A Survey of Decomposition Methods for Multi-objective Optimization

Santiago, Alejandro; Huacuja, Héctor Joaquín Fraire; Dorronsoro, Bernabè; Pecero, Johnatan E.; Gómez-Santillán, Claudia; Barbosa, Juan Javier González; Soto, Carlos

doi:10.1007/978-3-319-05170-3_31

Cited by 33 publications

(9 citation statements)

References 34 publications

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“…Decomposition transforms multi-objective problems into many single-objective optimization problems [42]. Such a technique can be either embedded in a multi-objective algorithm and solved simultaneously or independently using a single-objective optimizer.…”

Section: Decompositionmentioning

confidence: 99%

Pymoo: Multi-Objective Optimization in Python

2020

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A B S T R A C TPython has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related frameworks have arisen in the past few years. Only a few of them support optimization of multiple conflicting objectives at a time, but do not provide comprehensive tools for a complete multi-objective optimization task. To address this issue, we have developed pymoo, a multi-objective optimization framework in Python. We provide a guide to getting started with our framework by demonstrating the implementation of an exemplary constrained multiobjective optimization scenario. Moreover, we give a high-level overview of the architecture of pymoo to show its capabilities followed by an explanation of each module and its corresponding sub-modules. The implementations in our framework are customizable and algorithms can be modified/extended by supplying custom operators. Moreover, a variety of single, multi and many-objective test problems are provided and gradients can be retrieved by automatic differentiation out of the box. Also, pymoo addresses practical needs, such as the parallelization of function evaluations, methods to visualize low and high-dimensional spaces, and tools for multi-criteria decision making. For more information about pymoo, readers are encouraged to visit: https://pymoo.org

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Section: Decompositionmentioning

confidence: 99%

Pymoo: Multi-Objective Optimization in Python

2020

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“…Typically, an MOOP is solved with a decomposition strategy, which decomposes the original problem into several scalar optimization sub-problems and optimizes them simultaneously [30,31]. For example in the classic MOEA/D method, the Tchebycheff decomposition is used to measure the maximum weighted distance between the objectives and their minimums z * = ( z * T , z * C ):…”

Section: Approachmentioning

confidence: 99%

Energy-effective artificial internet-of-things application deployment in edge-cloud systems

Xiang

Zheng

et al. 2021

Peer-to-Peer Netw. Appl.

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Recently, the Internet-of-Things technique is believed to play an important role as the foundation of the coming Artificial Intelligence age for its capability to sense and collect real-time context information of the world, and the concept Artificial Intelligence of Things (AIoT) is developed to summarize this vision. However, in typical centralized architecture, the increasing of device links and massive data will bring huge congestion to the network, so that the latency brought by unstable and time-consuming long-distance network transmission limits its development. The multi-access edge computing (MEC) technique is now regarded as the key tool to solve this problem. By establishing a MEC-based AIoT service system at the edge of the network, the latency can be reduced with the help of corresponding AIoT services deployed on nearby edge servers. However, as the edge servers are resource-constrained and energy-intensive, we should be more careful in deploying the related AIoT services, especially when they can be composed to make complex applications. In this paper, we modeled complex AIoT applications using directed acyclic graphs (DAGs), and investigated the relationship between the AIoT application performance and the energy cost in the MEC-based service system by translating it into a multi-objective optimization problem, namely the CA$$^3$$ 3 D problem — the optimization problem was efficiently solved with the help of heuristic algorithm. Besides, with the actual simple or complex workflow data set like the Alibaba Cloud and the Montage project, we conducted comprehensive experiments to evaluate the results of our approach. The results showed that the proposed approach can effectively obtain balanced solutions, and the factors that may impact the results were also adequately explored.

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“…Some of recent studies focus on certain subareas of multiobjective optimization: multiobjective algorithms for data mining [Mukhopadhyay et al 2014a[Mukhopadhyay et al , 2014b and decomposition-based multiobjective algorithms [Santiago et al 2014], whereas some are more closely related to many-objective optimization. Ishibuchi et al [2008] demonstrated the difficulties of MaOPs through experiments and reviewed a number of techniques for improving scalability of MOEAs.…”

Section: Introductionmentioning

confidence: 99%

Many-Objective Evolutionary Algorithms

et al. 2015

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Multiobjective evolutionary algorithms (MOEAs) have been widely used in real-world applications. However, most MOEAs based on Pareto-dominance handle many-objective problems (MaOPs) poorly due to a high proportion of incomparable and thus mutually nondominated solutions. Recently, a number of many-objective evolutionary algorithms (MaOEAs) have been proposed to deal with this scalability issue. In this article, a survey of MaOEAs is reported. According to the key ideas used, MaOEAs are categorized into seven classes: relaxed dominance based, diversity-based, aggregation-based, indicator-based, reference set based, preference-based, and dimensionality reduction approaches. Several future research directions in this field are also discussed.

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A Survey of Decomposition Methods for Multi-objective Optimization

Cited by 33 publications

References 34 publications

Pymoo: Multi-Objective Optimization in Python

Pymoo: Multi-Objective Optimization in Python

Energy-effective artificial internet-of-things application deployment in edge-cloud systems

Many-Objective Evolutionary Algorithms

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