Resource optimization and scheduling is a costly, challenging problem that affects almost every aspect of our lives. One example that affects each of us is health care: Poor systems design and scheduling of resources can lead to higher rates of patient noncompliance and burnout of health care providers, as highlighted by the Institute of Medicine (Brandenburg et al. 2015). In aerospace manufacturing, every minute re-scheduling in response to dynamic disruptions in the build process of a Boeing 747 can cost up to $100.000. The military is also highly invested in the effective use of resources. In missile defense, for example, operators must =solve a challenging weapon-to-target problem, balancing the cost of expendable, defensive weapons while hedging against uncertainty in adversaries’ tactics. Researchers in artificial intelligence (AI) planning and scheduling strive to develop algorithms to improve resource allocation. However, there are two primary challenges. First, optimal task allocation and sequencing with upper and lower-bound temporal constraints (i.e., deadlines and wait constraints) is NP-Hard (Bertsimas and Weismantel 2005). Approximation techniques for scheduling exist and typically rely on the algorithm designer crafting heuristics based on domain expertise to decompose or structure the scheduling problem and prioritize the manner in which resources are allocated and tasks are sequenced (Tang and Parker 2005; Jones, Dias, and Stentz 2011). The second problem is this aforementioned reliance on crafting clever heuristics based on domain knowledge. Manually capturing domain knowledge within a scheduling algorithm remains a challenging process and leaves much to be desired (Ryan et al. 2013). The aim of my thesis is to develop an autonomous system that 1) learns the heuristics and implicit rules-of-thumb developed by domain experts from years of experience, 2) embeds and leverages this knowledge within a scalable resource optimization framework, and 3) provides decision support in a way that engages users and benefits them in their decision-making process. By intelligently leveraging the ability of humans to learn heuristics and the speed of modern computation, we can improve the ability to coordinate resources in these time and safety-critical domains.

This paper considers prescriptive evacuation planning for a region threatened by a natural disaster such a flood, a wildfire, or a hurricane. It proposes a Benders decomposition that generalizes the two-stage approach proposed in earlier work for convergent evacuation plans. Experimental results show that Benders decomposition provides significant improvements in solution quality in reasonable time: It finds provably optimal solutions to scenarios considered in prior work, closing these instances, and increases the number of evacuees by 10 to 15% on average on more complex flood scenarios.

Green security — protection of forests, fish and wildlife — is a critical problem in environmental sustainability. We focus on the problem  of  optimizing the defense of forests againstillegal logging, where often we are faced with the challenge of teaming up many different groups,  from national police to forest guards to NGOs, each with differing capabilities and costs. This paper introduces a new, yet fundamental problem: SimultaneousOptimization of Resource Teams and Tactics (SORT).  SORT contrasts with most previous game-theoretic research for green security — in particular based onsecurity games — that has solely focused on optimizing patrolling tactics, without consideration of team formation or coordination.  We develop new models and scalable algorithms to apply SORT towards illegal logging in large forest areas. We evaluate our methods on a variety of synthetic examples, as well as a real-world case study using data from our on-going collaboration in Madagascar .

Graph matching plays an important role in many fields in computer vision. It is a well-known general NP-hard problem and has been investigated for decades. Among the large amount of algorithms for graph matching, the algorithms utilizing the path following strategy exhibited state-of-art performances. However, the main drawback of this category of algorithms lies in their high computational burden. In this paper, we propose a novel path following strategy for graph matching aiming to improve its computation efficiency. We first propose a path estimation method to reduce the computational cost at each iteration, and subsequently a method of adaptive step length to accelerate the convergence. The proposed approach is able to be integrated into all the algorithms that utilize the path following strategy. To validate our approach, we compare our approach with several recently proposed graph matching algorithms on three benchmark image datasets. Experimental results show that, our approach improves significantly the computation efficiency of the original algorithms, and offers similar or better matching results.

