2021

Aziz, Haris; Cseh, Agnes; Dickerson, John; McElfresh, Duncan Optimal Kidney Exchange with ImmunosuppressantsConference on Artificial Intelligence (AAAI) 2021: 21–29
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Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.
@inproceedings{haris2021optimal, abstract = {Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.}, author = {Aziz, Haris and Cseh, Agnes and Dickerson, John and McElfresh, Duncan}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai agnescseh duncanmcelfresh harisaziz johndickerson year2021}, pages = {21-29}, title = {Optimal Kidney Exchange with Immunosuppressants}, year = 2021 }

Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Lowski, Stefanie; Melnichenko, Anna Selfish Creation of Social NetworksConference on Artificial Intelligence (AAAI) 2021: 5185–5193
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Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks. We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.
@inproceedings{bilo2021selfish, abstract = {Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks. We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.}, author = {Bilò, Davide and Friedrich, Tobias and Lenzner, Pascal and Lowski, Stefanie and Melnichenko, Anna}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai annamelnichenko davidebilo pascallenzner stefanielowski tobiasfriedrich year2021}, pages = {5185-5193}, title = {Selfish Creation of Social Networks}, year = 2021 }

2019

Friedrich, Tobias; Göbel, Andreas; Neumann, Frank; Quinzan, Francesco; Rothenberger, Ralf Greedy Maximization of Functions with Bounded Curvature Under Partition Matroid ConstraintsConference on Artificial Intelligence (AAAI) 2019: 2272–2279
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We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three real-world problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is well-suited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for (approximate) monotonicity to get good approximate solutions.
@inproceedings{AAAI19a, abstract = {We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three real-world problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is well-suited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for (approximate) monotonicity to get good approximate solutions.}, author = {Friedrich, Tobias and Göbel, Andreas and Neumann, Frank and Quinzan, Francesco and Rothenberger, Ralf}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai andreasgoebel francescoquinzan frankneumann ralfrothenberger tobiasfriedrich year2019}, pages = {2272-2279}, title = {Greedy Maximization of Functions with Bounded Curvature Under Partition Matroid Constraints}, year = 2019 }

Roostapour, Vahid; Neumann, Aneta; Neumann, Frank; Friedrich, Tobias Pareto Optimization for Subset Selection with Dynamic Cost ConstraintsConference on Artificial Intelligence (AAAI) 2019: 2354–2361
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In this paper, we consider subset selection problems for functions \(f\) with constraints where the constraint bound \(B\) changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a \( phi= (\alpha_f/2)(1-\frac{1}{e^{\alpha_f}})\)-approximation, where \(\alpha_f\) is the submodularity ratio, for each possible constraint bound \(b \leq B\). Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that \(B\) increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.
@inproceedings{AAAI19b, abstract = {In this paper, we consider subset selection problems for functions \(f\) with constraints where the constraint bound \(B\) changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a \( \phi= (\alpha_f/2)(1-\frac{1}{e^{\alpha_f}})\)-approximation, where \(\alpha_f\) is the submodularity ratio, for each possible constraint bound \(b \leq B\). Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that \(B\) increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.}, author = {Roostapour, Vahid and Neumann, Aneta and Neumann, Frank and Friedrich, Tobias}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai anetaneumann frankneumann tobiasfriedrich vahidroostapour year2019}, pages = {2354-2361}, title = {Pareto Optimization for Subset Selection with Dynamic Cost Constraints}, year = 2019 }

