Size constrained k simple polygons

Yang, KwangSoo; Nam, Kwang Woo; Qutbuddin, Ahmad; Reich, Aaron; Huhn, Valmer

doi:10.1007/s10707-020-00416-9

Cited by 1 publication

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yang et al. (2021) study a problem related to the PCGEP , namely, the size‐constrained

k

simple polygons ( SCkSP ) problem where, given a set of points with their corresponding benefits, the goal is to maximize the total benefit of the points enclosed by

k

simple polygons whose individual areas are bounded by a given parameter. They propose heuristics to solve the SCkSP and measure their effectiveness on instances derived from data sets of criminal and wildfire information.…”

Section: Introductionmentioning

confidence: 99%

Exact and heuristic solutions for the prize‐collecting geometric enclosure problem

Ramos,

Cano,

de Rezende

et al. 2024

Int Trans Operational Res

View full text Add to dashboard Cite

In the prize‐collecting geometric enclosure problem (PCGEP), a set S of points in the plane is given, each with an associated benefit. The goal is to find a simple polygon with vertices in S that maximizes the sum of the benefits of the points of S enclosed by minus the perimeter of multiplied by a given nonnegative cost. The PCGEP is NP‐complete and has applications to land surveying for exploration or preservation of natural resources. In this paper, we develop the first heuristic, called PCGEP‐GR, for the PCGEP and revisit a previously proposed integer linear programming (ILP) model to solve it to optimality. We conducted a comprehensive experimental study of that heuristic and an exact algorithm based on the ILP model. We show that a new set of constraints, together with the previous set, is necessary to guarantee the correctness of the ILP model and introduce preprocessing strategies that allow us to prove optimality 40% faster on average. The proposed heuristic is able to reach the optimum in 32% of our benchmark instances and, for those with unknown optima, PCGEP‐GR was found better than or at least as good solutions as the ones obtained by the cplex ILP solver in 54% of the cases. Notwithstanding these positive results, the design of effective heuristics for the PCGEP proved to be very challenging, which also led us to obtain a result that provides the theoretical foundation for future advances in the study of this problem.

show abstract

“…Yang et al. (2021) study a problem related to the PCGEP , namely, the size‐constrained

k

simple polygons ( SCkSP ) problem where, given a set of points with their corresponding benefits, the goal is to maximize the total benefit of the points enclosed by