Exact extension of the DIRECT algorithm to multiple objectives

Lovison, Alberto; Miettinen, Kaisa

doi:10.1063/1.5090020

Cited by 3 publications

(8 citation statements)

References 14 publications

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“…Alternative extensions of the concept of potential Pareto optimality are considered in [1,4,26]. In [4], a hyperinterval H is deemed potentially Pareto optimal if it is potentially optimal in the scalar sense (2) for at least one of the objective functions.…”

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

“…In [26], an exact extension of the geometrical interpretation of potential optimality is considered as a convex hull of the set of augmented objective vectors. In [1], the nondominated set of the set of the augmented objective vectors is used as the set of potential Pareto optima.…”

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

“…Also according to [26], H 1 , H 2 , H 4 and H 6 are deemed potentially Pareto optimal. In this case, H 5 is excluded because it belongs to a nonconvex part of the nondominated set of the σ -level.…”

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

“…In this case, H 5 is excluded because it belongs to a nonconvex part of the nondominated set of the σ -level. Nevertheless, the notion in [26] is less restrictive because it does not exclude at least the convex parts of the nondominated sets, while [4] can pick as potentially Pareto optimal only the extrema of the subfronts.…”

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

“…In [1], the set of potentially Pareto optimal hyperintervals is approximated by a set of nondominated vectors in the augmented objective space. In a previous paper [26], we have considered the convex hull of the set of nondominated vectors in the augmented objective space. As we will see in the following, the notions of [4] and [26] are too restrictive, while the one in [1] is too conservative.…”

Section: Question 1 Is It Possible To Characterize Geometrically the mentioning

confidence: 99%

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On the Extension of the DIRECT Algorithm to Multiple Objectives

Lovison

Miettinen

2020

J Glob Optim

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Deterministic global optimization algorithms like Piyavskii-Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm direct, analyze the available algorithms in the literature that extend direct to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in direct. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.

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Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

Section: Discussion and Comparison With The Selection Rules Of Other mentioning

confidence: 99%

Section: Question 1 Is It Possible To Characterize Geometrically the mentioning

confidence: 99%

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On the Extension of the DIRECT Algorithm to Multiple Objectives

Lovison

Miettinen

2020

J Glob Optim

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The DIRECT algorithm: 25 years Later

Jones

Martins

2020

J Glob Optim

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Introduced in 1993, the DIRECT global optimization algorithm provided a fresh approach to minimizing a black-box function subject to lower and upper bounds on the variables. In contrast to the plethora of nature-inspired heuristics, DIRECT was deterministic and had only one hyperparameter (the desired accuracy). Moreover, the algorithm was simple, easy to implement, and usually performed well on low-dimensional problems (up to six variables). Most importantly, DIRECT balanced local and global search (exploitation vs. exploration) in a unique way: in each iteration, several points were sampled, some for global and some for local search. This approach eliminated the need for “tuning parameters” that set the balance between local and global search. However, the very same features that made DIRECT simple and conceptually attractive also created weaknesses. For example, it was commonly observed that, while DIRECT is often fast to find the basin of the global optimum, it can be slow to fine-tune the solution to high accuracy. In this paper, we identify several such weaknesses and survey the work of various researchers to extend DIRECT so that it performs better. All of the extensions show substantial improvement over DIRECT on various test functions. An outstanding challenge is to improve performance robustly across problems of different degrees of difficulty, ranging from simple (unimodal, few variables) to very hard (multimodal, sharply peaked, many variables). Opportunities for further improvement may lie in combining the best features of the different extensions.

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Application Analysis of Multi-Intelligence Optimization Decision-Making Method in College Students’ Ideological and Political Education System

Tian¹,

Xie

Wei³

2022

Security and Communication Networks

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Today’s society is a society with diversified information. The rapid change of information also affects the ideological and political education in universities. Therefore, the fixed thinking of ideological and political education in universities tells students, which is an educational way in line with the development of the times. We should follow up with the rapidly changing times at any time, change with the times, and update the thinking and systematic way of the ideological and political education system at any time. In the ideological and political education of college students, diversified teaching methods and multiobjective recommendation systems are implemented and then combined with traditional ideological and political teaching methods. The two ways complement each other and promote each other so as to achieve higher learning efficiency and better learning effect. The optimization algorithm of multiobjective recommendation should be used to further improve the ideological and political education system. By analyzing the optimization results and performance comparison of various algorithms, we find the most suitable algorithm model for optimizing the ideological and political education system. The multiobjective-recommended ideological and political education system for college students needs to fully improve the teaching tasks of teachers and students in two stages. A reasonable and scientific system recommendation mechanism should take into account students’ own learning preferences, subject types, ideological and political teacher information, curriculum information, curriculum evaluation, curriculum relevance, and other multiobjective data. This paper achieves the highest performance and the lowest time cost of the ideological and political education system through multiobjective evolutionary optimization method.

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Exact extension of the DIRECT algorithm to multiple objectives

Cited by 3 publications

References 14 publications

On the Extension of the DIRECT Algorithm to Multiple Objectives

On the Extension of the DIRECT Algorithm to Multiple Objectives

The DIRECT algorithm: 25 years Later

Application Analysis of Multi-Intelligence Optimization Decision-Making Method in College Students’ Ideological and Political Education System

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