{"id":{"repo_id":"texas","oai_identifier":"oai:repositories.lib.utexas.edu:2152/131954"},"canonical_url":"https://search.dev.ndltd.org/etd/texas/oai:repositories.lib.utexas.edu:2152/131954","repository":{"repo_id":"texas","name":"University of Texas","base_url":"https://repositories.lib.utexas.edu/server/oai/request"},"display":{"title":"Distributionally robust solution schemes for two-stage optimization and interdiction problems under uncertainty","abstract":"Decision-makers often have to make decisions in the presence of uncertainty. One can use optimization models with uncertain parameters to formulate the decision problems. Despite its wide applications in real-world problems, optimization under uncertainty gives rise to computational challenges. This thesis aims to design tractable solution schemes with performance guarantees for two-stage optimization and interdiction problems. We utilize the distributionally robust optimization scheme to develop the solution framework, which is an emerging scheme in optimization under uncertainty. In addition, solution algorithms are designed for optimization problems to further reduce computational cost. The first part of the dissertation studies two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied by the uncertain parameters in both the objective function and the constraints. To mitigate the computational intractability of infinite-dimensional optimization, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. Based on the decision rule structure, we develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. The emerging optimization problem can be reformulated as an exact copositive program that admits tractable approximations in semidefinite programming. We then design a decomposition algorithm where smaller-size semidefinite programs can be solved in parallel, which further reduces the runtime. Through numerical examples, we empirically demonstrate that our method produces significantly better solutions with reasonable computational effort than the traditional sample-average approximation scheme, especially when the data is limited. Next, we study the interdiction problem under uncertainty, where partial information about the operations of the follower is unavailable when the leader makes interdiction decisions. The distributionally robust optimization scheme is applied to yield a secure but not too conservative interdiction decision. The problem admits a finite-dimensional copositive-based reformulation; however, the resulting mixed-binary conic program is still intractable. We propose a decomposition algorithm that iteratively finds the optimal solution by solving the relaxed master problem, which is constructed from the integer optimality cuts and the Benders cuts. Both cuts evaluate the performance at the current interdiction solution and provide underestimation at the other feasible points. We evaluate the performance of the distributionally robust interdiction decisions and showcase the effectiveness of the multi-cut decomposition algorithm on the competitive facility location problem and the 0-1 knapsack interdiction problem. The final project we explore is a network retrofit problem. Transportation network redundancy, an important dimension of resilience, is crucial for providing alternative travel choices during disastrous events. This chapter addresses a new way of improving network redundancy by retrofitting critical components to withstand future disasters. The transportation redundancy-oriented network retrofit problem aims to find the optimal retrofit resource allocation strategy that maintains the highest level of network redundancy under uncertain disastrous events. To cope with the uncertainty, we develop the distributionally robust optimization (RNRP-DRO) model with χ²-distance ambiguity set. However, the lack of explicit mathematical representation for the network redundancy leads to an intractable optimization model. To tackle this issue, we propose a linear regression approximation of the implicit loss of network redundancy function. The approximated RNRP-DRO problem is then reformulated as a mixed-binary second-order cone program, and a Benders decomposition algorithm is developed to improve the computational efficiency. We further discuss the theoretical properties of the model and solution algorithms. Numerical experiments in the realistic Winnipeg network demonstrate the practical importance of the proposed model and validate the effectiveness of the proposed solution approaches.","abstract_html":"Decision-makers often have to make decisions in the presence of uncertainty. One can use optimization models with uncertain parameters to formulate the decision problems. Despite its wide applications in real-world problems, optimization under uncertainty gives rise to computational challenges. This thesis aims to design tractable solution schemes with performance guarantees for two-stage optimization and interdiction problems. We utilize the distributionally robust optimization scheme to develop the solution framework, which is an emerging scheme in optimization under uncertainty. In addition, solution algorithms are designed for optimization problems to further reduce computational cost. The first part of the dissertation studies two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied by the uncertain parameters in both the objective function and the constraints. To mitigate the computational intractability of infinite-dimensional optimization, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. Based on the decision rule structure, we develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. The emerging optimization problem can be reformulated as an exact copositive program that admits tractable approximations in semidefinite programming. We then design a decomposition algorithm where smaller-size semidefinite programs can be solved in parallel, which further reduces the runtime. Through numerical examples, we empirically demonstrate that our method produces significantly better solutions with reasonable computational effort than the traditional sample-average approximation scheme, especially when the data is limited. Next, we study the interdiction problem under uncertainty, where partial information about the operations of the follower is unavailable when the leader makes interdiction decisions. The