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：本文介绍了定向问题的一种扩展形式，称为带子群的分群定向问题（COPS）。在该变体中，节点被组织成子群，子群进一步被划分为集群。每个子群对应一个收益，且仅当该子群的所有节点均被访问时才能获得该收益；但每个集群中最多只能访问一个子群。目标是在满足旅行预算约束的前提下最大化总收集收益。我们证明，该新模型不仅能建模并求解两种已知经典变体——分群定向问题（COP）和集合定向问题（SOP），还能处理本文引入的其他场景。为求解该问题，我们提出了整数线性规划（ILP）公式和基于禁忌搜索的启发式算法。实验结果表明，ILP方法虽能以时间为代价获得最优解，而元启发式算法则能以更合理的计算成本提供可比解。