Heuristic search through islands

A heuristic search strategy via islands is suggested to significantly decrease the number of nodes expanded. Algorithm I, which searches through a set of island nodes (“island set”), is presented assuming that the island set contains at least one node on an optimal cost path. This algorithm is shown to be admissible and expands no more nodes than A1. For cases where the island set does not contain an optimal cost path (or any path). Algorithm I', a modification of Algorithm I, is suggested. This algorithm ensures a suboptimal cost path (which may be optimal) and in extreme cases falls back to A1.     

Heuristic search for equivalence checking

Equivalence checking plays a crucial role in formal verification since it is a natural relation for expressing the matching of a system implementation against its specification. In this paper, we present an efficient procedure, based on heuristic search, for checking well-known bisimulation equivalences for concurrent systems specified through process algebras. The method tries to improve, with respect to other solutions, both the memory occupation and the time required for proving the equivalence of systems. A prototype has been developed to evaluate the approach on several examples of concurrent system specifications.     

Deception,dominance and implicit parallelism in genetic search

This paper presents several theorems concerning the nature of deception, its relationship to hyperplane dominance, and the central role that deception plays in function optimization using genetic algorithms. The theoretical results relate to four general themes. First, the concept of a deceptive attractor is introduced; it is shown that a deceptive attractor must be the complement of the global solution for a problem to be fully deceptive. It is also shown that the deceptive attractor must either be a local optimum in Hamming space, or adjacent to a local optimum in Hamming space if the problem is fully deceptive. Second, it can be shown that the global solution to nondeceptive problems can be inferred (theoretically and often in practice) by determining the winners of the order-1 hyperplanes. The third theme relates the concept of deception and dominance. If a dominance relationship exists between two hyperplanes then deception is impossible between those two partitions of hyperspace; analogously, deception between two hyperplanes precludes a dominance relationship. The fourth theme relates to deception and implicit parallelism. It can be shown that if a genetic algorithm reliably allocates exponentially more trials to the observed best, then implicit parallelism (and the 2-arm bandit analogy) breaks down when deception is present.     

In Scott-Strachey style denotational semantics,parallelism implies nondeterminism

A minimum algebraic structure needed in Scott-Strachey style denotational semantics for parallel programs is developed. Some elementary algebra shows that nondeterministic semantics is inherently and uniquely present. Conversely, any simple nondeterministic semantics provides uniquely a semantics for a minimal parallel computation capability.Research supported in part by National Science Foundation grants MCS77-08486 and MCS80-03433.     

Heuristic search for the stacking problem

This paper presents the Stacking Problem, a hard combinatorial optimization problem concerning handling and storage of items in a warehouse, where they are handled by a crane and organized into stacks. We define the problem, study its complexity class, and present a mathematical programming model to solve it. In order to tackle medium‐ or large‐scale instances, we propose a simulation‐based algorithm using semi‐greedy construction heuristics. This simple approach allows for multiple constructions, finding solutions within reasonable time even for large instances. Three semi‐greedy heuristics are proposed and compared in an extensive computational experiment, where we study the relation between the number of constructions and the best solution obtained using each heuristic.     

Heuristic search for scheduling flexible manufacturing systems using lower bound reachability matrix

For scheduling flexible manufacturing systems efficiently, we propose new heuristic functions for A^* algorithm that is based on the T-timed Petri net. In minimizing makespan, the proposed heuristic functions are usually more efficient than the previous functions in the required number of states and computation time. We prove that these heuristic functions are all admissible and one of them is more informed than that using resource cost reachability matrix. We also propose improved versions of these heuristic functions that find a first near-optimal solution faster. In addition, we modify the heuristic function of Yu, Reyes, Cang, and Lloyd (2003b) and propose an admissible version in all states. The experimental results using a random problem generator show that the proposed heuristic functions perform better as we expected.     

