Two-stage robust optimization for orienteering problem with stochastic weights

Abstract

In this paper, the two-stage orienteering problem with stochastic weights (OPSW) is considered, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. Two recourse models are introduced based on two different uncertainty realization ways, one is based on sequentially realized weights which leads to the recourse model proposed by Evers et al. (2014) and the other is based on concurrently realized weights which leads to a new recourse model with less variables and less constraints and is computationally more efficient. Subsequently two two-stage robust models are introduced for OPSW based on the two different recourse models, and the relationships between the two-stage robust models and their corresponding static robsut models are investigated. Theoretical conclusions are drawn which show that the two-stage robust models are equivalent to their corresponding static robust models with the box uncertainty set defined, and the two two-stage robust models are also equivalent to each other even though they are based on different recourse models. A case study is presented by comparing the two-stage robust models with an one-stage robust model for OPSW. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage OPSW.