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 present the Close Enough Orienteering Problem with Non-uniform Neighborhoods (CEOP-N), which extends CETSP by introducing variable prize attributes and non-uniform cost considerations for prize collection. To tackle CEOP-N, 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. We also compare the performance of the interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-N. Our results show 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 execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.

翻译：足够接近旅行商问题（CETSP）是经典旅行商问题的一个著名变体，其中智能体可以在目标邻域内的任意点完成任务。基于重叠邻域（称为斯坦纳区域（SZ））的启发式方法在处理CETSP方面备受关注。尽管SZ能有效逼近原始图，但其固有的重叠会限制搜索空间，可能与全局优化目标冲突。本文提出了非均匀邻域的足够接近定向运动问题（CEOP-N），该问题通过引入可变奖项属性和奖项采集的非均匀成本考量扩展了CETSP。为求解CEOP-N，我们开发了一种新方法，包括随机化斯坦纳区域离散化（RSZD）方案，以及基于粒子群优化（PSO）和蚁群系统（ACS）的混合算法——CRaSZe-AntS。RSZD方案识别PSO探索的子区域，ACS确定离散访问顺序。我们在基于已有CETSP实例构建的CEOP实例上评估了RSZD的离散化性能，并将CRaSZe-AntS与最先进的、专注于单邻域优化的CEOP启发式方法进行了比较。我们还针对CEOP-N问题，比较了SZ内部搜索与单个邻域边界搜索的性能。结果表明，与单邻域策略相比，CRaSZe-AntS能在显著减少计算时间的前提下达到相当的求解质量，其中奖项收集平均增加140.44%，执行时间减少55.18%。因此，CRaSZe-AntS在求解新兴的CEOP-N问题（例如卡车与无人机配送场景）中表现出高效性。