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 EOP (and CEOP-), we develop a new approach featuring a ndomized teiner on Discretization (RSZD) scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Colony ystem (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.

中文翻译：

---

解决邻域重叠的足够接近的定向问题


足够近的旅行商问题 (CETSP) 是经典旅行商问题的一个众所周知的变体，智能体可以在目标社区内的任何点完成其任务。基于重叠邻域（称为 Steiner 区域 (SZ)）的启发式方法在解决 CETSP 问题上受到了关注。虽然 SZ 提供了对原始图的有效近似，但它们固有的重叠对搜索空间施加了限制，可能与全局优化目标相冲突。在这里，我们展示了如何通过汇总重叠社区的奖品，将这些限制转化为足够接近定向问题（CEOP）中的优势。我们通过引入非均匀成本考虑因素来进一步扩展经典的非均匀邻域 CEOP（CEOP-）。为了解决 EOP（和 CEOP-），我们开发了一种新方法，采用随机化离散化 (RSZD) 方案以及基于粒子群优化 (PSO) 和群体系统 (ACS) 的混合算法 — CRaSZe-AntS。 RSZD 方案识别 PSO 探索的子区域，ACS 确定离散访问序列。我们评估了 RSZD 在源自已建立的 CETSP 实例的 CEOP 实例上的离散化性能，并将 CRaSZe-AntS 与专注于 CEOP 实例单邻域优化的最相关的最先进启发式进行比较。我们还比较了 SZ 内的内部搜索和 CEOP- 背景下各个邻域的边界搜索的性能。我们的实验结果表明，与单邻域策略相比，CRaSZe-AntS 可以产生可比的解质量，同时显着减少计算时间，我们观察到平均为 140。奖金收集增加 44%，算法执行时间减少 55.18%。因此，CRaSZe-AntS 在解决新兴 CEOP 方面非常有效，其中的例子包括卡车和无人机交付场景。