Construction of Hamiltonian paths in graphs of permutation polyhedra

Donec, G. A.; Kolechkina, L. M.

doi:10.1007/s10559-010-9178-1

Cited by 8 publications

(6 citation statements)

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“…CLM was original developed to solve a feasibility problem -to find x ∈ E n (G) satisfying equality f (x) = a T x − b = 0 [1,3]. It uses a reformulation of the problem as CPP (further referred as CPP1):…”

Section: The Modified Coordinate Localization Methods (Mclm)mentioning

confidence: 99%

“…To this formulation, different graph techniques become applicable [1][2][3], which can be combined with properties of the Euclidean space [26]. Finally, the graph G can be complemented by additional edges decreasing diameter of the G * = (E , E * ) (further referred to as an auxiliary graph), E * ⊃ E. In turn, forming a directed graph from G * based on a specifics of ECOP allows applying techniques from [2,3].…”

Section: Approaches To Multiobjective Euclidean Combinatorial Optimizationmentioning

confidence: 99%

“…[9,21]. Here should also be noted the method of directed structuring CLM described in [1][2][3] are highly promising for solving such a class of problems.…”

Section: Approaches To Multiobjective Euclidean Combinatorial Optimizationmentioning

confidence: 99%

“…In studies [1][2][3], methods for solving CP are presented, which are based on the properties of graphs of polytopes of combinatorial sets. Such methods have advantages over classical ones.…”

Section: Introductionmentioning

confidence: 99%

“…Note that CLM was originally developed to a feasibility problem with an equality constraint. Adapted to a COP, CLM allows reducing significantly the number of combinatorial configurations considered [1,3].…”

Section: Introductionmentioning

confidence: 99%

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Multiobjective Optimization on Permutations with Applications

Koliechkina¹,

Pichugina²

2019

dtcse

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A method of multiobjective optimization on permutations (MOP) is offered based on the Directed Structuring Method and using Graph Theory. Prospects of applying graph techniques are caused by representability of the feasible domain by graph vertices. It yields advantages in using traditional methods, as well as in developing new ones. Our method is a generalization of the Method for Sequential Analysis of Variants for multiobjective optimization on permutations and multi-permutations. Most problems on combinatorial configurations sets are NP-hard, and a search of an exact solution requires enumerating a factorial number of variants. To decrease it, the method includes: a choice of an unconstraint MOP method; a choice of a method for generating a sequence of feasible solutions for a constraint MOP adapted to objective function; constructing and examining a structural graph of the optimization problem; a polynomial algorithm choice for solving the problem on partially ordered vertices of the graph.

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Section: The Modified Coordinate Localization Methods (Mclm)mentioning

confidence: 99%

Section: Approaches To Multiobjective Euclidean Combinatorial Optimizationmentioning

confidence: 99%

“…[9,21]. Here should also be noted the method of directed structuring CLM described in [1][2][3] are highly promising for solving such a class of problems.…”

Section: Approaches To Multiobjective Euclidean Combinatorial Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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