Best-first Search Research Articles

Understanding Sample Generation Strategies for Learning Heuristic Functions in Classical Planning

We study the problem of learning good heuristic functions for classical planning tasks with neural networks based on samples represented by states with their cost-to-goal estimates. The heuristic function is learned for a state space and goal condition with the number of samples limited to a fraction of the size of the state space, and must generalize well for all states of the state space with the same goal condition. Our main goal is to better understand the influence of sample generation strategies on the performance of a greedy best-first heuristic search (GBFS) guided by a learned heuristic function. In a set of controlled experiments, we find that two main factors determine the quality of the learned heuristic: the algorithm used to generate the sample set and how close the sample estimates to the perfect cost-to-goal are. These two factors are dependent: having perfect cost-to-goal estimates is insufficient if the samples are not well distributed across the state space. We also study other effects, such as adding samples with high-value estimates. Based on our findings, we propose practical strategies to improve the quality of learned heuristics: three strategies that aim to generate more representative states and two strategies that improve the cost-to-goal estimates. Our practical strategies result in a learned heuristic that, when guiding a GBFS algorithm, increases by more than 30% the mean coverage compared to a baseline learned heuristic.

BF-BigGraph: An efficient subgraph isomorphism approach using machine learning for big graph databases

Graph databases are flexible NoSQL databases used to efficiently store and query complex and big data. One of the most difficult problems in graph databases is the problem of subgraph isomorphism, which involves finding a matching pattern in a given graph. Subgraph isomorphism algorithms generally encounter problems in the efficient processing of complex queries based on a lack of pruning methods and the use of a matching order. In this study, we present a new subgraph isomorphism approach based on the best-first search design strategy and name it BF-BigGraph. Our approach includes a machine learning technique to efficiently find the best matching order for various complex queries. The parameters we used in our approach as heuristics to improve the performance of complex queries on graph-based NoSQL databases are database volatility, database size, type of query, and the size of the query. We utilized the Random Forest machine learning method to narrow candidate nodes to a higher level of search and effectively reduce the search space for efficient querying and retrieval. We compared BF-BigGraph with state-of-the-art approaches, namely BB-Graph, Neo4j’s Cypher, DualIso, GraphQL, TurboIso, and VF3 using publicly available databases including undirected graphs; WorldCup, Pokec, Youtube, and a big graph database of a real demographic application (a population database) with approximately 70 million nodes of a big directed graph. The performance results of our approach for different types of complex queries on all these databases are significantly better in terms of computation time and required memory than other competing approaches in the literature.

On Bounding the Behavior of Neurons

A neuron with binary inputs and a binary output represents a Boolean function. Our goal is to extract this Boolean function into a tractable representation that will facilitate the explanation and formal verification of a neuron’s behavior. Unfortunately, extracting a neuron’s Boolean function is in general an NP-hard problem. However, it was recently shown that prime implicants of this Boolean function can be enumerated efficiently, with only polynomial time delay. Building on this result, we first propose a best-first search algorithm that is able to incrementally tighten the inner and outer bounds of a neuron’s Boolean function. Second, we show that these bounds correspond to truncated prime-implicant covers of the Boolean function. Next, we show how these bounds can be propagated in an elementary class of neural networks. Finally, we provide case studies that highlight our ability to bound the behavior of neurons.

Cross-Project Defect Prediction Based on Domain Adaptation and LSTM Optimization

Cross-project defect prediction (CPDP) aims to predict software defects in a target project domain by leveraging information from different source project domains, allowing testers to identify defective modules quickly. However, CPDP models often underperform due to different data distributions between source and target domains, class imbalances, and the presence of noisy and irrelevant instances in both source and target projects. Additionally, standard features often fail to capture sufficient semantic and contextual information from the source project, leading to poor prediction performance in the target project. To address these challenges, this research proposes Smote Correlation and Attention Gated recurrent unit based Long Short-Term Memory optimization (SCAG-LSTM), which first employs a novel hybrid technique that extends the synthetic minority over-sampling technique (SMOTE) with edited nearest neighbors (ENN) to rebalance class distributions and mitigate the issues caused by noisy and irrelevant instances in both source and target domains. Furthermore, correlation-based feature selection (CFS) with best-first search (BFS) is utilized to identify and select the most important features, aiming to reduce the differences in data distribution among projects. Additionally, SCAG-LSTM integrates bidirectional gated recurrent unit (Bi-GRU) and bidirectional long short-term memory (Bi-LSTM) networks to enhance the effectiveness of the long short-term memory (LSTM) model. These components efficiently capture semantic and contextual information as well as dependencies within the data, leading to more accurate predictions. Moreover, an attention mechanism is incorporated into the model to focus on key features, further improving prediction performance. Experiments are conducted on apache_lucene, equinox, eclipse_jdt_core, eclipse_pde_ui, and mylyn (AEEEM) and predictor models in software engineering (PROMISE) datasets and compared with active learning-based method (ALTRA), multi-source-based cross-project defect prediction method (MSCPDP), the two-phase feature importance amplification method (TFIA) on AEEEM and the two-phase transfer learning method (TPTL), domain adaptive kernel twin support vector machines method (DA-KTSVMO), and generative adversarial long-short term memory neural networks method (GB-CPDP) on PROMISE datasets. The results demonstrate that the proposed SCAG-LSTM model enhances the baseline models by 33.03%, 29.15% and 1.48% in terms of F1-measure and by 16.32%, 34.41% and 3.59% in terms of Area Under the Curve (AUC) on the AEEEM dataset, while on the PROMISE dataset it enhances the baseline models’ F1-measure by 42.60%, 32.00% and 25.10% and AUC by 34.90%, 27.80% and 12.96%. These findings suggest that the proposed model exhibits strong predictive performance.

