Hidden convex optimization is a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we study a family of hidden convex optimization that joints the classical trust region subproblem (TRS) with convex optimization (CO). It also includes p-regularized subproblem (p > 2) as a special case. We present a comprehensive study on local optimality conditions. In particular, a sufficient condition is given to ensure that there is at most one local nonglobal minimizer, and at this point, the standard second-order sufficient optimality condition is necessary. To our surprise, although (TRS) has at most one local nonglobal minimizer and (CO) has no local nonglobal minimizer, their joint problem could have any finite number of local nonglobal minimizers. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12171021, 12131004, and 11822103], the Beijing Natural Science Foundation [Grant Z180005], and the Fundamental Research Funds for the Central Universities. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2023.0089 .
{"title":"Local Optimality Conditions for a Family of Hidden Convex Optimization","authors":"Mengmeng Song, Yong Xia, Hongying Liu","doi":"10.1287/ijoo.2023.0089","DOIUrl":"https://doi.org/10.1287/ijoo.2023.0089","url":null,"abstract":"Hidden convex optimization is a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we study a family of hidden convex optimization that joints the classical trust region subproblem (TRS) with convex optimization (CO). It also includes p-regularized subproblem (p > 2) as a special case. We present a comprehensive study on local optimality conditions. In particular, a sufficient condition is given to ensure that there is at most one local nonglobal minimizer, and at this point, the standard second-order sufficient optimality condition is necessary. To our surprise, although (TRS) has at most one local nonglobal minimizer and (CO) has no local nonglobal minimizer, their joint problem could have any finite number of local nonglobal minimizers. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12171021, 12131004, and 11822103], the Beijing Natural Science Foundation [Grant Z180005], and the Fundamental Research Funds for the Central Universities. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2023.0089 .","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42537025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna Jacobson, Filippo Pecci, N. Sepulveda, Qingyu Xu, J. Jenkins
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or mixed integer linear programming (MILP) problems. Despite the relative efficiency and maturity of LP and MILP solvers, large scale problems are often intractable without abstractions that impact quality of results and generalizability of findings. We consider a macro-energy systems planning problem with detailed operations and policy constraints and formulate a computationally efficient Benders decomposition separating investments from operations and decoupling operational timesteps using budgeting variables in the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints coupling decisions across time periods (e.g., policy constraints) within a decomposed framework. Runtime scales linearly with temporal resolution; tests demonstrate substantial runtime improvement for all MILP formulations and for some LP formulations depending on problem size relative to analogous monolithic models solved with state-of-the-art commercial solvers. Our algorithm is applicable to planning problems in other domains (e.g., water, transportation networks, production processes) and can solve large-scale problems otherwise intractable. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty, improving recommendation accuracy. Funding: Funding for this work was provided by the Princeton Carbon Mitigation Initiative (funded by a gift from BP) and the Princeton Zero-carbon Technology Consortium (funded by gifts from GE, Google, ClearPath, and Breakthrough Energy). Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0005 .
{"title":"A Computationally Efficient Benders Decomposition for Energy Systems Planning Problems with Detailed Operations and Time-Coupling Constraints","authors":"Anna Jacobson, Filippo Pecci, N. Sepulveda, Qingyu Xu, J. Jenkins","doi":"10.1287/ijoo.2023.0005","DOIUrl":"https://doi.org/10.1287/ijoo.2023.0005","url":null,"abstract":"Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or mixed integer linear programming (MILP) problems. Despite the relative efficiency and maturity of LP and MILP solvers, large scale problems are often intractable without abstractions that impact quality of results and generalizability of findings. We consider a macro-energy systems planning problem with detailed operations and policy constraints and formulate a computationally efficient Benders decomposition separating investments from operations and decoupling operational timesteps using budgeting variables in the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints coupling decisions across time periods (e.g., policy constraints) within a decomposed framework. Runtime scales linearly with temporal resolution; tests demonstrate substantial runtime improvement for all MILP formulations and for some LP formulations depending on problem size relative to analogous monolithic models solved with state-of-the-art commercial solvers. Our algorithm is applicable to planning problems in other domains (e.g., water, transportation networks, production processes) and can solve large-scale problems otherwise intractable. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty, improving recommendation accuracy. Funding: Funding for this work was provided by the Princeton Carbon Mitigation Initiative (funded by a gift from BP) and the Princeton Zero-carbon Technology Consortium (funded by gifts from GE, Google, ClearPath, and Breakthrough Energy). Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0005 .","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41540210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study two-stage linear programs with uncertainty in the right-hand side in which the uncertain parameters of the problem are correlated with a variable called the side information, which is observed before an action is made. We propose an approach in which a linear regression model is used to provide a point prediction for the uncertain parameters of the problem. We use an approach called smart predict-then-optimize. Rather than minimizing a typical loss function for regression, such as squared error, we approximately minimize the objective value of the resulting solutions to the optimization problem. We conduct computational tests that compare our method with other approaches for optimization problems with side information. The results indicate that our method can provide better objective values in situations where the true model is reasonably close to a linear model. Although the procedure we propose requires a longer time for fitting than existing methods, it requires less time to produce a decision for each given observation of the side information. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0088 .