distributionally robust optimization scheme is applied to yield a secure but not too conservative interdiction decision. The problem admits a finite-dimensional copositive-based reformulation; however, the resulting mixed-binary conic program is still intractable. We propose a decomposition algorithm that iteratively finds the optimal solution by solving the relaxed master problem, which is constructed from the integer optimality cuts and the Benders cuts. Both cuts evaluate the performance at the current interdiction solution and provide underestimation at the other feasible points. We evaluate the performance of the distributionally robust interdiction decisions and showcase the effectiveness of the multi-cut decomposition algorithm on the competitive facility location problem and the 0-1 knapsack interdiction problem. The final project we explore is a network retrofit problem. Transportation network redundancy, an important dimension of resilience, is crucial for providing alternative travel choices during disastrous events. This chapter addresses a new way of improving network redundancy by retrofitting critical components to withstand future disasters. The transportation redundancy-oriented network retrofit problem aims to find the optimal retrofit resource allocation strategy that maintains the highest level of network redundancy under uncertain disastrous events. To cope with the uncertainty, we develop the distributionally robust optimization (RNRP-DRO) model with χ²-distance ambiguity set. However, the lack of explicit mathematical representation for the network redundancy leads to an intractable optimization model. To tackle this issue, we propose a linear regression approximation of the implicit loss of network redundancy function. The approximated RNRP-DRO problem is then reformulated as a mixed-binary second-order cone program, and a Benders decomposition algorithm is developed to improve the computational efficiency. We further discuss the theoretical properties of the model and solution algorithms. Numerical experiments in the realistic Winnipeg network demonstrate the practical importance of the proposed model and validate the effectiveness of the proposed solution approaches.","abstract_has_math":false,"creators":["Fan, Xiangyi"],"institution":"The University of Texas at Austin","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hanasusanto, Grani Adiwena"],"committee_chairs":[],"committee_members":["Leibowicz, Benjamin D","He, Long","Boyles, Stephen"],"year":2023,"date_issued":"2023-05","date_published":"2023-05","updated_at":"2026-07-24T05:01:10Z","subjects":["Optimization under uncertainty","Distributionally robust optimization"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.26153/tsw/59298"],"render_values":[{"text":"https://doi.org/10.26153/tsw/59298","href":"https://doi.org/10.26153/tsw/59298","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/2152/131954","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hanasusanto, Grani Adiwena"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Leibowicz, Benjamin D","He, Long","Boyles, Stephen"]},{"key":"dc:creator","label":"Author","values":["Fan, Xiangyi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-03-11T00:05:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-03-11T00:05:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The University of Texas at Austin"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Optimization under uncertainty","Distributionally robust optimization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2152/131954","https://doi.org/10.26153/tsw/59298"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Decision-makers often have to make decisions in the presence of uncertainty. One can use optimization models with uncertain parameters to formulate the decision problems. Despite its wide applications in real-world problems, optimization under uncertainty gives rise to computational challenges. This thesis aims to design tractable solution schemes with performance guarantees for two-stage optimization and interdiction problems. We utilize the distributionally robust optimization scheme to develop the solution framework, which is an emerging scheme in optimization under uncertainty. In addition, solution algorithms are designed for optimization problems to further reduce computational cost. The first part of the dissertation studies two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied by the uncertain parameters in both the objective function and the constraints. To mitigate the computational intractability of infinite-dimensional optimization, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. Based on the decision rule structure, we develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. The emerging optimization problem can be reformulated as an exact copositive program that admits tractable approximations in semidefinite programming. We then design a decomposition algorithm where smaller-size semidefinite programs can be solved in parallel, which further reduces the runtime. Through numerical examples, we empirically demonstrate that our method produces significantly better solutions with reasonable computational effort than the traditional sample-average approximation scheme, especially when the data is limited. Next, we study the interdiction problem under uncertainty, where partial information about the operations of the follower is unavailable when the leader makes interdiction decisions. The distributionally robust optimization scheme is applied to yield a secure but not too conservative interdiction decision. The problem admits a finite-dimensional copositive-based reformulation; however, the resulting mixed-binary conic program is still intractable. We propose a decomposition algorithm that iteratively finds the optimal solution by solving the relaxed master problem, which is constructed from the integer optimality cuts and the Benders cuts. Both cuts evaluate the performance at the current interdiction solution and provide underestimation at the other feasible points. We evaluate the performance of the distributionally robust interdiction decisions and showcase the effectiveness of the multi-cut decomposition algorithm on the competitive facility location problem and the 0-1 knapsack interdiction problem. The final project we explore is a network retrofit