Program Synthesis with Best-First Bottom-Up Search (Abstract Reprint)

Cost-guided bottom-up search (BUS) algorithms use a cost function to guide the search to solve program synthesis tasks. In this paper, we show that current state-of-the-art cost-guided BUS algorithms suffer from a common problem: they can lose useful information given by the model and fail to perform the search in a best-first order according to a cost function. We introduce a novel best-first bottom-up search algorithm, which we call Bee Search, that does not suffer information loss and is able to perform cost-guided bottom-up synthesis in a best-first manner. Importantly, Bee Search performs best-first search with respect to the generation of programs, i.e., it does not even create in memory programs that are more expensive than the solution program. It attains best-first ordering with respect to generation by performing a search in an abstract space of program costs. We also introduce a new cost function that better uses the information provided by an existing cost model. Empirical results on string manipulation and bit-vector tasks show that Bee Search can outperform existing cost-guided BUS approaches when employing more complex domain-specific languages (DSLs); Bee Search and previous approaches perform equally well with simpler DSLs. Furthermore, our new cost function with Bee Search outperforms previous cost functions on string manipulation tasks.

Rectangle Search: An Anytime Beam Search

Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known anytime search algorithms are based on best-first search. In this paper, we propose a new algorithm, rectangle search, that is instead based on beam search, a variant of breadth-first search. It repeatedly explores alternatives at all depth levels and is thus best-suited to problems featuring deep local minima. Experiments using a variety of popular search benchmarks suggest that rectangle search is competitive with fixed-width beam search and often performs better than the previous best anytime search algorithms.

Generalized planning as heuristic search: A new planning search-space that leverages pointers over objects

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not trivially extend to Generalized Planning (GP); GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in their number of objects, the initial and goal configuration of these objects and hence, in the number (and possible values) of the state variables. State-space search, as it is implemented by heuristic planners, becomes then impractical for GP. In this paper we adapt the planning as heuristic search paradigm to the generalization requirements of GP, and present the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines an upgraded version of our GP algorithm, called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space for GP. Lastly, the paper defines a set of evaluation and heuristic functions for BFGP that assess the structural complexity of the candidate GP solutions, as well as their fitness to a given input set of classical planning instances. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g. integers.

Chance-constrained stochastic assembly line balancing with branch, bound and remember algorithm

Assembly lines are widely used mass production techniques applied in various industries from electronics to automotive and aerospace. A branch, bound, and remember (BBR) algorithm is presented in this research to tackle the chance-constrained stochastic assembly line balancing problem (ALBP). In this problem variation, the processing times are stochastic, while the cycle time must be respected for a given probability. The proposed BBR method stores all the searched partial solutions in memory and utilizes the cyclic best-first search strategy to quickly achieve high-quality complete solutions. Meanwhile, this study also develops several new lower bounds and dominance rules by taking the stochastic task times into account. To evaluate the performance of the developed method, a large set of 1614 instances is generated and solved. The performance of the BBR algorithm is compared with two mixed-integer programming models and twenty re-implemented heuristics and metaheuristics, including the well-known genetic algorithm, ant colony optimization algorithm and simulated annealing algorithm. The comparative study demonstrates that the mathematical models cannot achieve high-quality solutions when solving large-size instances, for which the BBR algorithm shows clear superiority over the mathematical models. The developed BBR outperforms all the compared heuristic and metaheuristic methods and is the new state-of-the-art methodology for the stochastic ALBP.

Chemoenzymatic multistep retrosynthesis with transformer loops.

