Adaptive selection of search space in look ahead orthogonal matching pursuit

Compressive Sensing theory combines the signal sampling and compression for sparse signals resulting in reduction in sampling rate and computational complexity of the measurement system. In recent years, many recovery algorithms were proposed to reconstruct the signal efficiently. Look Ahead OMP (LAOMP) is a recently proposed method which uses a look ahead strategy and performs significantly better than other greedy methods. In this paper, we propose a modification to the LAOMP algorithm to choose the look ahead parameter L adaptively, thus reducing the complexity of the algorithm, without compromising on the performance. The performance of the algorithm is evaluated through Monte Carlo simulations.

On Selection of Search Space Dimension in Compressive Sampling Matching Pursuit

Compressive Sampling Matching Pursuit (CoSaMP) is one of the popular greedy methods in the emerging field of Compressed Sensing (CS). In addition to the appealing empirical performance, CoSaMP has also splendid theoretical guarantees for convergence. In this paper, we propose a modification in CoSaMP to adaptively choose the dimension of search space in each iteration, using a threshold based approach. Using Monte Carlo simulations, we show that this modification improves the reconstruction capability of the CoSaMP algorithm in clean as well as noisy measurement cases. From empirical observations, we also propose an optimum value for the threshold to use in applications.

Deploy and search strategy for multi-agent systems using Voronoi partitions

In this paper we analyze a deploy and search strategy for multi-agent systems. Mobile agents equipped with sensors carry out search operation in the search space. The lack of information about the search space is modeled as an uncertainty density distribution over the space, and is assumed to be known to the agents a priori. In each step, the agents deploy themselves in an optimal way so as to maximize per step reduction in the uncertainty density. We analyze the proposed strategy for convergence and spatial distributedness. The control law moving the agents has been analyzed for stability and convergence using LaSalle's invariance principle, and for spatial distributedness under a few realistic constraints on the control input such as constant speed, limit on maximum speed, and also sensor range limits. The simulation experiments show that the strategy successfully reduces the average uncertainty density below the required level.

Two-agent cooperative search using game models with endurance-time constraints

In this article, the problem of two Unmanned Aerial Vehicles (UAVs) cooperatively searching an unknown region is addressed. The search region is discretized into hexagonal cells and each cell is assumed to possess an uncertainty value. The UAVs have to cooperatively search these cells taking limited endurance, sensor and communication range constraints into account. Due to limited endurance, the UAVs need to return to the base station for refuelling and also need to select a base station when multiple base stations are present. This article proposes a route planning algorithm that takes endurance time constraints into account and uses game theoretical strategies to reduce the uncertainty. The route planning algorithm selects only those cells that ensure the agent will return to any one of the available bases. A set of paths are formed using these cells which the game theoretical strategies use to select a path that yields maximum uncertainty reduction. We explore non-cooperative Nash, cooperative and security strategies from game theory to enhance the search effectiveness. Monte-Carlo simulations are carried out which show the superiority of the game theoretical strategies over greedy strategy for different look ahead step length paths. Within the game theoretical strategies, non-cooperative Nash and cooperative strategy perform similarly in an ideal case, but Nash strategy performs better than the cooperative strategy when the perceived information is different. We also propose a heuristic based on partitioning of the search space into sectors to reduce computational overhead without performance degradation.

Multi-agent Search using Voronoi partitions

This paper addresses the problem of multiagent search in an unknown environment. The agents are autonomous in nature and are equipped with necessary sensors to carry out the search operation. The uncertainty, or lack of information about the search area is known a priori as a probability density function. The agents are deployed in an optimal way so as to maximize the one step uncertainty reduction. The agents continue to deploy themselves and reduce uncertainty till the uncertainty density is reduced over the search space below a minimum acceptable level. It has been shown, using LaSalle’s invariance principle, that a distributed control law which moves each of the agents towards the centroid of its Voronoi partition, modified by the sensor range leads to single step optimal deployment. This principle is now used to devise search trajectories for the agents. The simulations were carried out in 2D space with saturation on speeds of the agents. The results show that the control strategy per step indeed moves the agents to the respective centroid and the algorithm reduces the uncertainty distribution to the required level within a few steps.

