scholarly journals Search Progress and Potentially Expanded States in Greedy Best-First Search

2018 ◽  
Author(s):  
Manuel Heusner ◽  
Thomas Keller ◽  
Malte Helmert
Keyword(s):  
Classical Result ◽  
Search Behavior ◽  
Optimal Solution ◽  
Search Space ◽  
High Water ◽  
Search Algorithms ◽  
Clear Understanding ◽  
Optimal Search ◽  
High Water Mark ◽  
Best First Search

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f-value is below the optimal solution cost and no state whose f-value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behavior of greedy best-first search (GBFS) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a GBFS algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are expanded by at least one GBFS tie-breaking strategy and give us a clearer understanding of search progress.

scholarly journals Tie-Breaking Strategies for Cost-Optimal Best First Search

2017 ◽  
Vol 58 ◽  
pp. 67-121 ◽  
Author(s):  
Masataro Asai ◽  
Alex Fukunaga
Keyword(s):  
Search Algorithm ◽  
Search Space ◽  
Search Algorithms ◽  
Optimal Search ◽  
Diversification Strategy ◽  
Algorithm Performance ◽  
New Class ◽  
New Strategy ◽  
Best First Search ◽  
New Framework

Best-first search algorithms such as A* need to apply tie-breaking strategies in order to decide which node to expand when multiple search nodes have the same evaluation score. We investigate and improve tie-breaking strategies for cost-optimal search using A*. We first experimentally analyze the performance of common tie-breaking strategies that break ties according to the heuristic value of the nodes. We find that the tie-breaking strategy has a significant impact on search algorithm performance when there are 0-cost operators that induce large plateau regions in the search space. Based on this, we develop two new classes of tie-breaking strategies. We first propose a depth diversification strategy which breaks ties according to the distance from the entrance to the plateau, and then show that this new strategy significantly outperforms standard strategies on domains with 0-cost actions. Next, we propose a new framework for interpreting A* search as a series of satisficing searches within plateaus consisting of nodes with the same f-cost. Based on this framework, we investigate a second, new class of tie-breaking strategy, a multi-heuristic tie-breaking strategy which embeds inadmissible, distance-to-go variations of various heuristics within an admissible search. This is shown to further improve the performance in combination with the depth metric.

scholarly journals Effective Heuristics for Suboptimal Best-First Search

2016 ◽  
Vol 57 ◽  
pp. 273-306 ◽  
Author(s):  
Christopher Wilt ◽  
Wheeler Ruml
Keyword(s):  
Sustained Attention ◽  
Heuristic Search ◽  
Rank Correlation ◽  
Search Algorithms ◽  
Optimal Solutions ◽  
Heuristic Function ◽  
Optimal Search ◽  
Heuristic Search Algorithms ◽  
Best First Search ◽  
Goal Distance

Suboptimal heuristic search algorithms such as weighted A* and greedy best-first search are widely used to solve problems for which guaranteed optimal solutions are too expensive to obtain. These algorithms crucially rely on a heuristic function to guide their search. However, most research on building heuristics addresses optimal solving. In this paper, we illustrate how established wisdom for constructing heuristics for optimal search can fail when considering suboptimal search. We consider the behavior of greedy best-first search in detail and we test several hypotheses for predicting when a heuristic will be effective for it. Our results suggest that a predictive characteristic is a heuristic's goal distance rank correlation (GDRC), a robust measure of whether it orders nodes according to distance to a goal. We demonstrate that GDRC can be used to automatically construct abstraction-based heuristics for greedy best-first search that are more effective than those built by methods oriented toward optimal search. These results reinforce the point that suboptimal search deserves sustained attention and specialized methods of its own.

scholarly journals Online Relaxation Refinement for Satisficing Planning: On Partial Delete Relaxation, Complete Hill-Climbing, and Novelty Pruning

