This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is associated with each subgroup and is gained only if all of its nodes are visited; however, at most one subgroup can be visited per cluster. The objective is to maximize the total collected reward while attaining a travel budget. We show that our new formulation has the ability to model and solve two previous well-known variants, the Clustered Orienteering Problem (COP) and the Set Orienteering Problem (SOP), in addition to other scenarios introduced here. An Integer Linear Programming (ILP) formulation and a Tabu Search-based heuristic are proposed to solve the problem. Experimental results indicate that the ILP method can yield optimal solutions at the cost of time, whereas the metaheuristic produces comparable solutions within a more reasonable computational cost.

翻译：本文介绍了一种定向越野问题（OP）的扩展，称为带子群的分簇寻路问题（COPS）。在该变体中，节点被划分为子群，子群再组织成簇。每个子群关联一个奖励，且仅当该子群所有节点均被访问时才能获得该奖励；但每个簇最多只能访问一个子群。目标是在满足旅行预算约束下最大化总收集奖励。我们证明，该新模型不仅能求解本文引入的新场景，还能建模并求解两个已知变体——分簇定向越野问题（COP）和集合定向越野问题（SOP）。为求解该问题，提出了整数线性规划（ILP）模型和基于禁忌搜索的启发式算法。实验结果表明，ILP方法能以时间成本为代价获得最优解，而元启发式算法能在更合理的计算成本下产生可比较的解。