Performance of a class of multi-robot deploy and search strategies based on centroidal voronoi configurations

This article considers a class of deploy and search strategies for multi-robot systems and evaluates their performance. The application framework used is deployment of a system of autonomous mobile robots equipped with required sensors in a search space to gather information. The lack of information about the search space is modelled as an uncertainty density distribution. The agents are deployed to maximise single-step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for sequential deploy and search (SDS) and combined deploy and search (CDS) strategies. Completeness results are provided for both search strategies. The deployment strategy is analysed in the presence of constraints on robot speed and limit on sensor range for the convergence of trajectories with corresponding control laws responsible for the motion of robots. SDS and CDS strategies are compared with standard greedy and random search strategies on the basis of time taken to achieve reduction in the uncertainty density below a desired level. The simulation experiments reveal several important issues related to the dependence of the relative performances of the search strategies on parameters such as the number of robots, speed of robots and their sensor range limits.

Self assessment schemes for multi-agent cooperative search

In this paper, we present self assessment schemes (SAS) for multiple agents performing a search mission on an unknown terrain. The agents are subjected to limited communication and sensor ranges. The agents communicate and coordinate with their neighbours to arrive at route decisions. The self assessment schemes proposed here have very low communication and computational overhead. The SAS also has attractive features like scalability to large number of agents and fast decision-making capability. SAS can be used with partial or complete information sharing schemes during the search mission. We validate the performance of SAS using simulation on a large search space consisting of 100 agents with different information structures and self assessment schemes. We also compare the results obtained using SAS with that of a previously proposed negotiation scheme. The simulation results show that the SAS is scalable to large number of agents and can perform as good as the negotiation schemes with reduced communication requirement (almost 20% of that required for negotiation).

Automated Multi-Agent Search Using Centroidal Voronoi Configuration

This paper addresses the problem of automated multiagent search in an unknown environment. Autonomous agents equipped with sensors carry out a search operation in a search space, where the uncertainty, or lack of information about the environment, is known a priori as an uncertainty density distribution function. The agents are deployed in the search space to maximize single step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for the proposed sequential deploy and search strategy. It is shown that with the proposed control law the agent trajectories converge in a globally asymptotic manner to the centroidal Voronoi configuration. Simulation experiments are provided to validate the strategy. Note to Practitioners-In this paper, searching an unknown region to gather information about it is modeled as a problem of using search as a means of reducing information uncertainty about the region. Moreover, multiple automated searchers or agents are used to carry out this operation optimally. This problem has many applications in search and surveillance operations using several autonomous UAVs or mobile robots. The concept of agents converging to the centroid of their Voronoi cells, weighted with the uncertainty density, is used to design a search strategy named as sequential deploy and search. Finally, the performance of the strategy is validated using simulations.

Genetic search: Analysis using fitness moments

Genetic Algorithms are efficient and robust search methods that are being employed in a plethora of applications with extremely large search spaces. The directed search mechanism employed in Genetic Algorithms performs a simultaneous and balanced, exploration of new regions in the search space and exploitation of already discovered regions.This paper introduces the notion of fitness moments for analyzing the working of Genetic Algorithms (GAs). We show that the fitness moments in any generation may be predicted from those of the initial population. Since a knowledge of the fitness moments allows us to estimate the fitness distribution of strings, this approach provides for a method of characterizing the dynamics of GAs. In particular the average fitness and fitness variance of the population in any generation may be predicted. We introduce the technique of fitness-based disruption of solutions for improving the performance of GAs. Using fitness moments, we demonstrate the advantages of using fitness-based disruption. We also present experimental results comparing the performance of a standard GA and GAs (CDGA and AGA) that incorporate the principle of fitness-based disruption. The experimental evidence clearly demonstrates the power of fitness based disruption.

Multi-agent search using?sensors with heterogeneous capabilities

In this thesis we address the problem of multi-agent search. We formulate two deploy and search strategies based on optimal deployment of agents in search space so as to maximize the search effectiveness in a single step. We show that a variation of centroidal Voronoi configuration is the optimal deployment. When the agents have sensors with different capabilities, the problem will be heterogeneous in nature. We introduce a new concept namely, generalized Voronoi partition in order to formulate and solve the heterogeneous multi-agent search problem. We address a few theoretical issues such as optimality of deployment, convergence and spatial distributedness of the control law and the search strategies. Simulation experiments are carried out to compare performances of the proposed strategies with a few simple search strategies.

