Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in large-scale multi-agent systems. State-of-the-art anytime MAPF is based on Large Neighborhood Search (LNS), where a fast initial solution is iteratively optimized by destroying and repairing a fixed number of parts, i.e., the neighborhood of the solution, using randomized destroy heuristics and prioritized planning. Despite their recent success in various MAPF instances, current LNS-based approaches lack exploration and flexibility due to greedy optimization with a fixed neighborhood size which can lead to low-quality solutions in general. So far, these limitations have been addressed with extensive prior effort in tuning or offline machine learning beyond actual planning. In this paper, we focus on online learning in LNS and propose Bandit-based Adaptive LArge Neighborhood search Combined with Exploration (BALANCE). BALANCE uses a bi-level multi-armed bandit scheme to adapt the selection of destroy heuristics and neighborhood sizes on the fly during search. We evaluate BALANCE on multiple maps from the MAPF benchmark set and empirically demonstrate performance improvements of at least 50% compared to state-of-the-art anytime MAPF in large-scale scenarios. We find that Thompson Sampling performs particularly well compared to alternative multi-armed bandit algorithms.

Many real-world problems can be efficiently modeled as Mixed Integer Linear Programs (MILPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MILP backdoors, small sets of variables such that prioritizing branching on them when possible leads to faster running times. However, finding high-quality backdoors that improve running times remains an open question. Previous work learns to estimate the relative solver speed of randomly sampled backdoors through ranking and learns to decide whether to use the highest-ranked backdoor candidate. In this paper, we utilize the Monte-Carlo tree search method to collect backdoors for training, rather than relying on random sampling, and adapt a contrastive learning framework to train a Graph Attention Network model to predict backdoors. Our method, evaluated on several common MILP problem domains, demonstrates performance improvements over both Gurobi and previous models.

Deep generative models like GAN and VAE have shown impressive results in generating unconstrained objects like images. However, many design settings arising in industrial design, material science, computer graphics and more require that the generated objects satisfy hard combinatorial constraints or meet objectives in addition to modeling a data distribution. To address this, we propose GenCO, a generative framework that guarantees constraint satisfaction throughout training by leveraging differentiable combinatorial solvers to enforce feasibility. GenCO imposes the generative loss on provably feasible solutions rather than intermediate soft solutions, meaning that the deep generative network can focus on ensuring the generated objects match the data distribution without having to also capture feasibility. This shift enables practitioners to enforce hard constraints on the generated outputs during end-to-end training, enabling assessments of their feasibility and introducing additional combinatorial loss components to deep generative training. We demonstrate the effectiveness of our approach on a variety of generative combinatorial tasks, including game level generation, map creation for path planning, and photonic device design, consistently demonstrating its capability to yield diverse, high-quality solutions that verifiably adhere to user-specified combinatorial properties.

Mixed integer linear programs (MILP) are flexible and powerful tools for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning (ML)-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples. We also collect low-quality or infeasible solutions as negative samples using novel optimization-based or sampling approaches. We then learn to make discriminative predictions by contrasting the positive and negative samples. During testing, we predict and fix the assignments for a subset of integer variables and then solve the resulting reduced MILP to find high-quality solutions. Empirically, ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which solutions are found.

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose $\textbf{\emph{\texttt{SurCo}}}$ that learns linear $\underline{\text{Sur}}$rogate costs which can be used in existing $\underline{\text{Co}}$mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three $\texttt{SurCo}$ variants: $\texttt{SurCo}-\texttt{zero}$ for individual nonlinear problems, $\texttt{SurCo}-\texttt{prior}$ for problem distributions, and $\texttt{SurCo}-\texttt{hybrid}$ to combine both distribution and problem-specific information. We give theoretical intuition motivating $\texttt{SurCo}$, and evaluate it empirically. Experiments show that $\texttt{SurCo}$ finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high-quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a more efficient one with contrastive learning. We use graph attention networks and a richer set of features to further improve its performance.

Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer $\mathbf{g}$ to tackle these challenging problems with $f$ as the objective, the optimization process can be substantially accelerated by leveraging past experience. The optimizer can be trained with supervision from known optimal solutions or implicitly by optimizing the compound function $f\circ \mathbf{g}$. The implicit approach may not require optimal solutions as labels and is capable of handling problem uncertainty; however, it is slow to train and deploy due to frequent calls to optimizer $\mathbf{g}$ during both training and testing. The training is further challenged by sparse gradients of $\mathbf{g}$, especially for combinatorial solvers. To address these challenges, we propose using a smooth and learnable **Landscape Surrogate** $\mathcal{M}$ as a replacement for $f\circ \mathbf{g}$. This surrogate, learnable by neural networks, can be computed faster than the solver $\mathbf{g}$, provides dense and smooth gradients during training, can generalize to unseen optimization problems, and is efficiently learned via alternating optimization. We test our approach on both synthetic problems, including shortest path and multidimensional knapsack, and real-world problems such as portfolio optimization, achieving comparable or superior objective values compared to state-of-the-art baselines while reducing the number of calls to $\mathbf{g}$. Notably, our approach outperforms existing methods for computationally expensive high-dimensional problems.

