New models for the location of controversial facilities: A bilevel programming approach

Motivated by recent real-life applications in Location Theory in which the location decisions generate controversy, we propose a novel bilevel location model in which, on the one hand, there is a leader that chooses among a number of fixed potential locations which ones to establish. Next, on the second hand, there is one or several followers that, once the leader location facilities have been set, chooses his location points in a continuous framework. The leader’s goal is to maximize some proxy to the weighted distance to the follower’s location points, while the follower(s) aim is to locate his location points as close as possible to the leader ones. We develop the bilevel location model for one follower and for any polyhedral distance, and we extend it for several followers and any ℓp-norm, p ∈ Q, p ≥ 1. We prove the NP-hardness of the problem and propose different mixed integer linear programming formulations. Moreover, we develop alternative Benders decomposition algorithms for the problem. Finally, we report some computational results comparing the formulations and the Benders decompositions on a set of instances.Fonds de la Recherche Scientique - FNRSMinisterio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Campaigning Via LPs: Solving Blotto and Beyond

The competition between the Republican and the Democrat nominees in the U.S presidential election is known as Colonel Blotto in game theory. In the classical Colonel Blotto game -- introduced by Borel in 1921 -- two colonels simultaneously distribute their troops across multiple battlefields. The outcome of each battlefield is determined by a winner-take-all rule, independently of other battlefields. In the original formulation, the goal of each colonel is to win as many battlefields as possible. The Colonel Blotto game and its extensions have been used in a wide range of applications from political campaigns (exemplified by the U.S presidential election) to marketing campaigns, from (innovative) technology competitions, to sports competitions. For almost a century, there have been persistent efforts for finding the optimal strategies of the Colonel Blotto game, however it was left unanswered whether the optimal strategies are polynomially tractable. In this thesis, we present several algorithms for solving Blotto games in polynomial time and will discuss their applications in practice

Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity

Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an algorithm is governed by its adaptivity, which measures the number of sequential rounds needed if the algorithm can execute polynomially-many independent oracle queries in parallel. While low adaptivity is ideal, it is not sufficient for an algorithm to be efficient in practice---there are many applications of distributed submodular optimization where the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of submodular maximization. In this paper, we give the first constant-factor approximation algorithm for maximizing a non-monotone submodular function subject to a cardinality constraint $k$ that runs in $O(\log(n))$ adaptive rounds and makes $O(n \log(k))$ oracle queries in expectation. In our empirical study, we use three real-world applications to compare our algorithm with several benchmarks for non-monotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries.Comment: 12 pages, 8 figure

The Impact of Stealthy Attacks on Smart Grid Performance: Tradeoffs and Implications

The smart grid is envisioned to significantly enhance the efficiency of energy consumption, by utilizing two-way communication channels between consumers and operators. For example, operators can opportunistically leverage the delay tolerance of energy demands in order to balance the energy load over time, and hence, reduce the total operational cost. This opportunity, however, comes with security threats, as the grid becomes more vulnerable to cyber-attacks. In this paper, we study the impact of such malicious cyber-attacks on the energy efficiency of the grid in a simplified setup. More precisely, we consider a simple model where the energy demands of the smart grid consumers are intercepted and altered by an active attacker before they arrive at the operator, who is equipped with limited intrusion detection capabilities. We formulate the resulting optimization problems faced by the operator and the attacker and propose several scheduling and attack strategies for both parties. Interestingly, our results show that, as opposed to facilitating cost reduction in the smart grid, increasing the delay tolerance of the energy demands potentially allows the attacker to force increased costs on the system. This highlights the need for carefully constructed and robust intrusion detection mechanisms at the operator.Comment: Technical report - this work was accepted to IEEE Transactions on Control of Network Systems, 2016. arXiv admin note: substantial text overlap with arXiv:1209.176

A review of network location theory and models

Cataloged from PDF version of article.In this study, we review the existing literature on network location problems. The study has a broad scope that includes problems featuring desirable and undesirable facilities, point facilities and extensive facilities, monopolistic and competitive markets, and single or multiple objectives. Deterministic and stochastic models as well as robust models are covered. Demand data aggregation is also discussed. More than 500 papers in this area are reviewed and critical issues, research directions, and problem extensions are emphasized.Erdoğan, Damla SelinM.S

Learning Strategies in Decentralized Matching Markets under Uncertain Preferences

We study the problem of decision-making in the setting of a scarcity of shared resources when the preferences of agents are unknown a priori and must be learned from data. Taking the two-sided matching market as a running example, we focus on the decentralized setting, where agents do not share their learned preferences with a central authority. Our approach is based on the representation of preferences in a reproducing kernel Hilbert space, and a learning algorithm for preferences that accounts for uncertainty due to the competition among the agents in the market. Under regularity conditions, we show that our estimator of preferences converges at a minimax optimal rate. Given this result, we derive optimal strategies that maximize agents' expected payoffs and we calibrate the uncertain state by taking opportunity costs into account. We also derive an incentive-compatibility property and show that the outcome from the learned strategies has a stability property. Finally, we prove a fairness property that asserts that there exists no justified envy according to the learned strategies