Clustered Orienteering Problem with Function-Based Rewards

The Orienteering Problem is a well-studied problem that aims to determine an optimal route that maximizes the cumulative rewards while attaining a predefined travel budget. This classical formulation has been generalized in many forms, including grouping customers (locations) into clusters. However, such cluster-based formulation typically demands visiting all customers to collect the reward, thereby restricting its applicability. In this paper, we introduce a novel variant in which rewards associated with a cluster can be partially collected following a function that correlates with the number of customers attended within the cluster. This new formulation is a suitable alternative to model scenarios where the reward of the clusters can exhibit distinct and unique scaling patterns. We propose using an evolutionary algorithm to solve this problem and evaluate its performance considering different scenarios and aspects. The results demonstrate that our method effectively selects an appropriate number of clients to attend to based on the assigned function for each cluster.