2017

Friedrich, Tobias; Kötzing, Timo; Wagner, Markus A Generic Bet-and-Run Strategy for Speeding Up Stochastic Local SearchConference on Artificial Intelligence (AAAI) 2017: 801–807
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A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific problems (and specific algorithms), restarts are typically not regarded as a general tool to speed up an optimization algorithm. In fact, many optimization algorithms do not employ restarts at all. Recently, "bet-and-run" was introduced in the context of mixed-integer programming, where first a number of short runs with randomized initial conditions is made, and then the most promising run of these is continued. In this article, we consider two classical NP-complete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different bet-and-run strategies. In particular, our restart strategies do not take any problem knowledge into account, nor are tailored to the optimization algorithm. Therefore, they can be used off-the-shelf. We observe that state-of-the-art solvers for these problems can benefit significantly from restarts on standard benchmark instances.
@inproceedings{DBLP:conf/aaai/0001K017, abstract = {A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific problems (and specific algorithms), restarts are typically not regarded as a general tool to speed up an optimization algorithm. In fact, many optimization algorithms do not employ restarts at all. Recently, "bet-and-run" was introduced in the context of mixed-integer programming, where first a number of short runs with randomized initial conditions is made, and then the most promising run of these is continued. In this article, we consider two classical NP-complete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different bet-and-run strategies. In particular, our restart strategies do not take any problem knowledge into account, nor are tailored to the optimization algorithm. Therefore, they can be used off-the-shelf. We observe that state-of-the-art solvers for these problems can benefit significantly from restarts on standard benchmark instances.}, author = {Friedrich, Tobias and Kötzing, Timo and Wagner, Markus}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai markuswagner timokoetzing tobiasfriedrich year2017}, pages = {801-807}, title = {A Generic Bet-and-Run Strategy for Speeding Up Stochastic Local Search}, year = 2017 }

Friedrich, Tobias; Krohmer, Anton; Rothenberger, Ralf; Sutton, Andrew M. Phase Transitions for Scale-Free SAT FormulasConference on Artificial Intelligence (AAAI) 2017: 3893–3899
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Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scale-free formulas have a variable occurrence distribution that follows a power law. It has been conjectured that such a distribution is a more accurate model for some industrial instances than the uniform random model. Though it seems that there is already an awareness of a threshold phenomenon in such models, there is still a complete picture lacking. In contrast to the uniform model, the critical density threshold does not lie at a single point, but instead exhibits a functional dependency on the power-law exponent. For scale-free formulas with clauses of length \(k = 2\), we give a lower bound on the phase transition threshold as a function of the scaling parameter. We also perform computational studies that suggest our bound is tight and investigate the critical density for formulas with higher clause lengths. Similar to the uniform model, on formulas with \(k \geq 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.
@inproceedings{DBLP:conf/aaai/0001KRS17, abstract = {Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. In contrast to uniform random Boolean formulas, scale-free formulas have a variable occurrence distribution that follows a power law. It has been conjectured that such a distribution is a more accurate model for some industrial instances than the uniform random model. Though it seems that there is already an awareness of a threshold phenomenon in such models, there is still a complete picture lacking. In contrast to the uniform model, the critical density threshold does not lie at a single point, but instead exhibits a functional dependency on the power-law exponent. For scale-free formulas with clauses of length \(k = 2\), we give a lower bound on the phase transition threshold as a function of the scaling parameter. We also perform computational studies that suggest our bound is tight and investigate the critical density for formulas with higher clause lengths. Similar to the uniform model, on formulas with \(k \geq 3\), we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search.}, author = {Friedrich, Tobias and Krohmer, Anton and Rothenberger, Ralf and Sutton, Andrew M.}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai andrewmsutton antonkrohmer ralfrothenberger scalefree_sat tobiasfriedrich year2017}, pages = {3893-3899}, publisher = {AAAI Press}, title = {Phase Transitions for Scale-Free SAT Formulas}, year = 2017 }

Friedrich, Tobias; Neumann, Frank What’s Hot in Evolutionary ComputationConference on Artificial Intelligence (AAAI) 2017: 5064–5066
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We provide a brief overview on some hot topics in the area of evolutionary computation. Our main focus is on recent developments in the areas of combinatorial optimization and real-world applications. Furthermore, we highlight recent progress on the theoretical understanding of evolutionary computing methods.
@inproceedings{friedrich2017whats, abstract = {We provide a brief overview on some hot topics in the area of evolutionary computation. Our main focus is on recent developments in the areas of combinatorial optimization and real-world applications. Furthermore, we highlight recent progress on the theoretical understanding of evolutionary computing methods.}, author = {Friedrich, Tobias and Neumann, Frank}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai adelaide frankneumann tobiasfriedrich year2017}, pages = {5064-5066}, title = {What's Hot in Evolutionary Computation}, year = 2017 }

