Proportional packing of circles in a circular container

Research output: Contribution to journalResearch articleContributedpeer-review



The authors consider a problem of packing circles of given types in a circular container. Circles are allowed to cross the container boundary in a predefined neighborhood that depends on the circle type (pseudo-inclusion condition). A family of circles is placed in the container under the conditions of their non-intersection, pseudo-inclusion, and compliance with the given proportions of circle types (proportionality condition) in order to maximize the total number of circles. A mathematical model is constructed as a problem of mixed integer nonlinear programming. A heuristic algorithm is proposed that applies a nonlinear programming problem to pack a given number of circles in a circular container, maximizing the variable radii of the circles. The results of the computational experiments are given.


Original languageEnglish
Pages (from-to)82-89
Number of pages8
JournalCybernetics and Systems Analysis
Issue number1
Publication statusPublished - Jan 2023

External IDs

Scopus 85148534220
Mendeley f91061e1-ec0d-31cb-8b88-e2f6470401e5


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis


  • circles, circular container, optimization, proportional packing, pseudo-inclusion