828752
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called generalized monotone schemes. Convergence toward the entropy solution is proven via a new technique of proof, assuming that the initial data has a finite number of extremum values only, and the flux-function is strictly convex. We define discrete paths of extrema by tracking local extremum values in the approximate solution. In the course of the analysis we establish the pointwise convergence of the trace of the solution along a path of extremum. As a corollary, we obtain a proof of convergence for a MUSCL-type scheme that is second order accurate away from sonic points and extrema.
18986222
Concepts and Application of Time-Limiters to High Resolution Schemes
A new class of implicit high-order non-oscillatory time integration schemes is introduced in a method-of-lines framework. These schemes can be used in conjunction with an appropriate spatial discretization scheme for the numerical solution of time dependent conservation equations. The main concept behind these schemes is that the order of accuracy in time is dropped locally in regions where the time evolution of the solution is not smooth. By doing this, an attempt is made at locally satisfying monotonicity conditions, while maintaining a high order of accuracy in most of the solution domain. When a linear high order time integration scheme is used along with a high order spatial discretization, enforcement of monotonicity imposes severe time-step restrictions. We propose to apply limiters to these time-integration schemes, thus making them non-linear. When these new schemes are used with high order spatial discretizations, solutions remain non-oscillatory for much larger time-steps as compared to linear time integration schemes. Numerical results obtained on scalar conservation equations and systems of conservation equations are highly promising.
6396851
Multiagent diffusion and distributed optimization
Distributed problem solving by a multiagent system represents a promising approach to solving complex computational problems. However, many multiagent systems require certain degree of planning, coordination and negotiation to achieve the given goal. This paper presents a multiagent framework for tackling global optimization tasks inspired by diffusion in nature. The framework is designed for situations where agent communication must be kept to a minimal. Hence, complicated coordination and negotiation is not possible. Distributed agents in this framework share the common goal of finding the global optimal solution. They cooperate to achieve this common goal by sharing and updating a common belief that captures their estimation of the whereabouts of the optimal solution. To facilitate this, agents are naturally organized in families with a parent and its offsprings as members. This paper also presents an algorithm called Evolutionary Diffusion Optimization, which is implemented base on the proposed agent framework. Experimental results on some benchmark problems are presented together with performance comparison with a simulated annealing algorithm.
592449
Aggregating local behaviors based upon a discrete Lagrange multiplier method
When solving a distributed problem based on a multi-agent system, the local behaviors of agents are aggregated to the global behaviors of the multi-agent system towards a solution state. This work presents a distributed discrete Lagrange multiplier (DDLM) method for solving distributed constraint satisfaction problems (distributed CSPs). In this method, the local behaviors of agents are aggregated as a descent direction of an objective function corresponding to the problem at hand. Thus, a trend to a solution state are formed. Furthermore, we provide three techniques to speed up the aggregation of agents' local behaviors. Through experiments on benchmark graph coloring problems, we validate the effectiveness of the presented DDLM method as well as the three techniques in solving distributed CSPs.
15358098
Multi-agent oriented constraint satisfaction
This paper presents a multi-agent oriented method for solving CSPs (Constraint Satisfaction Problems). In this method, distributed agents represent variables and a two-dimensional grid-like environment in which the agents inhabit corresponds to the domains of the variables. Thus, the positions of the agents in such an environment constitute the solution to a CSP. In order to reach a solution state, the agents will rely on predefined local reactive behaviors; namely, better-move, least-move, and random-move. While presenting the formalisms and algorithm, we will analyze the correctness and complexity of the algorithm, and demonstrate the proposed method with two benchmark CSPs, i.e., n-queen problems and coloring problems. In order to further determine the effectiveness of different reactive behaviors, we will examine the performance of this method in deriving solutions based on behavior prioritization and different selection probabilities.
17616084
Modeling agent-based load balancing with time delays
In grid computing, agent-based load balancing is one of the most important problems. In this paper, we present a macroscopic model to describe the dynamics of agent-based load balancing with time delays. We concern the number and size of teams where tasks queue. The time gap, during which a single agent searches a suitable node and transfers a task to the node, is incorporated into balancing process as delay. Our model is composed of functional differential equations. By numerical simulations, we show that variables (the number and size of teams, etc.) in the model remain nonnegative, which is in agreement with the physical background of the variables. We show that although there is a period of oscillation, the dynamic behavior tends to a steady state, which is in agreement with the recent experiments on Anthill. An interesting phenomenon is shown: the larger the delay, the longer the period of oscillation, and the slower the converging speed of load balancing.
2364475
Combined functional partitioning and communication speed selection for networked voltage-scalable processors
This paper presents a new technique for global energy optimization through coordinated functional partitioning and speed selection for embedded processors interconnected by a high-speed serial bus. Many such serial interfaces are capable of operating at multiple speeds and can open up a new dimension of trade-offs to complement today's CPU-centric voltage scaling techniques for processors. We propose a multi-dimensional dynamic programming formulation for energy-optimal functional partitioning with CPU/communication speed selection for a class of data-regular applications under performance constraints. We demonstrate the effectiveness of our optimization techniques with an image processing application mapped onto a multi-processor architecture with a multi-speed Ethernet.