ◽  
pp. 1047-1060 ◽  
Author(s):  
Cheng Lin ◽  
Fengling Gao ◽  
Yingchun Bai
Keyword(s):  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Intelligent Sampling ◽  
Adaptive Weighted Sum ◽  
Sampling Approach

Bilevel Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

AIAA Journal ◽  
2008 ◽  
Vol 46 (10) ◽  
pp. 2611-2622 ◽  
Author(s):  
Ke-Shi Zhang ◽  
Zhong-Hua Han ◽  
Wei-Ji Li ◽  
Wen-Ping Song
Keyword(s):  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Adaptive Weighted Sum

Study on Multi-Objective Reconstruction of Random Media

2016 ◽  
Vol 825 ◽  
pp. 153-160
Author(s):  
Adéla Hlobilová ◽  
Matěj Lepš
Keyword(s):  
Genetic Algorithm ◽  
Random Media ◽  
Probability Function ◽  
Volume Fraction ◽  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Original Medium ◽  
Optimization Routine

This paper deals with a reconstruction of random media via multi-objective optimization. Two statistical descriptors, namely a two-point probability function and a two-point lineal path function, are repetitively evaluated for the original medium and the reconstructed image to appreciate the improvement in the optimization progress. Because of doubts of the weights setting in the weighted-sum method, purely multi-objective optimization routine Non-dominated Sorting Genetic Algorithm~II is utilized. Three operators are compared for creating new offspring populations that satisfy a prescribed volume fraction constraint. The main contribution is in the testing of the proposed methodology on several benchmark images.

Automatic Generation of Controllers for Embodied Legged Organisms: A Pareto Evolutionary Multi-Objective Approach

2004 ◽  
Vol 12 (3) ◽  
pp. 355-394 ◽  
Author(s):  
Jason Teo ◽  
Hussein A. Abbass
Keyword(s):  
Computational Cost ◽  
Automatic Generation ◽  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Self Adaptation ◽  
Adaptive Weighted Sum ◽  
Single Objective ◽  
Self Adaptive

In this paper, we investigate the use of a self-adaptive Pareto evolutionary multi-objective optimization (EMO) approach for evolving the controllers of virtual embodied organisms. The objective of this paper is to demonstrate the trade-off between quality of solutions and computational cost. We show empirically that evolving controllers using the proposed algorithm incurs significantly less computational cost when compared to a self-adaptive weighted sum EMO algorithm, a self-adaptive single-objective evolutionary algorithm (EA) and a hand-tuned Pareto EMO algorithm. The main contribution of the self-adaptive Pareto EMO approach is its ability to produce sufficiently good controllers with different locomotion capabilities in a single run, thereby reducing the evolutionary computational cost and allowing the designer to explore the space of good solutions simultaneously. Our results also show that self-adaptation was found to be highly beneficial in reducing redundancy when compared against the other algorithms. Moreover, it was also shown that genetic diversity was being maintained naturally by virtue of the system's inherent multi-objectivity.

scholarly journals Goal-Programming-Based Multi-Objective Optimization in Off-Grid Microgrids

2020 ◽  
Vol 12 (19) ◽  
pp. 8119
Author(s):  
Akhtar Hussain ◽  
Hak-Man Kim
Keyword(s):  
Energy Storage ◽  
Goal Programming ◽  
Optimization Problems ◽  
Renewable Energy Sources ◽  
Storage System ◽  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
The Impact

Renewable-based off-grid microgrids are considered as a potential solution for providing electricity to rural and remote communities in an environment-friendly manner. In such systems, energy storage is commonly utilized to cope with the intermittent nature of renewable energy sources. However, frequent usage may result in the fast degradation of energy storage elements. Therefore, a goal-programming-based multi-objective optimization problem has been developed in this study, which considers both the energy storage system (battery and electric vehicle) degradation and the curtailment of loads and renewables. Initially, goals are set for each of the parameters and the objective of the developed model is to minimize the deviations from those set goals. Degradation of battery and electric vehicles is quantified using deep discharging, overcharging, and cycling frequency during the operation horizon. The developed model is solved using two of the well-known approaches used for solving multi-optimization problems, the weighted-sum approach and the priority approach. Five cases are simulated for each of the methods by varying weight/priority of different objectives. Besides this, the impact of weight and priority values selected by policymakers is also analyzed. Simulation results have shown the superiority of the weighted-sum method over the priority method in solving the formulated problem.

scholarly journals Multi-load cases topological optimization by weighted sum method based on load case severity degree and ideality

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402094751
Author(s):  
Yongxin Li ◽  
Quanwei Yang ◽  
Tao Chang ◽  
Tao Qin ◽  
Fenghe Wu
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Weighted Sum ◽  
Weight Factor ◽  
Multi Objective Optimization ◽  
Load Case ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Loading Case ◽  
Severity Degree

Mechanical structures always bear multiple loads under working conditions. Topology optimization in multi-load cases is always treated as a multi-objective optimization problem, which is solved by the weighted sum method. However, different weight factor allocation strategies have led to discrepant optimization results, and when ill loading case problems appear, some unreasonable results are obtained by those alternatives. Moreover, many multi-objective optimization problems have certain optimization objective, and an evaluation formula to measure Pareto solution in the multi-objective optimization problem area is lacking. Regarding these two problems, a new method for calculating the weight factor is proposed based on the definition of load case severity degree. Additionally, an amplified load increment is derived and suggested in the minimum compliance with a volume constraint problem. Ideality is formulized from Pareto front to the ideal solution to evaluate the different optimization results. Benchmark topology optimization examples are solved and discussed. The results show that the load case severity degree is less affected by the different weighted sum functions and can avoid ill loading case phenomena, and the ideality of optimization result obtained by the load case severity degree is the best.

scholarly journals Multi-objective Optimization Approach to Malfatti's Problem

2021 ◽  
Vol 14 ◽  
pp. 82-90
Author(s):  
Rentsen Enkhbat ◽  
◽  
Gompil Battur ◽  
Keyword(s):  
Optimization Problem ◽  
Circle Packing ◽  
Stationary Points ◽  
Optimization Approach ◽  
Theory Approach ◽  
Weighted Sum ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Malfatti’S Problem

In this work, we consider the multi-objective optimization problem based on the circle packing problem, particularly, extended Malfatti's problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined for the first time from a view point of global optimization theory and algorithm in (Enkhbat, 2016). Also, a game theory approach has been applied to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply the the multi-objective optimization approach to the problem. Using the weighted sum method, we reduce this problem to optimization problem with nonconvex constraints. For solving numerically the weighted sum optimization problem, we apply KKT conditions and find Pareto stationary points. Also, we estimate upper bounds of the global value of the objective function by Lagrange duality. Numerical results are provided.

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