On the Production of Anorexic Plan Diagrams

A "plan diagram" is a pictorial enumeration of the execution plan choices of a database query optimizer over the relational selectivity space. We have shown recently that, for industrial-strength database engines, these diagrams are often remarkably complex and dense, with a large number of plans covering the space. However, they can often be reduced to much simpler pictures, featuring significantly fewer plans, without materially affecting the query processing quality. Plan reduction has useful implications for the design and usage of query optimizers, including quantifying redundancy in the plan search space, enhancing useability of parametric query optimization, identifying error-resistant and least-expected-cost plans, and minimizing the overheads of multi-plan approaches. We investigate here the plan reduction issue from theoretical, statistical and empirical perspectives. Our analysis shows that optimal plan reduction, w.r.t. minimizing the number of plans, is an NP-hard problem in general, and remains so even for a storage-constrained variant. We then present a greedy reduction algorithm with tight and optimal performance guarantees, whose complexity scales linearly with the number of plans in the diagram for a given resolution. Next, we devise fast estimators for locating the best tradeoff between the reduction in plan cardinality and the impact on query processing quality. Finally, extensive experimentation with a suite of multi-dimensional TPCH-based query templates on industrial-strength optimizers demonstrates that complex plan diagrams easily reduce to "anorexic" (small absolute number of plans) levels incurring only marginal increases in the estimated query processing costs.

A self-adaptive migration model genetic algorithm for data mining applications

Data mining involves nontrivial process of extracting knowledge or patterns from large databases. Genetic Algorithms are efficient and robust searching and optimization methods that are used in data mining. In this paper we propose a Self-Adaptive Migration Model GA (SAMGA), where parameters of population size, the number of points of crossover and mutation rate for each population are adaptively fixed. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions and a set of actual classification datamining problems. Michigan style of classifier was used to build the classifier and the system was tested with machine learning databases of Pima Indian Diabetes database, Wisconsin Breast Cancer database and few others. The performance of our algorithm is better than others.

Robust heuristics for scalable optimization of complex SQL queries

Modern database systems incorporate a query optimizer to identify the most efficient "query execution plan" for executing the declarative SQL queries submitted by users. A dynamic-programming-based approach is used to exhaustively enumerate the combinatorially large search space of plan alternatives and, using a cost model, to identify the optimal choice. While dynamic programming (DP) works very well for moderately complex queries with up to around a dozen base relations, it usually fails to scale beyond this stage due to its inherent exponential space and time complexity. Therefore, DP becomes practically infeasible for complex queries with a large number of base relations, such as those found in current decision-support and enterprise management applications. To address the above problem, a variety of approaches have been proposed in the literature. Some completely jettison the DP approach and resort to alternative techniques such as randomized algorithms, whereas others have retained DP by using heuristics to prune the search space to computationally manageable levels. In the latter class, a well-known strategy is "iterative dynamic programming" (IDP) wherein DP is employed bottom-up until it hits its feasibility limit, and then iteratively restarted with a significantly reduced subset of the execution plans currently under consideration. The experimental evaluation of IDP indicated that by appropriate choice of algorithmic parameters, it was possible to almost always obtain "good" (within a factor of twice of the optimal) plans, and in the few remaining cases, mostly "acceptable" (within an order of magnitude of the optimal) plans, and rarely, a "bad" plan. While IDP is certainly an innovative and powerful approach, we have found that there are a variety of common query frameworks wherein it can fail to consistently produce good plans, let alone the optimal choice. This is especially so when star or clique components are present, increasing the complexity of th- e join graphs. Worse, this shortcoming is exacerbated when the number of relations participating in the query is scaled upwards.

A Dynamic Migration Model for Self-adaptive Genetic Algorithms

In this paper, we propose a self Adaptive Migration Model for Genetic Algorithms, where parameters of population size, the number of points of crossover and mutation rate for each population are fixed adaptively. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions, when compared with Island model GA(IGA) and Simple GA(SGA).

A Dynamic Migration Model for self-adaptive Genetic Algorithms

In this paper, we propose a self Adaptive Migration Model for Genetic Algorithms, where parameters of population size, the number of points of crossover and mutation rate for each population are fixed adaptively. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions, when compared with Island model GA(IGA) and Simple GA(SGA).