We consider the problem of sampling from a discrete probability distribution specified by a graphical model. Exact samples can, in principle, be obtained by computing the mode of the original model perturbed with an exponentially many i.i.d. random variables. We propose a novel algorithm that views this as a combinatorial optimization problem and searches for the extreme state using a standard integer linear programming (ILP) solver, appropriately extended to account for the random perturbation. Our technique, GumbelMIP, leverages linear programming (LP) relaxations to evaluate the qualityof samples and prune large portions of the search space, and can thus scale to large tree-width models beyond the reach of current exact inference methods. Further, when the optimization problem is not solved to optimality, our method yields a novel approximate sampling technique. We empirically demonstrate that our approach parallelizes well, our exact sampler scales better than alternative approaches, and our approximate sampler yields better quality samples than a Gibbs sampler and a low-dimensional perturbation method.

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs to capture a penalty for early arrival. It is known that as non-linearity arises, the problem can become NP-hard and little is known on computing optimal solutions when in addition there is no monotonicity guarantee. We show that an approximately optimal non-simple path can be efficiently computed under some natural constraints. In particular, we provide a fully polynomial approximation scheme under hop constraints. Our approximation algorithm can extend to run in pseudo-polynomial time under an additional linear constraint that sometimes is useful. As a by-product, we show that our algorithm can be applied to the problem of finding a path that is most likely to be on time for a given deadline.

Uncertainty in activity durations is a key characteristic of many real world scheduling problems in manufacturing, logistics and project management. RCPSP/max with durational uncertainty is a general  model that can be used to represent durational uncertainty in a wide variety of scheduling problems where there exist resource constraints. However, computing schedules or execution strategies for RCPSP/max with durational uncertainty is NP-hard and hence we focus on providing approximation methods in this paper. We provide a principled approximation approach based on Sample Average Approximation (SAA) to compute proactive schedules for RCPSP/max  with durational uncertainty. We further contribute an extension to SAA for improving scalability significantly without sacrificing on solution quality. Not only is our approach able to compute schedules at comparable runtimes as existing approaches, it also provides lower α-quantile makespan (also referred to as α-robust makespan) values than the best known approach on benchmark problems from the literature.

Unsupervised feature selection (UFS) aims to reduce the time complexity and storage burden, as well as improve the generalization performance. Most existing methods convert UFS to supervised learning problem by generating labels with specific techniques (e.g., spectral analysis, matrix factorization and linear predictor). Instead, we proposed a novel coupled analysis-synthesis dictionary learning method, which is free of generating labels. The representation coefficients are used to model the cluster structure and data distribution. Specifically, the synthesis dictionary is used to reconstruct samples, while the analysis dictionary analytically codes the samples and assigns probabilities to the samples. Afterwards, the analysis dictionary is used to select features that can well preserve the data distribution. The effective L2p-norm (0 < p <1) regularization is imposed on the analysis dictionary to get much sparse solution and is more effective in feature selection.We proposed an iterative reweighted least squares algorithm to solve the L2p-norm optimization problem and proved it can converge to a fixed point. Experiments on benchmark datasets validated the effectiveness of the proposed method

In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to limited problem subclasses, or require careful setting of a smoothing parameter. In this paper, we propose a continuation algorithm that is applicable to a large class of nonsmooth regularized risk minimization problems, can be flexibly used with a number of existing solvers for the underlying smoothed subproblem, and with convergence results on the whole algorithm rather than just one of its subproblems. In particular, when accelerated solvers are used, the proposed algorithm achieves the fastest known rates of $O(1/T^2)$ on strongly convex problems, and $O(1/T)$ on general convex problems. Experiments on nonsmooth classification and regression tasks demonstrate that the proposed algorithm outperforms the state-of-the-art.

In many learning tasks with structural properties, structured sparse modeling usually leads to better interpretability and higher generalization performance. While great efforts have focused on the convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are still challenging, especially for the structured sparsity-inducing regularizers. In this paper, we propose a splitting method for solving nonconvex structured sparsity optimization problems. The proposed method alternates between a gradient step and an easily solvable proximal step, and thus enjoys low per-iteration computational complexity. We prove that the whole sequence generated by the proposed method converges to a critical point with at least sublinear convergence rate, relying on the Kurdyka-Łojasiewicz inequality. Experiments on both simulated and real-world data sets demonstrate the efficiency and efficacy of the proposed method.