2022 ◽  
Vol 73 ◽  
Author(s):  
Maximilian Fickert ◽  
Jörg Hoffmann
Keyword(s):  
Local Minimum ◽  
State Of The Art ◽  
Convergence Property ◽  
Search Space ◽  
Search Algorithms ◽  
Hill Climbing ◽  
Ai Planning ◽  
Best First Search ◽  
Refinement Procedure ◽  
Hill Climbing Algorithms

In classical AI planning, heuristic functions typically base their estimates on a relaxation of the input task. Such relaxations can be more or less precise, and many heuristic functions have a refinement procedure that can be iteratively applied until the desired degree of precision is reached. Traditionally, such refinement is performed offline to instantiate the heuristic for the search. However, a natural idea is to perform such refinement online instead, in situations where the heuristic is not sufficiently accurate. We introduce several online-refinement search algorithms, based on hill-climbing and greedy best-first search. Our hill-climbing algorithms perform a bounded lookahead, proceeding to a state with lower heuristic value than the root state of the lookahead if such a state exists, or refining the heuristic otherwise to remove such a local minimum from the search space surface. These algorithms are complete if the refinement procedure satisfies a suitable convergence property. We transfer the idea of bounded lookaheads to greedy best-first search with a lightweight lookahead after each expansion, serving both as a method to boost search progress and to detect when the heuristic is inaccurate, identifying an opportunity for online refinement. We evaluate our algorithms with the partial delete relaxation heuristic hCFF, which can be refined by treating additional conjunctions of facts as atomic, and whose refinement operation satisfies the convergence property required for completeness. On both the IPC domains as well as on the recently published Autoscale benchmarks, our online-refinement search algorithms significantly beat state-of-the-art satisficing planners, and are competitive even with complex portfolios.

scholarly journals Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem

2019 ◽  
Vol 27 (3) ◽  
pp. 525-558
Author(s):  
Mojgan Pourhassan ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithms ◽  
Local Search ◽  
Polynomial Time ◽  
Theoretical Perspective ◽  
Optimal Solution ◽  
Search Space ◽  
Search Algorithms ◽  
Variable Neighbourhood Search ◽  
Local Search Algorithms ◽  
Travelling Salesperson Problem

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl ( 2008 ) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the node-based approach solves the hard instance of the cluster-based approach presented in Corus et al. ( 2016 ) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the node-based approach for a class of Euclidean instances.

scholarly journals Universal Approach to Solution of Optimization Problems by Symbolic Regression

2021 ◽  
Vol 11 (11) ◽  
pp. 5081
Author(s):  
Elena Sofronova ◽  
Askhat Diveev
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Small Variation ◽  
Search Space ◽  
Search Algorithms ◽  
Symbolic Regression ◽  
Basic Solution ◽  
Potential Solution ◽  
Regression Methods ◽  
Universal Approach

Optimization problems and their solution by symbolic regression methods are considered. The search is performed on non-Euclidean space. In such spaces it is impossible to determine a distance between two potential solutions and, therefore, algorithms using arithmetic operations of multiplication and addition are not used there. The search of optimal solution is performed on the space of codes. It is proposed that the principle of small variations of basic solution be applied as a universal approach to create search algorithms. Small variations cause a neighborhood of a potential solution, and the solution is searched for within this neighborhood. The concept of inheritance property is introduced. It is shown that for non-Euclidean search space, the application of evolution and small variations of possible solutions is effective. Examples of using the principle of small variation of basic solution for different symbolic regression methods are presented.

scholarly journals On Hash-Based Work Distribution Methods for Parallel Best-First Search

2017 ◽  
Vol 60 ◽  
pp. 491-548 ◽  
Author(s):  
Yuu Jinnai ◽  
Alex Fukunaga
Keyword(s):  
Hash Function ◽  
Search Space ◽  
Search Algorithms ◽  
Communication Overhead ◽  
Distribution Method ◽  
Work Distribution ◽  
Projection Functions ◽  
Best First Search ◽  
Feature Projection ◽  
Almost All