Heuristic search for scheduling flexible manufacturing systems using lower bound reachability matrix

For scheduling flexible manufacturing systems efficiently, we propose new heuristic functions for A^* algorithm that is based on the T-timed Petri net. In minimizing makespan, the proposed heuristic functions are usually more efficient than the previous functions in the required number of states and computation time. We prove that these heuristic functions are all admissible and one of them is more informed than that using resource cost reachability matrix. We also propose improved versions of these heuristic functions that find a first near-optimal solution faster. In addition, we modify the heuristic function of Yu, Reyes, Cang, and Lloyd (2003b) and propose an admissible version in all states. The experimental results using a random problem generator show that the proposed heuristic functions perform better as we expected.     

Heuristic evaluation functions in artificial intelligence search algorithms

We consider a special case of heuristics, namely numeric heuristic evaluation functions, and their use in artificial intelligence search algorithms. The problems they are applied to fall into three general classes: single-agent path-finding problems, two-player games, and constraint-satisfaction problems. In a single-agent path-finding problem, such as the Fifteen Puzzle or the travelling salesman problem, a single agent searches for a shortest path from an initial state to a goal state. Two-player games, such as chess and checkers, involve an adversarial relationship between two players, each trying to win the game. In a constraint-satisfaction, problem, such as the 8-Queens problem, the task is to find a state that satisfies a set of constraints. All of these problems are computationally intensive, and heuristic evaluation functions are used to reduce the amount of computation required to solve them. In each case we explain the nature of the evaluation functions used, how they are used in search algorithms, and how they can be automatically learned or acquired.     

Heuristic search and pruning in polynomial constraints satisfaction

In this paper, we report how certain AI techniques can be used to speed up an algebraic algorithm for deciding the satisfiability of a system of polynomial equations, dis-equations, and inequalities. We begin by viewing the algebraic algorithm (Cylindrical Algebraic Decomposition) as a search procedure which searches for a solution of the given system. When viewed in this way, the algebraic algorithm is non-deterministic, in the sense that it can often achieve the same goal, but following different search paths requiring different amounts of computing times. Obviously one wishes to follow the least time-consuming path. However, in practice it is not possible to determine such an optimal path. Thus it naturally renders itself to the heuristic search techniques of AI. In particular we experimented with Best-First strategy. We also study a way to prune the search space, which proves to be useful especially when the given polynomial system is not satisfiable. The experimental results indicate that such AI techniques can often help in speeding up the algebraic method, sometimes dramatically. This revised version was published online in June 2006 with corrections to the Cover Date.     

Heuristic search for one-to-many shortest path queries

Annals of Mathematics and Artificial Intelligence - In this paper we study the One-to-Many Shortest Path Problem (OMSPP), which is the problem of solving k shortest path problems that share the...     

Heuristic search + local model checking in selective mu-calculus

Many tools for the automatic analysis or verification of finite-state distributed systems are based on construction of the global state graph of the system under consideration. Thus, they often fail because of the state explosion problem: the state space of a distributed system potentially increases exponentially in the number of its parallel components. To overcome this problem, we present a model checking procedure, based on the combination of heuristic searches with ideas taken from local model checking. We use heuristic mechanisms for exploration of the search space in order to avoid construction of the complete state graph.     

基于用户行为的启发式本体搜索机制

为了能够以较高的准确率搜索到用户所需要的领域本体,在分析本体搜索需求和研究用户搜索行为的基础上,提出了一种基于用户行为的启发式本体搜索机制,利用不同用户由于领域认知不同,输入的具有领域共性的搜索关键词不同,实现用户搜索关键词的启发式扩展和搜索匹配度的提高。实验表明,使用该方法执行本体搜索具有较高的准确率和召回率。     

Heuristic manipulation,tabu search and frequency assignment

Heuristic manipulation attempts to modify the search space of an optimization problem, using information provided by an underlying heuristic method. In this paper it is applied in combination with tabu search to the fixed spectrum frequency assignment problem.The frequency assignment problem involves the assignment of discrete channels (or frequencies) to the transmitters of a radio network, such as a mobile telephone network. Frequency separation is necessary to avoid interference by other transmitters to the signal received from the wanted transmitter at the reception points. Unnecessary separation causes an excess requirement for spectrum. Good assignments minimize interference and the spectrum required. In fixed spectrum frequency assignment the frequency spectrum available is given and the target is to minimize the interference in the network.Computational experiments confirm that the manipulation technique is able to drive the underlying tabu search algorithm towards improved solutions.     