{"title":"Smart Predict-then-Optimize for Two-Stage Linear Programs with Side Information","authors":"Alexander S. Estes, Jean-Philippe P. Richard","doi":"10.1287/ijoo.2023.0088","DOIUrl":"https://doi.org/10.1287/ijoo.2023.0088","url":null,"abstract":"We study two-stage linear programs with uncertainty in the right-hand side in which the uncertain parameters of the problem are correlated with a variable called the side information, which is observed before an action is made. We propose an approach in which a linear regression model is used to provide a point prediction for the uncertain parameters of the problem. We use an approach called smart predict-then-optimize. Rather than minimizing a typical loss function for regression, such as squared error, we approximately minimize the objective value of the resulting solutions to the optimization problem. We conduct computational tests that compare our method with other approaches for optimization problems with side information. The results indicate that our method can provide better objective values in situations where the true model is reasonably close to a linear model. Although the procedure we propose requires a longer time for fitting than existing methods, it requires less time to produce a decision for each given observation of the side information. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0088 .","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have access to the noisy evaluations of the objective and constraint functions, we propose and analyze stochastic zeroth-order algorithms for solving this class of stochastic optimization problem. When the domain of the functions is [Formula: see text], assuming there are m constraint functions, we establish oracle complexities of order [Formula: see text] and [Formula: see text] in the convex and nonconvex settings, respectively, where ϵ represents the accuracy of the solutions required in appropriately defined metrics. The established oracle complexities are, to our knowledge, the first such results in the literature for functionally constrained stochastic zeroth-order optimization problems. We demonstrate the applicability of our algorithms by illustrating their superior performance on the problem of hyperparameter tuning for sampling algorithms and neural network training. Funding: K. Balasubramanian was partially supported by a seed grant from the Center for Data Science and Artificial Intelligence Research, University of California–Davis, and the National Science Foundation [Grant DMS-2053918].
{"title":"Stochastic Zeroth-Order Functional Constrained Optimization: Oracle Complexity and Applications","authors":"A. Nguyen, K. Balasubramanian","doi":"10.1287/ijoo.2022.0085","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0085","url":null,"abstract":"Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have access to the noisy evaluations of the objective and constraint functions, we propose and analyze stochastic zeroth-order algorithms for solving this class of stochastic optimization problem. When the domain of the functions is [Formula: see text], assuming there are m constraint functions, we establish oracle complexities of order [Formula: see text] and [Formula: see text] in the convex and nonconvex settings, respectively, where ϵ represents the accuracy of the solutions required in appropriately defined metrics. The established oracle complexities are, to our knowledge, the first such results in the literature for functionally constrained stochastic zeroth-order optimization problems. We demonstrate the applicability of our algorithms by illustrating their superior performance on the problem of hyperparameter tuning for sampling algorithms and neural network training. Funding: K. Balasubramanian was partially supported by a seed grant from the Center for Data Science and Artificial Intelligence Research, University of California–Davis, and the National Science Foundation [Grant DMS-2053918].","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46633593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrew Mastin, Arden Baxter, Amelia Musselman, Jean-Paul Watson
We define the interdiction defense problem as a game over a set of targets with three stages: a first stage where the defender protects a subset of targets, a second stage where the attacker observes the defense decision and attacks a subset of targets, and a third stage where the defender optimizes a system using only the surviving targets. We present a novel algorithm for optimally solving such problems that uses repeated calls to an attacker’s best response oracle. For cases where the defender can defend at most k targets and the attacker can attack at most z targets, we prove that the algorithm makes at most [Formula: see text] calls to the oracle. In application to the direct current optimal power flow problem, we present a new mixed integer programming formulation with bounded big-M values to function as a best response oracle. We use this oracle along with the algorithm to solve a defender-attacker-defender version of the optimal power flow problem. On standard test instances, we find solutions with larger values of k and z than shown in previous studies and with runtimes that are an order of magnitude faster than column and constraint generation.