Katzmann, Maximilian; Komusiewicz, Christian Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover ProblemConference on Artificial Intelligence (AAAI) 2017: 846–852
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We investigate the potential of exhaustively exploring larger neighborhoods in local search algorithms for Minimum Vertex Cover. More precisely, we study whether, for moderate values of \(k\), it is feasible and worthwhile to determine, given a graph \(G\) with vertex cover \(C\), if there is a \(k\)-swap \(S\) such that \((C \setminus S) cup (S \setminus C)\) is a smaller vertex cover of \(G\). First, we describe an algorithm running in \(\Delta^{O(k) \cdot n\) time for searching the \(k\)-swap neighborhood on \(n\)-vertex graphs with maximum degree \(\Delta\). Then, we demonstrate that, by devising additional pruning rules that decrease the size of the search space, this algorithm can be implemented so that it solves the problem quickly for \(k \approx 20\). Finally, we show that it is worthwhile to consider moderately-sized \(k\)-swap neighborhoods. For our benchmark data set, we show that when combining our algorithm with a hill-climbing approach, the solution quality improves quickly with the radius \(k\) of the local search neighborhood and that in most cases optimal solutions can be found by setting \(k = 21\).
@inproceedings{DBLP:conf/aaai/KatzmannK17, abstract = {We investigate the potential of exhaustively exploring larger neighborhoods in local search algorithms for Minimum Vertex Cover. More precisely, we study whether, for moderate values of \(k\), it is feasible and worthwhile to determine, given a graph \(G\) with vertex cover \(C\), if there is a \(k\)-swap \(S\) such that \((C \setminus S) \cup (S \setminus C)\) is a smaller vertex cover of \(G\). First, we describe an algorithm running in \(\Delta^{O(k)} \cdot n\) time for searching the \(k\)-swap neighborhood on \(n\)-vertex graphs with maximum degree \(\Delta\). Then, we demonstrate that, by devising additional pruning rules that decrease the size of the search space, this algorithm can be implemented so that it solves the problem quickly for \(k \approx 20\). Finally, we show that it is worthwhile to consider moderately-sized \(k\)-swap neighborhoods. For our benchmark data set, we show that when combining our algorithm with a hill-climbing approach, the solution quality improves quickly with the radius \(k\) of the local search neighborhood and that in most cases optimal solutions can be found by setting \(k = 21\).}, author = {Katzmann, Maximilian and Komusiewicz, Christian}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {AAAI maximiliankatzmann year2017}, pages = {846-852}, title = {Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem}, year = 2017 }

2012

Sutton, Andrew M.; Neumann, Frank A Parameterized Runtime Analysis of Evolutionary Algorithms for the Euclidean Traveling Salesperson ProblemConference on Artificial Intelligence (AAAI) 2012
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Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound the runtime of simple evolutionary algorithms. Our analysis studies the runtime in dependence of the number of inner points \(k\) and shows that \((\mu + \lambda)\) evolutionary algorithms solve the Euclidean TSP in expected time \(O((\mu / \lambda) cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon)+(\mu / \lambda) cdot n^4k(2k-1)!)\) where \(\gamma\) is a function of the minimum angle \(epsilon\) between any three points. Finally, our analysis provides insights into designing a mutation operator that improves the upper bound on expected runtime. We show that a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps results in an upper bound of \(O((\mu / \lambda) cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon) + (\mu / \lambda) cdot n^2k(k-1)!)\) for the \((\mu + \lambda)\) EA.
@inproceedings{DBLP:conf/aaai/SuttonN12, abstract = {Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound the runtime of simple evolutionary algorithms. Our analysis studies the runtime in dependence of the number of inner points \(k\) and shows that \((\mu + \lambda)\) evolutionary algorithms solve the Euclidean TSP in expected time \(O((\mu / \lambda) \cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon)+(\mu / \lambda) \cdot n^{4k}(2k-1)!)\) where \(\gamma\) is a function of the minimum angle \(epsilon\) between any three points. Finally, our analysis provides insights into designing a mutation operator that improves the upper bound on expected runtime. We show that a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps results in an upper bound of \(O((\mu / \lambda) \cdot n^3 \gamma(\epsilon) + n \gamma(\epsilon) + (\mu / \lambda) \cdot n^{2k}(k-1)!)\) for the \((\mu + \lambda)\) EA.}, author = {Sutton, Andrew M. and Neumann, Frank}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai andrewmsutton frankneumann imported year2012}, publisher = {{AAAI} Press}, title = {A Parameterized Runtime Analysis of Evolutionary Algorithms for the Euclidean Traveling Salesperson Problem}, year = 2012 }