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths for a team of agents in a common environment. MAPF is NP-hard to solve optimally and, in some cases, also bounded-suboptimally. It is thus time-consuming for (bounded-sub)optimal solvers to solve large MAPF instances. Anytime algorithms find solutions quickly for large instances and then improve them to close-to-optimal ones over time. In this paper, we improve the current state-of-the-art anytime solver MAPF-LNS, that first finds an initial solution fast and then repeatedly replans the paths of subsets of agents via Large Neighborhood Search (LNS). It generates the subsets of agents for replanning by randomized destroy heuristics, but not all of them increase the solution quality substantially. We propose to use machine learning to learn how to select a subset of agents from a collection of subsets, such that replanning increases the solution quality more. We show experimentally that our solver, MAPF-ML-LNS, significantly outperforms MAPF-LNS on the standard MAPF benchmark set in terms of both the speed of improving the solution and the final solution quality.

In this work, we examine a line of recent publications that propose to use deep neural networks to approximate the goal distances of states for heuristic search. We present a first step toward showing that this work suffers from inherent scalability limitations since --- under the assumption that P≠NP --- such approaches require network sizes that scale exponentially in the number of states to achieve the necessary (high) approximation accuracy.

Prioritized Planning (PP) is a fast and popular framework for solving Multi-Agent Path Finding, but its solution quality depends heavily on the predetermined priority ordering of the agents. Current PP algorithms use either greedy policies or random assignments to determine a total priority ordering, but none of them dominates the others in terms of the success rate and solution quality (measured by the sum-of-costs). We propose a machine-learning (ML) framework to learn a good priority ordering for PP. We develop two models, namely ML-T, which is trained on a total priority ordering, and ML-P, which is trained on a partial priority ordering. We propose to boost the effectiveness of PP by further applying stochastic ranking and random restarts. The results show that our ML-guided PP algorithms outperform the existing PP algorithms in success rate, runtime, and solution quality on small maps in most cases and are competitive with them on large maps despite the difficulty of collecting training data on these maps.

Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. On the high level, CBS repeatedly detects conflicts and resolves one of them by splitting the current problem into two subproblems. Previous work chooses the conflict to resolve by categorizing conflicts into three classes and always picking one from the highest-priority class. In this work, we propose an oracle for conflict selection that results in smaller search tree sizes than the one used in previous work. However, the computation of the oracle is slow. Thus, we propose a machine-learning (ML) framework for conflict selection that observes the decisions made by the oracle and learns a conflict-selection strategy represented by a linear ranking function that imitates the oracle's decisions accurately and quickly. Experiments on benchmark maps indicate that our approach, ML-guided CBS, significantly improves the success rates, search tree sizes and runtimes of the current state-of-the-art CBS solver.

As disasters such as earthquakes and floods become more frequent and detrimental, it is increasingly important that water infrastructure resilience be strategically enhanced to support post-disaster functionality and recovery. In this paper, we focus on the problem of strategically building seismic-resilient pipe networks to ensure direct water supply to critical customers and certain proximity to water sources for residential areas, which we formalize as the Steiner Network Problem with Coverage Constraints. We provide complexity statements of the problem and present an efficient mixed-integer linear program encoding to solve the problem. We also investigate the problem of planning partial network installments to maximize efficiency over time and propose a fast and effective sequential planning algorithm to solve it. We evaluate our algorithms on synthetic water networks and also apply them to a case study on a water service zone in Los Angeles, which demonstrate the effectiveness of our methods for large-scale real-world applications.

Although security games have attracted intensive research attention over the past years, few existing works consider how information from local communities would affect the game. In this paper, we introduce a new player -- a strategic informant, who can observe and report upcoming attacks -- to the defender-attacker security game setting. Characterized by a private type, the informant has his utility structure that leads to his strategic behaviors. We model the game as a 3-player extensive-form game and propose a novel solution concept of Strong Stackelberg-perfect Bayesian equilibrium. To compute the optimal defender strategy, we first show that although the informant can have infinitely many types in general, the optimal defense plan can only include a finite (exponential) number of different patrol strategies. We then prove that there exists a defense plan with only a linear number of patrol strategies that achieve the optimal defender's utility, which significantly reduces the computational burden and allows us to solve the game in polynomial time using linear programming. Finally, we conduct extensive experiments to show the effect of the strategic informant and demonstrate the effectiveness of our algorithm.