Bistra Dilkina

Solving connected subgraph problems in wildlife conservation

We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this work we focus on the budget-constrained version, where we maximize the total profit of the nodes in the subgraph subject to a budget constraint on the total cost. We propose several mixed-integer formulations for enforcing the subgraph connectivity requirement, which plays a key role in the combinatorial structure of the problem. We show that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow. We test our formulations on synthetic instances as well as on real-world instances of an important problem in environmental conservation concerning the design of wildlife corridors. Our encoding results in a much tighter LP relaxation, and more importantly, it results in finding better integer feasible solutions as well as much better upper bounds on the objective (often proving optimality or within less than 1% of optimality), both when considering the synthetic instances as well as the real-world wildlife corridor instances.

Scalable diffusion-aware optimization of network topology

How can we optimize the topology of a networked system to bring a flu under control, propel a video to popularity, or stifle a network malware in its infancy? Previous work on information diffusion has focused on modeling the diffusion dynamics and selecting nodes to maximize/minimize influence. Only a paucity of recent studies have attempted to address the network modification problems, where the goal is to either facilitate desirable spreads or curtail undesirable ones by adding or deleting a small subset of network nodes or edges. In this paper, we focus on the widely studied linear threshold diffusion model, and prove, for the first time, that the network modification problems under this model have supermodular objective functions. This surprising property allows us to design efficient data structures and scalable algorithms with provable approximation guarantees, despite the hardness of the problems in question. Both the time and space complexities of our algorithms are linear in the size of the network, which allows us to experiment with millions of nodes and edges. We show that our algorithms outperform an array of heuristics in terms of their effectiveness in controlling diffusion processes, often beating the next best by a significant margin.

The 2014 International Planning Competition: Progress and Trends

We review the 2014 International Planning Competition (IPC-2014), the eighth in a series of competitions starting in 1998. IPC-2014 was held in three separate parts to assess state-of-the-art in three prominent areas of planning research: the deterministic (classical) part (IPCD), the learning part (IPCL), and the probabilistic part (IPPC). Each part evaluated planning systems in ways that pushed the edge of existing planner performance by introducing new challenges, novel tasks, or both. The competition surpassed again the number of competitors than its predecessor, highlighting the competition’s central role in shaping the landscape of ongoing developments in evaluating planning systems.

Backdoors to Combinatorial Optimization: Feasibility and Optimality

There has been considerable interest in the identification of structural properties of combinatorial problems that lead, directly or indirectly, to the development of efficient algorithms for solving them. One such concept is that of a backdoor set--a set of variables such that once they are instantiated, the remaining problem simplifies to a tractable form. While backdoor sets were originally defined to capture structure in decision problems with discrete variables, here we introduce a notion of backdoors that captures structure in optimization problems, which often have both discrete and continuous variables. We show that finding a feasible solution and proving optimality are characterized by backdoors of different kinds and size. Surprisingly, in certain mixed integer programming problems, proving optimality involves a smaller backdoor set than finding the optimal solution. We also show extensive results on the number of backdoors of various sizes in optimization problems. Overall, this work demonstrates that backdoors, appropriately generalized, are also effective in capturing problem structure in optimization problems.

A Hybrid Schema for Systematic Local Search

We present a new hybrid constraint solving schema which retains some systematicity of constructive search while incorporating the heuristic guidance and lack of commitment to variable assignment of local search. Our method backtracks through a space of complete but possibly inconsistent solutions while supporting the freedom to move arbitrarily under heuristic guidance. The version of the schema described here combines minconflicts local search with conflict-directed backjumping. It is parametrized by a variable ordering relation which controls the order in which the search space is explored. Preliminary experimental results are given comparing two instances of the schema to forward checking with conflict-directed backjumping [17] (FC-CBJ).

Upgrading shortest paths in networks

We introduce the Upgrading Shortest Paths Problem, a new combinatorial problem for improving network connectivity with a wide range of applications from multicast communication to wildlife habitat conservation. We define the problem in terms of a network with node delays and a set of node upgrade actions, each associated with a cost and an upgraded (reduced) node delay. The goal is to choose a set of upgrade actions to minimize the shortest delay paths between demand pairs of terminals in the network, subject to a budget constraint. We show that this problem is NP-hard. We describe and test two greedy algorithms against an exact algorithm on synthetic data and on a real-world instance from wildlife habitat conservation. While the greedy algorithms can do arbitrarily poorly in the worst case, they perform fairly well in practice. For most of the instances, taking the better of the two greedy solutions accomplishes within 5% of optimal on our benchmarks.

