Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of TSP 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 CETSP. While SZs offer effective approximations to the original graph, their inherent overlap imposes constraints on search space, potentially conflicting with global optimization objectives. Here we show how such limitations can be converted into advantages in a Close Enough Orienteering Problem (CEOP) by aggregating prizes across overlapped neighborhoods. We further extend classic CEOP with Non-uniform Neighborhoods (CEOP-N) by introducing non-uniform costs for prize collection. To tackle CEOP and 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 instances. 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 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 average 140.44% increase in prize collection and a 55.18% reduction in algorithm execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.

翻译：接近足够旅行商问题（CETSP）是旅行商问题（TSP）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。基于重叠邻域的启发式方法，即斯坦纳区域（SZ），在解决CETSP中受到关注。虽然SZ提供了对原始图的有效近似，但其固有的重叠对搜索空间施加了约束，可能影响全局优化目标。本文展示了如何通过聚合重叠邻域中的奖励，将这些局限性转化为接近足够定向问题（CEOP）中的优势。我们进一步扩展了经典CEOP，引入具有非均匀邻域（CEOP-N）的变体，其中对奖励收集设置了非均匀成本。为求解CEOP和CEOP-N，我们提出了一种新方法，包含随机斯坦纳区域离散化（RSZD）方案，并结合基于粒子群优化（PSO）和蚁群系统（ACS）的混合算法CRaSZe-AntS。RSZD方案识别用于PSO探索的子区域，而ACS确定离散访问序列。我们在从现有CETSP实例衍生的CEOP实例上评估RSZD的离散化性能，并将CRaSZe-AntS与最先进的、专注于CEOP实例单邻域优化的启发式方法进行比较。同时，我们在CEOP-N背景下比较了SZ内部搜索与单个邻域边界搜索的性能。实验结果表明，与单邻域策略相比，CRaSZe-AntS能以显著减少的计算时间获得可比的解质量，其中我们观察到奖励收集平均增加140.44%，算法执行时间减少55.18%。因此，CRaSZe-AntS在求解新兴的CEOP-N（例如卡车与无人机配送场景）中非常有效。