Improving local search heuristics for some scheduling problems - I

Local search techniques like simulated annealing and tabu search are based on a neighborhood structure defined on a set of feasible solutions of a discrete optimization problem. For the scheduling problems $P2||C_{max}, 1|prec|\sum C_i$ and $1||\sum T_i$ we replace a simple neighborhood by a neighborhood on the set of all locally optimal solutions. This allows local search on the set of solutions that are locally optimal

Adaptive Parallel Iterative Deepening Search

Many of the artificial intelligence techniques developed to date rely on heuristic search through large spaces. Unfortunately, the size of these spaces and the corresponding computational effort reduce the applicability of otherwise novel and effective algorithms. A number of parallel and distributed approaches to search have considerably improved the performance of the search process. Our goal is to develop an architecture that automatically selects parallel search strategies for optimal performance on a variety of search problems. In this paper we describe one such architecture realized in the Eureka system, which combines the benefits of many different approaches to parallel heuristic search. Through empirical and theoretical analyses we observe that features of the problem space directly affect the choice of optimal parallel search strategy. We then employ machine learning techniques to select the optimal parallel search strategy for a given problem space. When a new search task is input to the system, Eureka uses features describing the search space and the chosen architecture to automatically select the appropriate search strategy. Eureka has been tested on a MIMD parallel processor, a distributed network of workstations, and a single workstation using multithreading. Results generated from fifteen puzzle problems, robot arm motion problems, artificial search spaces, and planning problems indicate that Eureka outperforms any of the tested strategies used exclusively for all problem instances and is able to greatly reduce the search time for these applications

Development of 2MASS Catalog Server Kit

We develop a software kit called "2MASS Catalog Server Kit" to easily construct a high-performance database server for the 2MASS Point Source Catalog (includes 470,992,970 objects) and several all-sky catalogs. Users can perform fast radial search and rectangular search using provided stored functions in SQL similar to SDSS SkyServer. Our software kit utilizes open-source RDBMS, and therefore any astronomers and developers can install our kit on their personal computers for research, observation, etc. Out kit is tuned for optimal coordinate search performance. We implement an effective radial search using an orthogonal coordinate system, which does not need any techniques that depend on HTM or HEALpix. Applying the xyz coordinate system to the database index, we can easily implement a system of fast radial search for relatively small (less than several million rows) catalogs. To enable high-speed search of huge catalogs on RDBMS, we apply three additional techniques: table partitioning, composite expression index, and optimization in stored functions. As a result, we obtain satisfactory performance of radial search for the 2MASS catalog. Our system can also perform fast rectangular search. It is implemented using techniques similar to those applied for radial search. Our way of implementation enables a compact system and will give important hints for a low-cost development of other huge catalog databases.Comment: 2011 PASP accepte

Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at http://www.youtube.com/watch?v=TQIoCC48gp

Generalized Quantum Search with Parallelism

We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's algorithm succeeding after n iterations. We show that the fully generalized formula reduces to the special cases considered by previous authors. We then use the generalized formula to determine the optimal strategy for using the unstructured quantum search algorithm. On average the optimal strategy is about 12% better than the naive use of Grover's algorithm. The speedup obtained is not dramatic but it illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. We extend the analysis to the case of a society of k quantum searches acting in parallel. We derive an analytic formula that connects the degree of parallelism with the optimal strategy for k-parallel quantum search. We then derive the formula for the expected speed of k-parallel quantum search.Comment: 14 pages, 2 figure