problem. Transportation network redundancy, an important dimension of resilience, is crucial for providing alternative travel choices during disastrous events. This chapter addresses a new way of improving network redundancy by retrofitting critical components to withstand future disasters. The transportation redundancy-oriented network retrofit problem aims to find the optimal retrofit resource allocation strategy that maintains the highest level of network redundancy under uncertain disastrous events. To cope with the uncertainty, we develop the distributionally robust optimization (RNRP-DRO) model with χ²-distance ambiguity set. However, the lack of explicit mathematical representation for the network redundancy leads to an intractable optimization model. To tackle this issue, we propose a linear regression approximation of the implicit loss of network redundancy function. The approximated RNRP-DRO problem is then reformulated as a mixed-binary second-order cone program, and a Benders decomposition algorithm is developed to improve the computational efficiency. We further discuss the theoretical properties of the model and solution algorithms. Numerical experiments in the realistic Winnipeg network demonstrate the practical importance of the proposed model and validate the effectiveness of the proposed solution approaches."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Distributionally robust solution schemes for two-stage optimization and interdiction problems under uncertainty"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hanasusanto, Grani Adiwena"],"dc:contributor.committeemember":["Leibowicz, Benjamin D","He, Long","Boyles, Stephen"],"dc:creator":["Fan, Xiangyi"],"dc:date.accessioned":["2025-03-11T00:05:58Z"],"dc:date.available":["2025-03-11T00:05:58Z"],"dc:date.issued":["2023-05"],"dc:description.abstract":["Decision-makers often have to make decisions in the presence of uncertainty. One can use optimization models with uncertain parameters to formulate the decision problems. Despite its wide applications in real-world problems, optimization under uncertainty gives rise to computational challenges. This thesis aims to design tractable solution schemes with performance guarantees for two-stage optimization and interdiction problems. We utilize the distributionally robust optimization scheme to develop the solution framework, which is an emerging scheme in optimization under uncertainty. In addition, solution algorithms are designed for optimization problems to further reduce computational cost. The first part of the dissertation studies two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied by the uncertain parameters in both the objective function and the constraints. To mitigate the computational intractability of infinite-dimensional optimization, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. Based on the decision rule structure, we develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. The emerging optimization problem can be reformulated as an exact copositive program that admits tractable approximations in semidefinite programming. We then design a decomposition algorithm where smaller-size semidefinite programs can be solved in parallel, which further reduces the runtime. Through numerical examples, we empirically demonstrate that our method produces significantly better solutions with reasonable computational effort than the traditional sample-average approximation scheme, especially when the data is limited. Next, we study the interdiction problem under uncertainty, where partial information about the operations of the follower is unavailable when the leader makes interdiction decisions. The distributionally robust optimization scheme is applied to yield a secure but not too conservative interdiction decision. The problem admits a finite-dimensional copositive-based reformulation; however, the resulting mixed-binary conic program is still intractable. We propose a decomposition algorithm that iteratively finds the optimal solution by solving the relaxed master problem, which is constructed from the integer optimality cuts and the Benders cuts. Both cuts evaluate the performance at the current interdiction solution and provide underestimation at the other feasible points. We evaluate the performance of the distributionally robust interdiction decisions and showcase the effectiveness of the multi-cut decomposition algorithm on the competitive facility location problem and the 0-1 knapsack interdiction problem. The final project we explore is a network retrofit problem. Transportation network redundancy, an important dimension of resilience, is crucial for providing alternative travel choices during disastrous events. This chapter addresses a new way of improving network redundancy by retrofitting critical components to withstand future disasters. The transportation redundancy-oriented network retrofit problem aims to find the optimal retrofit resource allocation strategy that maintains the highest level of network redundancy under uncertain disastrous events. To cope with the uncertainty, we develop the distributionally robust optimization (RNRP-DRO) model with χ²-distance ambiguity set. However, the lack of explicit mathematical representation for the network redundancy leads to an intractable optimization model. To tackle this issue, we propose a linear regression approximation of the implicit loss of network redundancy function. The approximated RNRP-DRO problem is then reformulated as a mixed-binary second-order cone program, and a Benders decomposition algorithm is developed to improve the computational efficiency. We further discuss the theoretical properties of the model and solution algorithms. Numerical experiments in the realistic Winnipeg network demonstrate the practical importance of the proposed model and validate the effectiveness of the proposed solution approaches."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2152/131954","https://doi.org/10.26153/tsw/59298"],"dc:language.iso":["en"],"dc:subject":["Optimization under uncertainty","Distributionally robust optimization"],"dc:title":["Distributionally robust solution schemes for two-stage optimization and interdiction problems under uncertainty"],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The University of Texas at Austin"]},"updated_at":"2026-07-24T05:01:10Z"}