The Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of the classic Traveling
Salesman Problem whereby the agent may complete its mission at any point within a target neighborhood.
Heuristics based on overlapped neighborhoods, known as Steiner Zones (SZ), have gained attention in
addressing CETSPs. While SZs offer effective approximations to the original graph, their inherent overlap
imposes constraints on the search space, potentially conflicting with global optimization objectives. Here we
show how such limitations can be converted into advantages in the Close Enough Orienteering Problem (CEOP)
by aggregating prizes across overlapped neighborhoods. We further extend the classic CEOP with Non-uniform
Neighborhoods (CEOP-) by introducing non-uniform cost considerations for prize collection. To tackle CEOP
(and CEOP-), we develop a new approach featuring a Randomized Steiner Zone Discretization (RSZD)
scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Ant Colony System
(ACS) — CRaSZe-AntS. The RSZD scheme identifies sub-regions for PSO exploration, and ACS determines
the discrete visiting sequence. We evaluate the RSZD’s discretization performance on CEOP instances derived
from established CETSP instances and compare CRaSZe-AntS against the most relevant state-of-the-art heuristic
focused on single-neighborhood optimization for CEOP instances. We also compare the performance of the
interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-. Our
experimental results show that CRaSZe-AntS can yield comparable solution quality with significantly reduced
computation time compared to the single neighborhood strategy, where we observe an averaged 140.44%
increase in prize collection and 55.18% reduction of algorithm execution time. CRaSZe-AntS is thus highly
effective in solving emerging CEOP-, examples of which include truck-and-drone delivery scenarios.