Addressing High Dimensional Multi-objective Optimization Problems by Coevolutionary Islands with Overlapping Search Spaces

2016 ◽  
pp. 107-117 ◽  
Author(s):  
Pablo García-Sánchez ◽  
Julio Ortega ◽  
Jesús González ◽  
Pedro A. Castillo ◽  
Juan J. Merelo
Keyword(s):  
Optimization Problems ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Search Spaces

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.

Pareto-Optimal Equilibrium Points in non-Cooperative Multi-Objective Optimization Problems

2021 ◽  
pp. 114995
Author(s):  
Mohammadali Saniee Monfared ◽  
Sayyed Ehsan Monabbati ◽  
Atefeh Rajabi Kafshgar
Keyword(s):  
Optimization Problems ◽  
Equilibrium Points ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective

Injecting domain knowledge in multi-objective optimization problems: A semantic approach

2021 ◽  
pp. 103546
Author(s):  
Cristóbal Barba-González ◽  
Antonio J. Nebro ◽  
José García-Nieto ◽  
María del Mar Roldán-García ◽  
Ismael Navas-Delgado ◽  
...  
Keyword(s):  
Domain Knowledge ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Semantic Approach ◽  
Multi Objective
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