128 research outputs found
On the Impact of Multiobjective Scalarizing Functions
Recently, there has been a renewed interest in decomposition-based approaches
for evolutionary multiobjective optimization. However, the impact of the choice
of the underlying scalarizing function(s) is still far from being well
understood. In this paper, we investigate the behavior of different scalarizing
functions and their parameters. We thereby abstract firstly from any specific
algorithm and only consider the difficulty of the single scalarized problems in
terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes.
Secondly, combining the outcomes of independent single-objective runs allows
for more general statements on set-based performance measures. Finally, we
investigate the correlation between the opening angle of the scalarizing
function's underlying contour lines and the position of the final solution in
the objective space. Our analysis is of fundamental nature and sheds more light
on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
An Improvement Study of the Decomposition-based Algorithm Global WASF-GA for Evolutionary Multiobjective Optimization
The convergence and the diversity of the decompositionbased evolutionary algorithm Global WASF-GA (GWASF-GA) relies
on a set of weight vectors that determine the search directions for new non-dominated solutions in the objective space. Although using weight vectors whose search directions are widely distributed may lead to a well-diversified approximation of the Pareto front (PF), this may not be enough to obtain a good approximation for complicated PFs (discontinuous, non-convex, etc.). Thus, we propose to dynamically adjust the weight vectors once GWASF-GA has been run for a certain number of generations. This adjustment is aimed at re-calculating some of the weight vectors, so that search directions pointing to overcrowded regions of the PF are redirected toward parts with a lack of solutions that may be hard to be approximated. We test different parameters settings of the dynamic adjustment in optimization problems with three, five, and six objectives, concluding that GWASF-GA performs better when adjusting the weight vectors dynamically than without applying the adjustment.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
New Insights to Approximate the Pareto Optimal Front in Evolutionary Multiobjective Optimization. An Application to Students’ Satisfaction
Los resultados de la segunda parte demuestran el buen comportamiento de la combinación de técnicas
econométricas y multiobjetivo, especialmente cuando utilizamos algoritmos evolutivos, para la resolución de problemas socio-económicos con la finalidad de encontrar la compensación (trade-offs) entre los objetivos estudiados y así poder sugerir mejoras, en este caso, en economía de la educación.La tesis presentada se basa en el desarrollo de nuevos algoritmos evolutivos para resolver problemas de optimización multiobjetivo, especialmente problemas con más de tres funciones objetivos, y en la modelización y resolución de un problema de economía de la educación. Dicha tesis está realizada en la modalidad de compendio de artículos y se compone de tres de los mismos. Los dos primeros relacionados con el desarrollo de un nuevo algoritmo evolutivo. En ellos, partiendo del algoritmo Global Weighting Achievement Scalarizing Fucntion
Genetic Algorithm (GWASF-GA) (Saborido, Ruiz, and Luque, 2017), se plantea y desarrolla un nuevo algoritmo centrado en la adaptación de los vectores de pesos durante el proceso de ejecución, que ofrece muy buenos resultados en comparación con algoritmos muy conocidos y muy contrastados dentro del campo de los algoritmos evolutivos. El tercer artículo se centra en la modelización y resolución de un problema multiobjetivo obtenido a partir del análisis econométrico de datos referidos al rendimiento académico y satisfacción de los estudiantes andaluces con diferentes aspectos del proceso enseñanza-aprendizaje en los colegios de secundaria. Con los resultados obtenidos y teniendo en cuenta los algoritmos considerados, aunque los frentes óptimos de Pareto aproximados por A-GWASF-GA no sean los mejores en todos los casos (especialmente para los problemas con tres funciones objetivo), podemos asegurar que el nuevo algoritmo algoritmo evolutivo aquí propuesto (A-GWASF-GA) muestra resultados muy prometedores en problemas con más de tres funciones objetivo. De esta
forma, A-GWASF-GA se autodefine como un algoritmo para trabajar con problemas manyobjective (con más de tres objetivos)
On the use of two reference points in decomposition based multiobjective evolutionary algorithms
Decomposition based multiobjective evolutionary algorithms approximate the Pareto front of a multiobjective optimization problem by optimizing a set of subproblems in a collaborative manner. Often, each subproblem is associated with a direction vector and a reference point. The settings of these parameters have a very critical impact on convergence and diversity of the algorithm. Some work has been done to study how to set and adjust direction vectors to enhance algorithm performance for particular problems. In contrast, little effort has been made to study how to use reference points for controlling diversity in decomposition based algorithms. In this paper, we first study the impact of the reference point setting on selection in decomposition based algorithms. To balance the diversity and convergence, a new variant of the multiobjective evolutionary algorithm based on decomposition with both the ideal point and the nadir point is then proposed. This new variant also employs an improved global replacement strategy for performance enhancement. Comparison of our proposed algorithm with some other state-of-the-art algorithms is conducted on a set of multiobjective test problems. Experimental results show that our proposed algorithm is promising
Scalarizing Functions in Bayesian Multiobjective Optimization
Scalarizing functions have been widely used to convert a multiobjective
optimization problem into a single objective optimization problem. However,
their use in solving (computationally) expensive multi- and many-objective
optimization problems in Bayesian multiobjective optimization is scarce.
