How to deal with mixed-variable optimization problems: An overview of algorithms and formulations
| Autor: | Mathieu Balesdent, Loïc Brevault, Julien Pelamatti, Yannick Guerin, El-Ghazali Talbi |
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| Přispěvatelé: | ONERA, Université de Toulouse [Toulouse], ONERA-PRES Université de Toulouse, Optimisation de grande taille et calcul large échelle (BONUS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), ONERA, Université Paris Saclay (COmUE) [Palaiseau], ONERA-Université Paris Saclay (COmUE), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
021103 operations research Optimization problem Computer science Mixed-variable optimization 0211 other engineering and technologies Particle swarm optimization 02 engineering and technology Function (mathematics) Engineering optimization Domain (software engineering) Categorical variables [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing [INFO]Computer Science [cs] Categorical variable Variable-size design space Integer (computer science) Variable (mathematics) |
| Zdroj: | Advances in Structural and Multidisciplinary Optimization Advances in Structural and Multidisciplinary Optimization, Springer, pp.64-82, 2018, ⟨10.1007/978-3-319-67988-4_5⟩ Advances in Structural and Multidisciplinary Optimization ISBN: 9783319679877 |
| Popis: | International audience; Real world engineering optimization problems often involve discrete variables (e.g., categorical variables) characterizing choices such as the type of material to be used or the presence of certain system components. From an analytical perspective, these particular variables determine the definition of the objective and constraint functions, as well as the number and type of parameters that characterize the problem. Furthermore, due to the inherent discrete and potentially non-numerical nature of these variables, the concept of metrics is usually not definable within their domain, thus resulting in an unordered set of possible choices. Most modern optimization algorithms were developed with the purpose of solving design problems essentially characterized by integer and continuous variables and by consequence the introduction of these discrete variables raises a number of new challenges. For instance, in case an order can not be defined within the variables domain, it is unfeasible to use optimization algorithms relying on measures of distances, such as Particle Swarm Optimization. Furthermore, their presence results in non-differentiable objective and constraint functions, thus limiting the use of gradient-based optimization techniques. Finally, as previously mentioned, the search space of the problem and the definition of the objective and constraint functions vary dynamically during the optimization process as a function of the discrete variables values.This paper presents a comprehensive survey of the scientific work on the optimization of mixed-variable problems characterized by continuous and discrete variables. The strengths and limitations of the presented methodologies are analyzed and their adequacy for mixed-variable problems with regards to the particular needs of complex system design is discussed, allowing to identify several ways of improvements to be further investigated. |
| Databáze: | OpenAIRE |
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