Classification of applied methods of combinatorial optimization

Сергиенко, И. В.; Hulianytskyi, L. F.; Sirenko, S. I.

doi:10.1007/s10559-009-9134-0

Cited by 32 publications

(15 citation statements)

References 41 publications

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“…In addition to those, metaheuristics can require additional memory, have different parameter tuning processes (tuneless, easy or hard) and pose variable degrees of difficulty in implementation (low, medium or high). Sergienko et al (2009) provide schemes designed for the classification of combinatorial optimisation algorithms. One scheme is suitable for framework categorisation, the other one is appropriate for extracting classification criteria.…”

Section: Classification Schemes In Literaturementioning

confidence: 99%

Classifying Metaheuristics: Towards a unified multi-level classification system

Stegherr¹,

Heider²,

Hähner³

2020

Nat Comput

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Metaheuristics provide the means to approximately solve complex optimisation problems when exact optimisers cannot be utilised. This led to an explosion in the number of novel metaheuristics, most of them metaphor-based, using nature as a source of inspiration. Thus, keeping track of their capabilities and innovative components is an increasingly difficult task. This can be resolved by an exhaustive classification system. Trying to classify metaheuristics is common in research, but no consensus on a classification system and the necessary criteria has been established so far. Furthermore, a proposed classification system can not be deemed complete if inherently different metaheuristics are assigned to the same class by the system. In this paper we provide the basis for a new comprehensive classification system for metaheuristics. We first summarise and discuss previous classification attempts and the utilised criteria. Then we present a multi-level architecture and suitable criteria for the task of classifying metaheuristics. A classification system of this kind can solve three main problems when applied to metaheuristics: organise the huge set of existing metaheuristics, clarify the innovation in novel metaheuristics and identify metaheuristics suitable to solve specific optimisation tasks.

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Section: Classification Schemes In Literaturementioning

confidence: 99%

Classifying Metaheuristics: Towards a unified multi-level classification system

Stegherr¹,

Heider²,

Hähner³

2020

Nat Comput

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“…Найбільш поширеною серед них є множина перестановок і її різні підмножини. Додаткові обмеження на параметри в таких задачах дозволяють виділити наступні відомі в літературі класи множин перестановок [1][2][3][4][5][6]: перестановки різних елементів, перестановки з повтореннями, перестановки з n елементів, k з яких різні, циклічні перестановки, перестановки кортежів, композиції перестановок, перестановки містять (що не містять) шаблон (pattern), поліперестановки та інші.…”

Section: вступunclassified

Cyclic Permutations in the Methods of Combinatorial Optimization on the Basis of Cyclic Transfers

Grebennik¹,

Chorna²

2019

Scientific journal “Bionics of Intelligence”

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Permutations sets are very often considered in theoretical and applied research in the field of combinatorics andcombinatorial optimization. By now many properties of permutations have been investigated, in particular those associatedwith the cyclic structure of permutations. To solve optimization problems on combinatorial sets, a number of methodshave been developed and successfully used. Among them, there are methods for finding exact, approximate, and heuristicsolutions. Among the search methods for an approximate solution, search methods in the neighborhood are widely used.Among the combinatorial search methods in the neighborhood, it is necessary to distinguish a group of methods that usescyclic transfers. A general search scheme using cyclic transfers is known. It is based on the search for a cyclic transferin the auxiliary graph. But the features of the tasks being solved sometimes do not allow constructing an auxiliary graphand using the existing search methods. In such cases, an alternative approach is proposed. This is a general strategy forsolving problems using cyclic transfers, which is a modification of the strategy of Thompson and Orlin. We propose theconstruction of cyclic transfers based not on the use of an auxiliary graph, but based on the set of cyclic permutationsand its properties to obtain cyclic transfers. To demonstrate the strategy for solving combinatorial optimization problemsdescribed in the article, one of the vehicle routing problems was solved. Computational experiments were conducted todemonstrate the effectiveness of the proposed strategy. Their results are given in the article.

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“…The methods and algorithms are used across different application areas. Grossmann et al (2002), Gutin et al (2003), Pentico (2007), and Sergienko et al (2009) try to classify methods and types of CO problems.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Different Approaches to the Cutting Plan Scheduling

Bober

2011

QIP Journal

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Classification of applied methods of combinatorial optimization

Cited by 32 publications

References 41 publications

Classifying Metaheuristics: Towards a unified multi-level classification system

Classifying Metaheuristics: Towards a unified multi-level classification system

Cyclic Permutations in the Methods of Combinatorial Optimization on the Basis of Cyclic Transfers

Comparison of Different Approaches to the Cutting Plan Scheduling

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