Integrating enzymatic reactions into computer-aided synthesis planning (CASP) should help devise more selective, economical, and greener synthetic routes. Herein we report the triple-transformer loop algorithm with biocatalysis (TTLAB) as a new CASP tool for chemo-enzymatic multistep retrosynthesis. Single-step retrosyntheses are performed using two triple transformer loops (TTL), one trained with chemical reactions from the US Patent Office (USPTO-TTL), the second one obtained by multitask transfer learning combining the USPTO dataset with preparative biotransformations from the literature (ENZR-TTL). Each TTL performs single-step retrosynthesis independently by tagging potential reactive sites in the product, predicting for each site possible starting materials (T1) and reagents or enzymes (T2), and validating the predictions via a forward transformer (T3). TTLAB combines predictions from both TTLs to explore multistep sequences using a heuristic best-first tree search and propose short routes from commercial building blocks including enantioselective biocatalytic steps. TTLAB can be used to assist chemoenzymatic route design.

Advanced Recursive Best-First Search (RBFS) based Routing Protocol for Multi-hop and Multi-Channel Cognitive Wireless Mesh Networks

Cognitive Wireless Mesh Network (CWMN) is an opportunistic network in which radio channels can be assigned according to their availability to establish connections among nodes. After establishing a radio connection among nodes, it is necessary to find an optimal route from the source node to the destination node in the network. If there remain more channels among nodes, the minimum weighted channel should be taken into account to establish expected routes. The graph theoretic approach fails to model the multi-channel cognitive radio networks due to abrupt failure in finding new successful routes as it can’t figure multi-channel networks. In this paper, a multi-edged graph model is being proposed to overcome the problems of cognitive radio networks, such as flooding problems, channel accessing problems etc. A new channel accessing algorithm has been introduced, and optimal routes have been selected using a heuristic algorithm named RBFS. Simulation results are compared with DJKSTRA based routing protocols.

A scalable, distributed framework for significant subgroup discovery

Subgroup discovery is a supervised data mining technique having many applications in medical domains, market basket analysis, and social media analysis. It helps in mining subgroups (or patterns) with a high association to a target property, measured using a quality function. However, the process is computationally intensive as it is necessary to go through the search space of all subgroups to find the top-k interesting ones w.r.t. the quality function. Further, as we verify many associations, it is quite possible that a certain level of association might be achieved by chance. To address this issue, the state-of-the-art TopKWY algorithm employs permutation testing to control false discoveries. Still, testing multiple subgroups against thousands of permuted target labels further increases computational complexity. Additionally, TopKWY is limited to a specific quality function and lacks a parallel/distributed implementation to handle scalability challenges. In this paper, we propose a parallel and distributed framework for subgroup discovery named ParaDiS that extends permutation testing to a broader class of quality functions. ParaDiS scales to large datasets while effectively controlling the false discovery rate. It features different optimizations to reduce communication/computation overheads and a distributed best-first search strategy to improve pruning across different workers. We compare its performance for several real-world datasets and achieve an order of magnitude reduction in the execution time compared to the sequential approach.

Efficiency analysis of path-finding algorithms in a 2D grid environment

<p>This paper offers a focused overview of pathfinding algorithms, particularly emphasizing Greedy Best First Search (G-BFS) and Rapidly-Exploring Random Trees (RRT). Their performance is evaluated within a 2D grid setting tailored for Unmanned Aerial Vehicles (UAVs). Divided into two main sections, the study first expounds on the theoretical underpinnings of these algorithms, followed by empirical validation. A series of systematic experiments, involving varied 2D grid dimensions and traversal patterns, facilitates a comparative analysis between G-BFS and RRT. Importantly, the real-world implementation of these algorithms in UAV navigation underscores their practicality, illuminating their respective execution times and resource utilization. While G-BFS thrives in straightforward scenarios, RRT, especially RRT*, displays superior capability in navigating more intricate and expansive terrains, albeit with marginally extended execution durations attributed to its explorative nature.</p>

Software/Code for "DIVERSITREE: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems"

Although most methods for solving mixed-integer optimization problems com-pute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Furthermore, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets.

DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems

Although most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Furthermore, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Army Research Office [Grant W911NF-21-1-0079]. The views expressed in this study do not represent those of the U.S. Government, the U.S. Department of Defense, or the U.S. Army. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0164 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0164 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Techniques for accelerating branch-and-bound algorithms dedicated to sparse optimization

Sparse optimization–fitting data with a low-cardinality linear model–is addressed through the minimization of a cardinality-penalized least-squares function, for which dedicated branch-and-bound algorithms clearly outperform generic mixed-integer-programming solvers. Three acceleration techniques are proposed for such algorithms. Convex relaxation problems at each node are addressed with dual approaches, which can early prune suboptimal nodes. Screening methods are implemented, which fix variables to their optimal value during the node evaluation, reducing the subproblem size. Numerical experiments show that the efficiency of such techniques depends on the node cardinality and on the structure of the problem matrix. Last, different exploration strategies are proposed to schedule the nodes. Best-first search is shown to outperform the standard depth-first search used in the related literature. A new strategy is proposed which first explores the nodes with the lowest least-squares value, which is shown to be the best at finding the optimal solution–without proving its optimality. A C++ solver with compiling and usage instructions is made available.