Extending systematic local search for job shop scheduling problems

Hybrid search methods synthesize desirable aspects of both constructive and local search methods. Constructive methods are systematic and complete, but exhibit poor performance on large problems because bad decisions made early in the search persist for exponentially long times. In contrast, stochastic local search methods are immune to the tyranny of early mistakes. Local search methods replace systematicity with stochastic techniques for diversifying the search. However, the lack of systematicity makes remembering the history of past states problematic. Typically, hybrid methods introduce a stochastic element into a basically constructive search framework. Lynce [6] uses randomized backtracking in a complete boolean satisfiability solver which incorporates clause (nogood) learning to ensure completeness. Jussein & Lhomme [4] perform a constructive search while keeping conflict sets (nogoods) in a Tabu list and backtrack via a stochastic local search in the space of conflict sets. Our method, called Systematic Local Search (SysLS) [3], follows the opposite approach. We incorporate systematicity within an inherently stochastic search method (like [2]). SysLS searches through a space of complete variable assignments and relaxes the requirement for maintaining feasibility. It preserves full freedom to move heuristically in the search space with maximum heuristic information available. While many local search methods easily get trapped in local optima, SysLS records local optima as nogoods in a search memory. Nogoods force the search away from these maximally consistent but unacceptable solutions. Our method is analogous to other diversification mechanisms in local search (eg-Tabu search) but is systematic and inherits the sound resolution rule for nogood learning. In this paper, we extend SysLS for optimization and, in particular, for job shop scheduling problems.

Trade-offs and efficiencies in optimal budget-constrained multispecies corridor networks

Conservation biologists recognize that a system of isolated protected areas will be necessary but insufficient to meet biodiversity objectives. Current approaches to connecting core conservation areas through corridors consider optimal corridor placement based on a single optimization goal: commonly, maximizing the movement for a target species across a network of protected areas. We show that designing corridors for single species based on purely ecological criteria leads to extremely expensive linkages that are suboptimal for multispecies connectivity objectives. Similarly, acquiring the least-expensive linkages leads to ecologically poor solutions. We developed algorithms for optimizing corridors for multispecies use given a specific budget. We applied our approach in western Montana to demonstrate how the solutions may be used to evaluate trade-offs in connectivity for 2 species with different habitat requirements, different core areas, and different conservation values under different budgets. We evaluated corridors that were optimal for each species individually and for both species jointly. Incorporating a budget constraint and jointly optimizing for both species resulted in corridors that were close to the individual species movement-potential optima but with substantial cost savings. Our approach produced corridors that were within 14% and 11% of the best possible corridor connectivity for grizzly bears (Ursus arctos) and wolverines (Gulo gulo), respectively, and saved 75% of the cost. Similarly, joint optimization under a combined budget resulted in improved connectivity for both species relative to splitting the budget in 2 to optimize for each species individually. Our results demonstrate economies of scale and complementarities conservation planners can achieve by optimizing corridor designs for financial costs and for multiple species connectivity jointly. We believe that our approach will facilitate corridor conservation by reducing acquisition costs and by allowing derived corridors to more closely reflect conservation priorities.

Learning to Run Heuristics in Tree Search

“Primal heuristics” are a key contributor to the improved performance of exact branch-and-bound solvers for combinatorial optimization and integer programming. Perhaps the most crucial question concerning primal heuristics is that of at which nodes they should run, to which the typical answer is via hard-coded rules or fixed solver parameters tuned, offline, by trial-and-error. Alternatively, a heuristic should be run when it is most likely to succeed, based on the problem instance’s characteristics, the state of the search, etc. In this work, we study the problem of deciding at which node a heuristic should be run, such that the overall (primal) performance of the solver is optimized. To our knowledge, this is the first attempt at formalizing and systematically addressing this problem. Central to our approach is the use of Machine Learning (ML) for predicting whether a heuristic will succeed at a given node. We give a theoretical framework for analyzing this decision-making process in a simplified setting, propose a ML approach for modeling heuristic success likelihood, and design practical rules that leverage the ML models to dynamically decide whether to run a heuristic at each node of the search tree. Experimentally, our approach improves the primal performance of a stateof-the-art Mixed Integer Programming solver by up to 6% on a set of benchmark instances, and by up to 60% on a family of hard Independent Set instances.

Optimal Patrol Planning for Green Security Games with Black-Box Attackers.

Motivated by the problem of protecting endangered animals, there has been a surge of interests in optimizing patrol planning for conservation area protection. Previous efforts in these domains have mostly focused on optimizing patrol routes against a specific boundedly rational poacher behavior model that describes poachers’ choices of areas to attack. However, these planning algorithms do not apply to other poaching prediction models, particularly, those complex machine learning models which are recently shown to provide better prediction than traditional bounded-rationality-based models. Moreover, previous patrol planning algorithms do not handle the important concern whereby poachers infer the patrol routes by partially monitoring the rangers’ movements. In this paper, we propose OPERA, a general patrol planning framework that: (1) generates optimal implementable patrolling routes against a black-box attacker which can represent a wide range of poaching prediction models; (2) incorporates entropy maximization to ensure that the generated routes are more unpredictable and robust to poachers’ partial monitoring. Our experiments on a real-world dataset from Uganda’s Queen Elizabeth Protected Area (QEPA) show that OPERA results in better defender utility, more efficient coverage of the area and more unpredictability than benchmark algorithms and the past routes used by rangers at QEPA.