Inverse Max + Sum spanning tree problem by modifying the sum-cost vector under weighted $$l_\infty $$ l ∞ Norm

Guan, Xiucui; Pardalos, Pãnos M.; Zuo, Xu

doi:10.1007/s10898-014-0140-z

Cited by 17 publications

(8 citation statements)

References 20 publications

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“…Moreover, if the capacity of an arc ∈ is modified then the cost of modifying the capacity is ( ). In order to solve IMCP, a set ⊆ has to be found so that if the arcs belonging to are eliminated from , no longer communicates with through a directed path and the distance , obtained from (12) or (13), is minimized. So, the following theorem is immediate.…”

Section: Maximum Capacity Path Problemmentioning

confidence: 99%

See 1 more Smart Citation

Inverse Maximum Capacity Path Problems Under Sum-Type and Max-Type Distances and Their Practical Application to Transportation Networks

Deaconu

Tayyebi

2020

IEEE Access

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Section: Maximum Capacity Path Problemmentioning

confidence: 99%

“…There is also a very fast algorithm proposed in [6] to solve MCP in linear time. Inverse optimization is a relatively new research domain and it has been intensively studied [7,8,9,10,11,12,13]. Many papers have recently been published in this domain and are still being published nowadays.…”

Section: Introductionmentioning

confidence: 99%

Inverse Maximum Capacity Path Problems Under Sum-Type and Max-Type Distances and Their Practical Application to Transportation Networks

Deaconu

Tayyebi

2020

IEEE Access

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“…The binary search identifies the solution with the required precision γ . For some recent uses of the binary search in optimization, see, e.g., [14,15].…”

Section: Possible and Necessary Improvementmentioning

confidence: 99%

“…Since in this case it is impossible to determine the relative improvement, only the absolute one may be of interest to the DM. Note, however, that the optimization problems with non-linear objective functions (10)(11)(12)(13)(14) are even more difficult to solve than these discussed in Sect. 5.2.1.…”

Section: Remarks On Standardization Of Performance Values Distance Mmentioning

confidence: 99%

Post factum analysis for robust multiple criteria ranking and sorting

et al. 2015

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Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference model. Investigating the influence of this indetermination on the suggested recommendation, we may obtain the necessary, possible and extreme results confirmed by, respectively, all, at least one, or the most and least advantageous preference model instances compatible with the input preference information. We propose a framework for answering questions regarding stability of these results. In particular, we are investigating the minimal improvement that warrants feasibility of some currently impossible outcome as well as the maximal deterioration by which some already attainable result still holds. Taking into account the setting of multiple criteria ranking and sorting problems, we consider such questions in view of pairwise preference relations, or attaining some rank, or assignment. The improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive score. The proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targets. It is also important for robustness concern because it finds which parts of the recommendation are robust or sensitive with respect to the modification of the alternatives' performance values or scores. Application of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.

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“…Wang et al [23] also discussed a class of inverse dominant problems under the weighted l ∞ norm in the area of combinatorial optimization. Similarly, Yang and Zhang [24] considered some inverse min-max or max-min network problems not only under the weighted l ∞ norm but also the weighted l 1 norm, while Guan et al [7] initially studied an inverse problem of optimization problems with combined minmax-minsum objective functions. Besides, Wang [22] proposed two models for the partial inverse most unbalanced spanning tree problem under the weighted Hamming distance and the weighted l 1 norm.…”

Section: Introductionmentioning

confidence: 99%

Models for inverse minimum spanning tree problem with fuzzy edge weights

Zhang

Zhou

2014

Journal of Intelligent &Amp; Fuzzy Systems

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An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, a type of fuzzy inverse minimum spanning tree problem is introduced from a LAN reconstruction problem, where the weights of edges are assumed to be fuzzy variables. The concept of fuzzy α-minimum spanning tree is initialized, and subsequently a fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria. In order to solve the two fuzzy models, a fuzzy simulation for computing credibility is designed and then embedded into a genetic algorithm to produce some hybrid intelligent algorithms. Finally, some computational examples are given to illustrate the effectiveness of the proposed algorithms.

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Inverse Max + Sum spanning tree problem by modifying the sum-cost vector under weighted $$l_\infty $$ l ∞ Norm

Cited by 17 publications

References 20 publications

Inverse Maximum Capacity Path Problems Under Sum-Type and Max-Type Distances and Their Practical Application to Transportation Networks

Inverse Maximum Capacity Path Problems Under Sum-Type and Max-Type Distances and Their Practical Application to Transportation Networks

Post factum analysis for robust multiple criteria ranking and sorting

Models for inverse minimum spanning tree problem with fuzzy edge weights

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