Sistem Pakar untuk Mendiagnosa Gangguan pada Sistem Endokrin Berbasis Android Mobile

<p><em>This research discusses how to design an expert system that can be used to diagnose disorders of the endocrine system based on the symptoms suffered by the patient, so that there are advice on the problems encountered by the user. The objective is to assist prospective doctors, general practitioners and specialists in diagnosing disorders of the endocrine system like an expert, to provide information quickly, and to create an interactive application that can be easily understood by the users. The expert system is created using the Best-First Search method and using the Forward Chaining technique. The system contains the knowledge of an expert obtained during research at Permata Ibu Hospital and a knowledge base designed to be able to store new diseases. The expert system is developed based on smartphone technology or more specifically Android on the client side, PHP (Hypertext Preprocessor) and MySQL base on the server side. The system contains 6 disease data and 10 disease symptom data. It also has been tested and validated by experts and several users. The result reaching a percentage of 83.3% shows that the expert system application is quite efficient and effective</em><em>.</em></p>

Program Synthesis with Best-First Bottom-Up Search

Cost-guided bottom-up search (BUS) algorithms use a cost function to guide the search to solve program synthesis tasks. In this paper, we show that current state-of-the-art cost-guided BUS algorithms suffer from a common problem: they can lose useful information given by the model and fail to perform the search in a best-first order according to a cost function. We introduce a novel best-first bottom-up search algorithm, which we call Bee Search, that does not suffer information loss and is able to perform cost-guided bottom-up synthesis in a best-first manner. Importantly, Bee Search performs best-first search with respect to the generation of programs, i.e., it does not even create in memory programs that are more expensive than the solution program. It attains best-first ordering with respect to generation by performing a search in an abstract space of program costs. We also introduce a new cost function that better uses the information provided by an existing cost model. Empirical results on string manipulation and bit-vector tasks show that Bee Search can outperform existing cost-guided BUS approaches when employing more complex domain-specific languages (DSLs); Bee Search and previous approaches perform equally well with simpler DSLs. Furthermore, our new cost function with Bee Search outperforms previous cost functions on string manipulation tasks.

Novelty and Lifted Helpful Actions in Generalized Planning

It has been shown recently that successful techniques in classical planning, such as goal-oriented heuristics and landmarks, can improve the ability to compute planning programs for generalized planning (GP) problems. In this work, we introduce the notion of action novelty rank, which computes novelty with respect to a planning program, and propose novelty-based generalized planning solvers, which prune a newly generated planning program if its most frequent action repetition is greater than a given bound v, implemented by novelty-based best-first search BFS(v) and its progressive variant PGP(v). Besides, we introduce lifted helpful actions in GP derived from action schemes, and propose new evaluation functions and structural program restrictions to scale up the search. Our experiments show that the new algorithms BFS(v) and PGP(v) outperform the state-of-the-art in GP over the standard generalized planning benchmarks. Practical findings on the above-mentioned methods in generalized planning are briefly discussed.

A Best-First Search Algorithm for FOND Planning and Heuristic Functions to Optimize Decompressed Solution Size

In this work, we study fully-observable non-deterministic (FOND) planning, which models uncertainty through actions with non-deterministic effects. We present a best-first heuristic search algorithm called AND* that searches the policy-space of the FOND task to find a solution policy. We generalize the concepts of optimality, admissibility, and goal-awareness for FOND. Using these new concepts, we formalize the concept of heuristic functions that can guide a policy-space search. We analyze different aspects of the general structure of FOND solutions to introduce and characterize a set of FOND heuristics that estimate how far a policy is from becoming a solution. One of these heuristics applies a novel insight. Guided by them AND* returns only solutions with the minimal possible number of mapped states. We systematically study these FOND heuristics theoretically and empirically. We observe that our best heuristic makes AND* much more effective than the straightforward heuristics. We believe that our work allows a better understanding of how to design algorithms and heuristics to solve FOND tasks.

Landmark Progression in Heuristic Search

The computation of high-quality landmarks and orderings for heuristic state-space search is often prohibitively expensive to be performed in every generated state. Computing information only for the initial state and progressing it from every state to its successors is a successful alternative, exploited for example in classical planning by the LAMA planner. We propose a general framework for using landmarks in any kind of best-first search. Its core component, the progression function, uses orderings and search history to determine which landmarks must still be achieved. We show that the progression function that is used in LAMA infers invalid information in the presence of reasonable orderings. We define a sound progression function that allows to exploit reasonable orderings in cost-optimal planning and show empirically that our new progression function is beneficial both in satisficing and optimal planning.