Parallel best-first search algorithms such as Hash Distributed A* (HDA*) distribute work among the processes using a global hash function. We analyze the search and communication overheads of state-of-the-art hash-based parallel best-first search algorithms, and show that although Zobrist hashing, the standard hash function used by HDA*, achieves good load balance for many domains, it incurs significant communication overhead since almost all generated nodes are transferred to a different processor than their parents. We propose Abstract Zobrist hashing, a new work distribution method for parallel search which, instead of computing a hash value based on the raw features of a state, uses a feature projection function to generate a set of abstract features which results in a higher locality, resulting in reduced communications overhead. We show that Abstract Zobrist hashing outperforms previous methods on search domains using hand-coded, domain specific feature projection functions. We then propose GRAZHDA*, a graph-partitioning based approach to automatically generating feature projection functions. GRAZHDA* seeks to approximate the partitioning of the actual search space graph by partitioning the domain transition graph, an abstraction of the state space graph. We show that GRAZHDA* outperforms previous methods on domain-independent planning.

scholarly journals Enhanced Simplified Memory-bounded A Star (SMA*+)

10.29007/v7zc ◽  
2018 ◽  
Author(s):  
Justin Lovinger ◽  
Xiaoqin Zhang
Keyword(s):  
Explicit Memory ◽  
Search Algorithm ◽  
A Priori ◽  
Search Space ◽  
Search Algorithms ◽  
Search Performance ◽  
Heuristic Function ◽  
Optimal Search ◽  
Comparison Results ◽  
Memory Efficient

In 1992, Stuart Russell briefly introduced a series of memory efficient optimal search algorithms. Among which is the Simplified Memory-bounded A Star (SMA*) algorithm, unique for its explicit memory bound. Despite progress in memory efficient A Star variants, search algorithms with explicit memory bounds are absent from progress. SMA* remains the premier memory bounded optimal search algorithm. In this paper, we present an enhanced version of SMA* (SMA*+), providing a new open list, simplified implementation, and a culling heuristic function, which improves search performance through a priori knowledge of the search space. We present benchmark and comparison results with state-of-the-art optimal search algorithms, and examine the performance characteristics of SMA*+.

The ultrastructure of the abdominal musculature of an orchestid amphipod

1990 ◽  
Vol 48 (3) ◽  
pp. 464-465
Author(s):  
Martin A. Levin ◽  
Lisa L. Cale ◽  
Valerie Lynch-Holm
Keyword(s):  
Intertidal Zone ◽  
High Water ◽  
Abdominal Muscles ◽  
Abdominal Musculature ◽  
Dorsal Muscle ◽  
High Water Mark ◽  
Thoracic Legs ◽  
Orchestia Cavimana

Orchestia is a genus of amphipod in the crustacean class Malacostraca. The order Amphipoda contains over 6000 species commonly called side swimmers, scuds and beach fleas(1). Most are marine bottom-dwellers utilizing their thoracic legs and posterior abdominal uropods for walking, crawling and swimming. However, some, like those in the genera Orchestia and Hyale are semiterrestrial. These amphipods, commonly referred to as “beach fleas,' “beach hoppers” or “sand fleas” can hop vigorously for great distances (up to 50 times their length) by extending their abdomens and telsons against the sand(2).In our study, the ultrastructure of the dorsal muscle cord of Orchestia grillus was examined. Vogel(3) described the abdominal muscles of Orchestia cavimana as consisting of two groups of muscles: a strong, complex, dorsal muscle cord used mainly for hopping and a group of weaker, ventral, longitudinal and oblique muscles.The specimens were collected in clumps of decaying seaweed and other detritus from the intertidal zone near the high water mark at Avery Point Beach, Connecticut.

High Water Mark Bias - A New Hedge Fund Index Bias

2014 ◽  
Author(s):  
James Skeggs ◽  
Lianyan Liu
Keyword(s):  
Hedge Fund ◽  
High Water ◽  
High Water Mark
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