{"title":"Best Response Intersection: An Optimal Algorithm for Interdiction Defense","authors":"Andrew Mastin, Arden Baxter, Amelia Musselman, Jean-Paul Watson","doi":"10.1287/ijoo.2022.0081","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0081","url":null,"abstract":"We define the interdiction defense problem as a game over a set of targets with three stages: a first stage where the defender protects a subset of targets, a second stage where the attacker observes the defense decision and attacks a subset of targets, and a third stage where the defender optimizes a system using only the surviving targets. We present a novel algorithm for optimally solving such problems that uses repeated calls to an attacker’s best response oracle. For cases where the defender can defend at most k targets and the attacker can attack at most z targets, we prove that the algorithm makes at most [Formula: see text] calls to the oracle. In application to the direct current optimal power flow problem, we present a new mixed integer programming formulation with bounded big-M values to function as a best response oracle. We use this oracle along with the algorithm to solve a defender-attacker-defender version of the optimal power flow problem. On standard test instances, we find solutions with larger values of k and z than shown in previous studies and with runtimes that are an order of magnitude faster than column and constraint generation.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43633304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a holistic framework for prescriptive analytics. Given side data x, decisions z, and uncertain quantities y that are functions of x and z, we propose a framework that simultaneously predicts y and prescribes the “should be” optimal decisions [Formula: see text]. The algorithm can accommodate a large number of predictive machine learning models as well as continuous and discrete decisions of high cardinality. It also allows for constraints on these decision variables. We show wide applicability and strong computational performances on synthetic experiments and on two real-world case studies.
{"title":"Holistic Prescriptive Analytics for Continuous and Constrained Optimization Problems","authors":"D. Bertsimas, O. Skali Lami","doi":"10.1287/ijoo.2022.0080","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0080","url":null,"abstract":"We present a holistic framework for prescriptive analytics. Given side data x, decisions z, and uncertain quantities y that are functions of x and z, we propose a framework that simultaneously predicts y and prescribes the “should be” optimal decisions [Formula: see text]. The algorithm can accommodate a large number of predictive machine learning models as well as continuous and discrete decisions of high cardinality. It also allows for constraints on these decision variables. We show wide applicability and strong computational performances on synthetic experiments and on two real-world case studies.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44426521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a discussion and evaluation of presolving methods for mixed-integer semidefinite programs. We generalize methods from the mixed-integer linear case and introduce new methods that depend on the semidefinite condition. The methods considered include adding linear constraints, deriving bounds relying on 2 × 2 minors of the semidefinite constraints, tightening of variable bounds based on solving a semidefinite program with one variable, and scaling of the matrices in the semidefinite constraints. Tightening the bounds of variables can also be used in a node presolving step. Along the way, we discuss how to solve semidefinite programs with one variable using a semismooth Newton method and the convergence of iteratively applying bound tightening. We then provide an extensive computational comparison of the different presolving methods, demonstrating their effectiveness with an improvement in running time of about 22% on average. The impact depends on the instance type and varies across the methods.
{"title":"Presolving for Mixed-Integer Semidefinite Optimization","authors":"Frederic Matter, M. Pfetsch","doi":"10.1287/ijoo.2022.0079","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0079","url":null,"abstract":"This paper provides a discussion and evaluation of presolving methods for mixed-integer semidefinite programs. We generalize methods from the mixed-integer linear case and introduce new methods that depend on the semidefinite condition. The methods considered include adding linear constraints, deriving bounds relying on 2 × 2 minors of the semidefinite constraints, tightening of variable bounds based on solving a semidefinite program with one variable, and scaling of the matrices in the semidefinite constraints. Tightening the bounds of variables can also be used in a node presolving step. Along the way, we discuss how to solve semidefinite programs with one variable using a semismooth Newton method and the convergence of iteratively applying bound tightening. We then provide an extensive computational comparison of the different presolving methods, demonstrating their effectiveness with an improvement in running time of about 22% on average. The impact depends on the instance type and varies across the methods.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43555374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a new approach to sensitivity analysis of the objective function coefficients in mixed-integer linear programming (MILP). We determine the maximal region of the coefficients for which the current solution remains optimal. The region is maximal in the sense that, for variations beyond this region, the optimal solution changes. For variations in a single objective function coefficient, we show how to obtain the region by biobjective mixed-integer linear programming. In particular, we prove that it suffices to determine the two extreme nondominated points adjacent to the optimal solution of the MILP problem. Furthermore, we show how to extend the methodology to simultaneous changes to two or more coefficients by use of multiobjective analysis. Two examples illustrate the applicability of the approach.
