English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The problem of packing a set of circles into the smallest surroundingcontainer is considered. This problem arises in different application areassuch as automobile, textile, food, and chemical industries. The so-calledcircle packing problem can be cast as a nonconvex quadratically constrainedprogram, and is difficult to solve in general. An iterative solution approachbased on a bisection-type algorithm on the radius of the larger circle isprovided. The present algorithm discretizes the container into small cells andsolves two different integer linear programming formulations proposed for arestricted and a relaxed version of the original problem. The present algorithmis enhanced with solution space reduction, bound tightening and variableelimination techniques. Then, a computational study is performed to evaluatethe performance of the algorithm. The present algorithm is compared with BARONand Gurobi that solve the original nonlinear formulation and heuristic methodsfrom literature, and obtain promising results.

Discretization-Based Solution Approaches for the Circle Packing Problem