Generating combinatorial sets with given properties

Grebennik, Igor; Lytvynenko, Oleksandr

doi:10.1007/s10559-012-9469-9

Cited by 8 publications

(2 citation statements)

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“…For example, the GenBase algorithm was used for generation of a large number of combinatorial sets [35] as well as for optimization of a linear function in a set of cyclic permutations [40].…”

Section: Discussionmentioning

confidence: 99%

An Heuristic Approach to Solving the one-to-one Pickup and Delivery Problem with Threedimensional Loading Constraints

Dupas

Grebennik²,

Lytvynenko³

et al. 2017

IJITCS

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Abstract-A mathematical model and a solving strategy for the Pickup and Delivery Problem with threedimensional loading constraints regarding a combinatorial configuration instead of a traditional approach that utilizes Boolean variables is proposed. A traditional one-to-one Pickup and Delivery Problem in a combination with a problem of packing transported items into vehicles by means of the proposed combinatorial generation algorithm is solved.

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Section: Discussionmentioning

confidence: 99%

An Heuristic Approach to Solving the one-to-one Pickup and Delivery Problem with Threedimensional Loading Constraints

Dupas

Grebennik²,

Lytvynenko³

et al. 2017

IJITCS

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show abstract

“…The algorithm proposed in [43] The following constraints for i S have to be fulfilled for each PDP route: the vertex repetition in i t is not allowed; for each pickup-delivery pair a vehicle should visit the pickup point before the corresponding delivery point; the next unit will be loaded into the vehicle and 3Dconstraints have to be monitored if a)…”

Section: Exact Algorithm For the Lower Levelmentioning

confidence: 99%

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

Dupas¹,

Grebennik²,

Litvinchev³

et al. 2018

EAI Endorsed Transactions on Energy Web

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One-to-one Pickup and Delivery Problem (PDP) with loading constraints is studied. Mathematical model is presented using combinatorial configurations approach for pickup and delivery and the phi-function technique for loading constraints. Two-stage solution strategy is used. The first stage has two levels: a) clustering the set of pickup and delivery points regarding to the set of vehicles and b) solving the PDP problem with 3D loading constraints for each vehicle within the appropriate cluster. The second stage improves the solution found at the previous stage and is based on the cyclic transfer approach and cyclic permutations. Computational results are presented to support efficiency of the approach.

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