{"title":"MILP Sensitivity Analysis for the Objective Function Coefficients","authors":"K. A. Andersen, T. Boomsma, Lars Relund Nielsen","doi":"10.1287/ijoo.2022.0078","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0078","url":null,"abstract":"This paper presents a new approach to sensitivity analysis of the objective function coefficients in mixed-integer linear programming (MILP). We determine the maximal region of the coefficients for which the current solution remains optimal. The region is maximal in the sense that, for variations beyond this region, the optimal solution changes. For variations in a single objective function coefficient, we show how to obtain the region by biobjective mixed-integer linear programming. In particular, we prove that it suffices to determine the two extreme nondominated points adjacent to the optimal solution of the MILP problem. Furthermore, we show how to extend the methodology to simultaneous changes to two or more coefficients by use of multiobjective analysis. Two examples illustrate the applicability of the approach.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48051485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a distributionally robust optimization model based on kernel density estimation (KDE) and mean entropic value-at-risk (EVaR) is proposed, where the ambiguity set is defined as a KDE-[Formula: see text]-divergence “ball” centered at the empirical distribution in the weighted KDE distribution function family, which is a finite-dimensional set. Instead of the joint probability distribution of the random vector, the one-dimensional probability distribution of the random loss function is approximated by the univariate weighted KDE for dimensionality reduction. Under the mild conditions of the kernel and [Formula: see text]-divergence function, the computationally tractable reformulation of the corresponding distributionally robust mean-EVaR optimization model is derived by Fenchel’s duality theory. Convergence of the optimal value and the solution set of the distributionally robust optimization problem based on KDE and mean-EVaR to those of the corresponding stochastic programming problem with the true distribution is proved. For some special cases, including portfolio selection, newsvendor problem, and linear two-stage stochastic programming problem, concrete tractable reformulations are given. Primary empirical test results for portfolio selection and project management problems show that the proposed model is promising.
{"title":"Distributionally Robust Optimization Based on Kernel Density Estimation and Mean-Entropic Value-at-Risk","authors":"Wei Liu, Li Yang, Bo Yu","doi":"10.1287/ijoo.2022.0076","DOIUrl":"https://doi.org/10.1287/ijoo.2022.0076","url":null,"abstract":"In this paper, a distributionally robust optimization model based on kernel density estimation (KDE) and mean entropic value-at-risk (EVaR) is proposed, where the ambiguity set is defined as a KDE-[Formula: see text]-divergence “ball” centered at the empirical distribution in the weighted KDE distribution function family, which is a finite-dimensional set. Instead of the joint probability distribution of the random vector, the one-dimensional probability distribution of the random loss function is approximated by the univariate weighted KDE for dimensionality reduction. Under the mild conditions of the kernel and [Formula: see text]-divergence function, the computationally tractable reformulation of the corresponding distributionally robust mean-EVaR optimization model is derived by Fenchel’s duality theory. Convergence of the optimal value and the solution set of the distributionally robust optimization problem based on KDE and mean-EVaR to those of the corresponding stochastic programming problem with the true distribution is proved. For some special cases, including portfolio selection, newsvendor problem, and linear two-stage stochastic programming problem, concrete tractable reformulations are given. Primary empirical test results for portfolio selection and project management problems show that the proposed model is promising.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46522569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Niloufar Daemi, J. S. Borrero, Balabhaskar Balasundaram
The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly knit communities, whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this article, we consider a defender that can disrupt vertices of the adversarial network to minimize its threat, which leads us to consider a maximum s-club interdiction problem, where interdiction is penalized in the objective function. Using a new notion of H-heredity in s-clubs, we provide a mixed-integer linear programming formulation for this problem that uses far fewer constraints than the formulation based on standard techniques. We show that the linear programming relaxation of this formulation has no redundant constraints and identify facets of the convex hull of integral feasible solutions under special conditions. We further relate H-heredity to latency-s-connected dominating sets and design a decomposition branch-and-cut algorithm for the problem. Our implementation solves benchmark instances with more than 10,000 vertices in a matter of minutes and is orders of magnitude faster than algorithms based on the standard formulation.
{"title":"Interdicting Low-Diameter Cohesive Subgroups in Large-Scale Social Networks","authors":"Niloufar Daemi, J. S. Borrero, Balabhaskar Balasundaram","doi":"10.1287/ijoo.2021.0068","DOIUrl":"https://doi.org/10.1287/ijoo.2021.0068","url":null,"abstract":"The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly knit communities, whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this article, we consider a defender that can disrupt vertices of the adversarial network to minimize its threat, which leads us to consider a maximum s-club interdiction problem, where interdiction is penalized in the objective function. Using a new notion of H-heredity in s-clubs, we provide a mixed-integer linear programming formulation for this problem that uses far fewer constraints than the formulation based on standard techniques. We show that the linear programming relaxation of this formulation has no redundant constraints and identify facets of the convex hull of integral feasible solutions under special conditions. We further relate H-heredity to latency-s-connected dominating sets and design a decomposition branch-and-cut algorithm for the problem. Our implementation solves benchmark instances with more than 10,000 vertices in a matter of minutes and is orders of magnitude faster than algorithms based on the standard formulation.","PeriodicalId":73382,"journal":{"name":"INFORMS journal on optimization","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43220610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：