Scalarizing functions can play a crucial role on the quality and number of
evaluations required when doing the optimization. In this article, we study and
review 15 different scalarizing functions in the framework of Bayesian
multiobjective optimization and build Gaussian process models (as surrogates,
metamodels or emulators) on them. We use expected improvement as infill
criterion (or acquisition function) to update the models. In particular, we
compare different scalarizing functions and analyze their performance on
several benchmark problems with different number of objectives to be optimized.
The review and experiments on different functions provide useful insights when
using and selecting a scalarizing function when using a Bayesian multiobjective
optimization method
CES-485 Approximating the Set of Pareto Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm
Most existing multiobjective evolutionary algorithms aim at approximating the PF, the distribution of the Pareto optimal
solutions in the objective space. In many real-life applications, however, a good approximation to the PS, the distribution of the
Pareto optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of MOPs, in
which the dimensionalities of the PS and PF are different so that a good approximation to the PF might not approximate the PS
very well. It proposes a probabilistic model based multiobjective evolutionary algorithm, called MMEA, for approximating the PS
and the PF simultaneously for a MOP in this class. In the modelling phase of MMEA, the population is clustered into a number
of subpopulations based on their distribution in the objective space, the PCA technique is used to detect the dimensionality of the
centroid of each subpopulation, and then a probabilistic model is built for modelling the distribution of the Pareto optimal solutions
in the decision space. Such modelling procedure could promote the population diversity in both the decision and objective spaces.
To ease the burden of setting the number of subpopulations, a dynamic strategy for periodically adjusting it has been adopted in
MMEA. The experimental comparison between MMEA and the two other methods, KP1 and Omni-Optimizer on a set of test
instances, some of which are proposed in this paper, have been made in this paper. It is clear from the experiments that MMEA
has a big advantage over the two other methods in approximating both the PS and the PF of a MOP when the PS is a nonlinear
manifold, although it might not be able to perform significantly better in the case when the PS is a linear manifold
Cultural Algorithm based on Decomposition to solve Optimization Problems
Decomposition is used to solve optimization problems by introducing many simple scalar optimization subproblems and optimizing them simultaneously. Dynamic Multi-Objective Optimization Problems (DMOP) have several objective functions and constraints that vary over time. As a consequence of such dynamic changes, the optimal solutions may vary over time, affecting the performance of convergence. In this thesis, we propose a new Cultural Algorithm (CA) based on decomposition (CA/D). The objective of the CA/D algorithm is to decompose DMOP into a number of subproblems that can be optimized using the information shared by neighboring problems. The proposed CA/D approach is evaluated using a number of CEC 2015 optimization benchmark functions. When compared to CA, Multi-population CA (MPCA), and MPCA incorporating game strategies (MPCA-GS), the results obtained showed that CA/D outperformed them in 7 out of the 15 benchmark functions
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