Homotopy Strategies

Hillermeier, Claus

doi:10.1007/978-3-0348-8280-4_6

Cited by 4 publications

(4 citation statements)

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“…Continuation methods (Hillermeier et al. 2001; Schtze, Dell'Aere & Dellnitz 2005; Gkaragkounis et al. 2018; Peitz, Ober-Blöbaum & Dellnitz 2019; Vasilopoulos et al.…”

Section: Multi-objective Optimizationmentioning

confidence: 99%

Understanding trade-offs in stellarator design with multi-objective optimization

Bindel,

Landreman,

Padidar

2023

J. Plasma Phys.

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In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils.

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“…Continuation methods (Hillermeier et al. 2001; Schtze, Dell'Aere & Dellnitz 2005; Gkaragkounis et al. 2018; Peitz, Ober-Blöbaum & Dellnitz 2019; Vasilopoulos et al.…”

Section: Multi-objective Optimizationmentioning

confidence: 99%

Understanding trade-offs in stellarator design with multi-objective optimization

Bindel,

Landreman,

Padidar

2023

J. Plasma Phys.

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“…Otherwise, the direction is saved (to avoid trying it a second time). See Hillermeier ( 2001 ) and Schütze et al. ( 2005 ) for examples and more detailed descriptions.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

A tutorial on multiobjective optimization: fundamentals and evolutionary methods

2018

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In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.

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“…Thus, the trade-offs decisions should be taken between these objectives. Most of the multiobjective algorithms are proposed based on the Pareto Sort [ 2 , 49 ] theory, so the optimization result is not usually a single solution but rather a set of solutions named as a Pareto nondominated set.…”

Section: Background Concepts and Related Technologiesmentioning

confidence: 99%

“…These problems are known as multiobjective optimization problems (MOPs) which can be found in many disciplines such as engineering, transportation, economics, medicine, and bioinformatics [ 1 ]. Most of the multiobjective techniques have been designed based on the theories of Pareto Sort [ 2 ] and nondominated solutions. Thus, the optimum solution for this kind of problem is not a single solution as in the mono-objective case, but rather a set of solutions known as the Pareto optimal set.…”

Section: Introductionmentioning

confidence: 99%

An Optimization Framework of Multiobjective Artificial Bee Colony Algorithm Based on the MOEA Framework

Huo

Liu

2018

Computational Intelligence and Neuroscience

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The artificial bee colony (ABC) algorithm has become one of the popular optimization metaheuristics and has been proven to perform better than many state-of-the-art algorithms for dealing with complex multiobjective optimization problems. However, the multiobjective artificial bee colony (MOABC) algorithm has not been integrated into the common multiobjective optimization frameworks which provide the integrated environments for understanding, reusing, implementation, and comparison of multiobjective algorithms. Therefore, a unified, flexible, configurable, and user-friendly MOABC algorithm framework is presented which combines a multiobjective ABC algorithm named RMOABC and the multiobjective evolution algorithms (MOEA) framework in this paper. The multiobjective optimization framework aims at the development, experimentation, and study of metaheuristics for solving multiobjective optimization problems. The framework was tested on the Walking Fish Group test suite, and a many-objective water resource planning problem was utilized for verification and application. The experiment's results showed the framework can deal with practical multiobjective optimization problems more effectively and flexibly, can provide comprehensive and reliable parameters sets, and can complete reference, comparison, and analysis tasks among multiple optimization algorithms.

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Homotopy Strategies

Cited by 4 publications

References 0 publications

Understanding trade-offs in stellarator design with multi-objective optimization

Understanding trade-offs in stellarator design with multi-objective optimization

A tutorial on multiobjective optimization: fundamentals and evolutionary methods

An Optimization Framework of Multiobjective Artificial Bee Colony Algorithm Based on the MOEA Framework

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