Approximate string matching using withinword parallelism

Given a text string, a pattern string, and an integer k, the problem of approximate string matching with k differences is to find all substrings of the text string whose edit distance from the pattern string is less than k. The edit distance between two strings is defined as the minimum number of differences, where a difference can be a substitution, insertion, or deletion of a single character. An implementation of the dynamic programming algorithm for this problem is given that packs several characters and mod-4 integers into a computer word. Thus, it is a parallelization of the conventional implementation that runs on ordinary processors. Since a small alphabet means that characters have short binary codes, the degree of parallelism is greatest for small alphabets and for processors with long words. For an alphabet of size 8 or smaller and a 64 bit processor, a 21-fold parallelism over the conventional algorithm can be obtained. Empirical comparisons to the basic dynamic programming algorithm, to a version of Ukkonen's algorithm, to the algorithm of Galil and Park, and to a limited implementation of the Wu-Manber algorithm are given.     

Achieving full parallelism using multidimensional retiming

Most scientific and digital signal processing (DSP) applications are recursive or iterative. Transformation techniques are usually applied to get optimal execution rates in parallel and/or pipeline systems. The retiming technique is a common and valuable transformation tool in one-dimensional problems, when loops are represented by data flow graphs (DFGs). In this paper, uniform nested loops are modeled as multidimensional data flow graphs (MDFGs). Full parallelism of the loop body, i.e., all nodes in the MDFG executed in parallel, substantially decreases the overall computation time. It is well known that, for one-dimensional DFGs, retiming can not always achieve full parallelism. Other existing optimization techniques for nested loops also can not always achieve full parallelism. This paper shows an important and counter-intuitive result, which proves that we can always obtain full-parallelism for MDFGs with more than one dimension. This result is obtained by transforming the MDFG into a new structure. The restructuring process is based on a multidimensional retiming technique. The theory and two algorithms to obtain full parallelism are presented in this paper. Examples of optimization of nested loops and digital signal processing designs are shown to demonstrate the effectiveness of the algorithms     

Data and task parallelism in ILP using MapReduce

Nearly two decades of research in the area of Inductive Logic Programming (ILP) have seen steady progress in clarifying its theoretical foundations and regular demonstrations of its applicability to complex problems in very diverse domains. These results are necessary, but not sufficient, for ILP to be adopted as a tool for data analysis in an era of very large machine-generated scientific and industrial datasets, accompanied by programs that provide ready access to complex relational information in machine-readable forms (ontologies, parsers, and so on). Besides the usual issues about the ease of use, ILP is now confronted with questions of implementation. We are concerned here with two of these, namely: can an ILP system construct models efficiently when (a) Dataset sizes are too large to fit in the memory of a single machine; and (b) Search space sizes becomes prohibitively large to explore using a single machine. In this paper, we examine the applicability to ILP of a popular distributed computing approach that provides a uniform way for performing data and task parallel computations in ILP. The MapReduce programming model allows, in principle, very large numbers of processors to be used without any special understanding of the underlying hardware or software involved. Specifically, we show how the MapReduce approach can be used to perform the coverage-test that is at the heart of many ILP systems, and to perform multiple searches required by a greedy set-covering algorithm used by some popular ILP systems. Our principal findings with synthetic and real-world datasets for both data and task parallelism are these: (a) Ignoring overheads, the time to perform the computations concurrently increases with the size of the dataset for data parallelism and with the size of the search space for task parallelism. For data parallelism this increase is roughly in proportion to increases in dataset size; (b) If a MapReduce implementation is used as part of an ILP system, then benefits for data parallelism can only be expected above some minimal dataset size, and for task parallelism can only be expected above some minimal search-space size; and (c) The MapReduce approach appears better suited to exploit data-parallelism in ILP.