TY - JOUR

T1 - Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

AU - Shang, Ke

AU - Chan, Felix T.S.

AU - Karungaru, Stephen

AU - Terada, Kenji

AU - Feng, Zuren

AU - Ke, Liangjun

N1 - Funding Information:
This work was supported by the National Natural Science Foundation of China (Grant nos. 62002152, 61876075, and 71971143), Guangdong Provincial Key Laboratory (Grant no. 2020B121201001), the Program for Guangdong Introducing Innovative and Enterpreneurial Teams (Grant no. 2017ZT07X386), Shenzhen Science and Technology Program (Grant no. KQTD2016112514355531), and the Program for University Key Laboratory of Guangdong Province (Grant no. 2017KSYS008).
Publisher Copyright:
© 2020 Ke Shang et al.

PY - 2020/11/16

Y1 - 2020/11/16

N2 - In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. 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 orienteering problem with stochastic weights.

AB - In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. 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 orienteering problem with stochastic weights.

UR - http://www.scopus.com/inward/record.url?scp=85097089326&partnerID=8YFLogxK

U2 - 10.1155/2020/5649821

DO - 10.1155/2020/5649821

M3 - Review article

AN - SCOPUS:85097089326

VL - 2020

JO - Complexity

JF - Complexity

SN - 1076-2787

M1 - 5649821

ER -