Admissible heuristic

About: Admissible heuristic is a research topic. Over the lifetime, 197 publications have been published within this topic receiving 15329 citations. The topic is also known as: admissible heuristics.

Bounded Suboptimal Heuristic Search in Linear Space

Abstract: It is commonly appreciated that solving search problems optimally can overrun time and memory constraints Bounded suboptimal search algorithms trade increased solution cost for reduced solving time and memory consumption However, even suboptimal search can overrun memory on large problems The conventional approach to this problem is to combine a weighted admissible heuristic with an optimal linear space algorithm, resulting in algorithms such as Weighted IDA* (wIDA*) However, wIDA* does not exploit distance-to-go estimates or inadmissible heuristics, which have recently been shown to be helpful for suboptimal search In this paper, we present a linear space analogue of Explicit Estimation Search (EES), a recent algorithm specifically designed for bounded suboptimal search We call our method Iterative Deepening EES (IDEES) In an empirical evaluation, we show that IDEES dramatically outperforms wIDA* on domains with non-uniform edge costs and can scale to problems that are out of reach for the original EES

Learning admissible heuristics while solving problems

Abstract: A method is presented that causes A* to return high quality solutions while solving a set of problems using a non-admissible heuristic. The heuristic guiding the search changes as new information is learned during the search, and it converges to an admissible heuristic which 'contains the insight' of the original nonadmissible one. After a finite number of problems, A* returns only optimal solutions. Experiments on sliding tile problems suggest that learning occurs very fast. Beginning with hundreds of randomly generated problems and an overestimating heuristic, the system learned sufficiently fast that only the first problem was solved non-optimally. As an application we show how one may construct heuristics for finding high quality solutions at lower cost than those returned by A* using available admissible heuristics.

Learning Differentiable Programs with Admissible Neural Heuristics

Abstract: We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

Network Flow Modeling for Flexible Manufacturing Systems with Re-entrant Lines

Abstract: A relaxed version of the process planning problem for flexible manufacturing systems/cells (FMS/FMC) and processing networks, such as flexible flow shops and general job shops, is formulated using a simple extension of multicom-modity network flow problems. Our multistage multicommodity network formulation allows for simultaneous routing and resource allocation and also captures the case of re-entrant lines (recirculation). It can be used to perform rapid, albeit crude, explorations of the combinatorial space of possible configurations and failure scenarios. The technique can also provide bounds on the limits of system performance (eg: throughput, link usage, bottlenecks, etc). This can be used to guide the design of robust FMS architectures with high degree of redundancy in machines and routes, as demonstrated in numerical examples. Being a relaxation to the full discrete problem, our method could potentially be used as an admissible heuristic for pruning AI-based planning methods. We demonstrate our approach on a realistic industrial problem.

Optimal automatic table layout

Abstract: Automatic layout of tables is useful in word processing applications and is required in on-line applications because of the need to tailor the layout to the viewport width, choice of font and dynamic content. However, if the table contains text, minimizing the height of the table for a fixed maximum width is a difficult combinatorial optimization problem. We present three different approaches to finding the minimum height layout based on standard approaches for combinatorial optimization. All are guaranteed to find the optimal solution. The first is an A*-based approach that uses an admissible heuristic based on the area of the cell content. The second and third are constraint programming (CP) approaches using the same CP model. The second approach uses traditional CP search, while the third approach uses a hybrid CP/SAT approach, lazy clause generation, that uses learning to reduce the search required. We provide a detailed empirical evaluation of the three approaches and also compare them with two mixed integer programming (MIP) encodings due to Bilauca and Healy.