Learning to Resolve Conflicts for Multi-Agent Path Finding with Conflict-Based Search

Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. At 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 the conflict into three classes and always picking a conflict 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 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 method significantly improves the success rates, the search tree sizes and runtimes over the current state-of-the-art CBS solver

Adaptive Anytime Multi-Agent Path Finding Using Bandit-Based Large Neighborhood Search

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 cost 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.Comment: Accepted to AAAI 202

Local Branching Relaxation Heuristics for Integer Linear Programs

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks

Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

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 new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance

Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information

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 $M$ 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

Evaluation of the Santa Helena dam impacts on the Jacuípe river estuary, north coast of Bahia - Brazil

A construção de barramentos fluviais normalmente causa impactos hidráulicos e hidrológicos no sistema estuarino localizado próximo à foz do rio. A literatura relaciona como consequências hidráulicas comuns associadas à regulação das descargas, o aumento da vazão média e a redução das vazões instantâneas, com atenuação dos picos de cheia. Este estudo objetivou caracterizar a hidrodinâmica e os padrões de mistura do estuário do rio Jacuípe (litoral norte do Estado da Bahia) e avaliar a influência da Barragem de Santa Helena, erguida em 2001, no fluxo estuarino. Observou-se que a barragem alterou o regime de vazão fluvial, afetando todas as faixas de vazão. No entanto, os resultados são inversos aos relatados na literatura, com redução das vazões médias e aumento das descargas de pico. A liberação de água doce atingiu os extremos da curva de descarga, e a ausência de descarga passou a ocorrer com períodos mais prolongados. O estuário apresentou-se parcialmente misturado em marés de quadratura e bem misturado em sizígia, mas, em ambas as condições de maré, com pequena descarga da barragem ou descarga nula, predominou a circulação gravitacional. Valores elevados de descarga fluvial (70 m3 s-1) causam a expulsão da água marinha do estuário e o bombeamento fluvial, com fluxo exclusivamente de vazante. Com o início da planejada transposição de água (10 m3 s-1) para a vizinha bacia do rio Joanes, os efeitos da barragem sobre o estuário serão alterados, com redução dos picos de cheia e provável assoreamento da calha e canal de entrada. Este processo poderá causar degradação da qualidade ambiental do estuário.River dams are normally associated to hydraulic and hydrologic impacts in estuaries. Hydraulic consequences, reported in literature, are the increase of the mean and the reduction of maximum discharges, with the attenuation of the flood waves. This study aimed to characterize the hydrodynamics and mixing patterns of the Jacuipe river estuary (northern State of Bahia), and to evaluate the influence of Santa Helena dam, erected in 2001, upon the estuarine flow. It was observed that the dam altered the natural discharge regime, impacting all ranges of fluvial discharge. The changes were, however, opposite to those related in the literature, as post-dam mean discharge value was reduced and peak discharge values were increased. Water release rates topped the extreme of the natural discharge curve, whereas null discharges were sustained for a much longer period. The estuary was partially mixed during neap and well mixed during spring tides, with gravitational circulation predominating with low and null dam discharge values in both tidal conditions. Larger discharge values (70 m3 s-1) expelled the salt water from the estuary and caused ebbing flow throughout the tidal cycle. The implementation of water transposition from Santa Helena dam to the neighboring Joanes river will reduce peak flows and probably cause shoaling of the estuary channel and inlet. This process is likely to cause degrading environmental conditions in the estuary