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Fast Combinatorial Algorithm for Optimizing the Spread of Cascades
... We then create a very fast algorithm, based on the sample average approximation (SAA) (Sheldon et al. 2010;Wu, Sheldon, and Zilberstein 2015) and network design algorithms, to compute a high quality solution for the GPTNP problem in large-scale networks. In our algorithm, we recast the GPTNP problem as a deterministic optimization problem using the SAA method and a novel sampling procedure. ...
... The resulting problem is called Prize-Collecting Set Weighted Shortest Path Steiner Graph (PCSW-SPSG). A bisection procedure (Wu, Sheldon, and Zilberstein 2015) is then used to find a value of β for which the near optimal solution of PCSW-SPSG is also a near optimal solution of the BSW-SPSG problem. Finally, we derive a primal-dual algorithm (Williamson and Shmoys 2011) to solve the PCSW-SPSG problem approximately. ...
... Otherwise, the higher half is abandoned. The details of this method are in (Wu, Sheldon, and Zilberstein 2015). while there exists some active pairs do 8: ...
We propose a decision making framework to optimize the resilience of road networks to natural disasters such as floods. Our model generalizes an existing one for this problem by allowing roads with a broad class of stochastic delay models. We then present a fast algorithm based on the sample average approximation (SAA) method and network design techniques to solve this problem approximately. On a small existing benchmark, our algorithm produces near-optimal solutions and the SAA method converges quickly with a small number of samples. We then apply our algorithm to a large real-world problem to optimize the resilience of a road network to failures of stream crossing structures to minimize travel times of emergency medical service vehicles. On medium-sized networks, our algorithm obtains solutions of comparable quality to a greedy baseline method but is 30–60 times faster. Our algorithm is the only existing algorithm that can scale to the full network, which has many thousands of edges.
... Problem (5) can be formulated as a MIP. Using the maxflow encoding from one source to multiple targets, we introduce a more compact MIP formulation than the one in paper[Wu et al., 2015]which uses O(|V |) times more variables (|V | is the number of nodes). This new compact formulation is shown inFig. ...
... However, their algorithms only work for tree-structured networks, and they also assume that stochastic events are all independent. Recently, several fast approximate algorithms based on the primal-dual technique have been developed to solve several deterministic network design problems similar to our problem (5)[Wu et al., 2015;, but they do not guarantee to produce the optimal solutions. It is an interesting future work to see how we can combine their algorithms and XOR sampling techniques to tradeoff the optimality with efficiency on large-scale networks.Xue et al. (2017)use an optimization algorithm by adding XOR constraints to solve a related landscape connectivity problem. ...
Many network optimization problems can be formulated as stochastic network design problems in which edges are present or absent stochastically. Furthermore, protective actions can guarantee that edges will remain present. We consider the problem of finding the optimal protection strategy under a budget limit in order to maximize some connectivity measurements of the network. Previous approaches rely on the assumption that edges are independent. In this paper, we consider a more realistic setting where multiple edges are not independent due to natural disasters or regional events that make the states of multiple edges stochastically correlated. We use Markov Random Fields to model the correlation and define a new stochastic network design framework. We provide a novel algorithm based on Sample Average Approximation (SAA) coupled with a Gibbs or XOR sampler. The experimental results on real road network data show that the policies produced by SAA with the XOR sampler have higher quality and lower variance compared to SAA with Gibbs sampler.
... Problem (5) can be formulated as a MIP. Using the maxflow encoding from one source to multiple targets, we introduce a more compact MIP formulation than the one in paper[Wu et al., 2015]which uses O(|V |) times more variables (|V | is the number of nodes). This new compact formulation is shown inFig. ...
... However, their algorithms only work for treestructured networks, and they also assume that stochastic events are all independent. Recently, several fast approximate algorithms based on the primal-dual technique have been developed to solve several deterministic network design problems similar to our problem (5)[Wu et al., 2015;, but they do not guarantee to produce the optimal solutions. It is an interesting future work to see how we can combine their algorithms and XOR sampling techniques to tradeoff the optimality with efficiency on large-scale networks.Xue et al. (2017)use an optimization algorithm by adding XOR constraints to solve a related landscape connectivity problem. ...
Many network optimization problems can be formulated as stochastic network design problems in which edges are present or absent stochastically. Furthermore, protective actions can guarantee that edges will remain present. We consider the problem of finding the optimal protection strategy under a budget limit in order to maximize some connectivity measurements of the network. Previous approaches rely on the assumption that edges are independent. In this paper, we consider a more realistic setting where multiple edges are not independent due to natural disasters or regional events that make the states of multiple edges stochastically correlated. We use Markov Random Fields to model the correlation and define a new stochastic network design framework. We provide a novel algorithm based on Sample Average Approximation (SAA) coupled with a Gibbs or XOR sampler. The experimental results on real road network data show that the policies produced by SAA with the XOR sampler have higher quality and lower variance compared to SAA with Gibbs sampler.
... As a motivating SMC application, stochastic connectivity optimization searches for the optimal plan to reinforce the network structure so its connectivity is preserved under stochastic events -a central problem for a city planner who works on securing her residents multiple paths to emergency shelters in case of natural disasters. This problem is useful for disaster preparation (Wu, Sheldon, and Zilberstein 2015), bio-diversity protection , internet resilience (Israeli and Wood 2002), social influence maximization (Kempe, Kleinberg, and Tardos 2005), energy security (Almeida et al. 2019), etc. It requires symbolic reasoning (satisfiability) to decide which roads to reinforce and where to place emergency shelters, and statistical inference (model counting) to reason about the number of paths to shelters and the probabilities of natural disasters. ...
Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical AI. SMC searches for policy interventions to control probabilistic outcomes. Solving SMC is challenging because of its highly intractable nature (NP^PP-complete), incorporating statistical inference and symbolic reasoning. Previous research on SMC solving lacks provable guarantees and/or suffers from suboptimal empirical performance, especially when combinatorial constraints are present. We propose XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly intractable SMC problems with constant approximation guarantees. XOR-SMC transforms the highly intractable SMC into satisfiability problems by replacing the model counting in SMC with SAT formulae subject to randomized XOR constraints. Experiments on solving important SMC problems in AI for social good demonstrate that XOR-SMC outperforms several baselines both in solution quality and running time.
... Conservation strategies, which correspond to network design, include deciding which land parcels to purchase for conservation within a fixed budget. This problem has recently received much attention in the AI community (Sheldon et al. 2010;Ahmadizadeh et al. 2010;Golovin et al. 2011;Kumar, Wu, and Zilberstein 2012;Wu et al. 2013;Wu, Sheldon, and Zilberstein 2014;Xue, Fern, and Sheldon 2014;Wu, Sheldon, and Zilberstein 2015). ...
We address the problem of robust decision making for stochastic network design. Our work is motivated by spatial conservation planning where the goal is to take management decisions within a fixed budget to maximize the expected spread of a population of species over a network of land parcels. Most previous work for this problem assumes that accurate estimates of different network parameters (edge activation probabilities, habitat suitability scores) are available, which is an unrealistic assumption. To address this shortcoming, we assume that network parameters are only partially known, specified via interval bounds. We then develop a decision making approach that computes the solution with minimax regret. We provide new theoretical results regarding the structure of the minmax regret solution which help develop a computationally efficient approach. Empirically, we show that previous approaches that work on point estimates of network parameters result in high regret on several standard benchmarks, while our approach provides significantly more robust solutions.
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