A distributed optimization method for the geographically distributed data centres problem

The geographically distributed data centres problem (GDDC) is a naturally distributed resource allocation problem. The problem involves allocating a set of virtual machines (VM) amongst the data centres (DC) in each time period of an operating horizon. The goal is to optimize the allocation of workload across a set of DCs such that the energy cost is minimized, while respecting limitations on data centre capacities, migrations of VMs, etc. In this paper, we propose a distributed optimization method for GDDC using the distributed constraint optimization (DCOP) framework. First, we develop a new model of the GDDC as a DCOP where each DC operator is represented by an agent. Secondly, since traditional DCOP approaches are unsuited to these types of large-scale problem with multiple variables per agent and global constraints, we introduce a novel semi-asynchronous distributed algorithm for solving such DCOPs. Preliminary results illustrate the benefits of the new method

Combining search strategies for distributed constraint satisfaction.

Many real-life problems such as distributed meeting scheduling, mobile frequency allocation and resource allocation can be solved using multi-agent paradigms. Distributed constraint satisfaction problems (DisCSPs) is a framework for describing such problems in terms of related subproblems, called a complex local problem (CLP), which are dispersed over a number of locations, each with its own constraints on the values their variables can take. An agent knows the variables in its CLP plus the variables (and their current value) which are directly related to one of its own variables and the constraints relating them. It knows little about the rest of the problem. Thus, each CLP is solved by an agent which cooperates with other agents to solve the overall problem. Algorithms for solving DisCSPs can be classified as either systematic or local search with the former being complete and the latter incomplete. The algorithms generally assume that each agent has only one variable as they can solve DisCSP with CLPs using virtual agents. However, in large DisCSPs where it is appropriate to trade completeness off against timeliness, systematic search algorithms can be expensive when compared to local search algorithms which generally converge quicker to a solution (if a solution is found) when compared to systematic algorithms. A major drawback of local search algorithms is getting stuck at local optima. Significant researches have focused on heuristics which can be used in an attempt to either escape or avoid local optima. This thesis makes significant contributions to local search algorithms for DisCSPs. Firstly, we present a novel combination of heuristics in DynAPP (Dynamic Agent Prioritisation with Penalties), which is a distributed synchronous local search algorithm for solving DisCSPs having one variable per agent. DynAPP combines penalties on values and dynamic agent prioritisation heuristics to escape local optima. Secondly, we develop a divide and conquer approach that handles DisCSP with CLPs by exploiting the structure of the problem. The divide and conquer approach prioritises the finding of variable instantiations which satisfy the constraints between agents which are often more expensive to satisfy when compared to constraints within an agent. The approach also exploits concurrency and combines the following search strategies: (i) both systematic and local searches; (ii) both centralised and distributed searches; and (iii) a modified compilation strategy. We also present an algorithm that implements the divide and conquer approach in Multi-DCA (Divide and Conquer Algorithm for Agents with CLPs). DynAPP and Multi-DCA were evaluated on several benchmark problems and compared to the leading algorithms for DisCSPs and DisCSPs with CLPs respectively. The results show that at the region of difficult problems, combining search heuristics and exploiting problem structure in distributed constraint satisfaction achieve significant benefits (i.e. generally used less computational time and communication costs) over existing competing methods

Application of Techniques for MAP Estimation to Distributed Constraint Optimization Problem

The problem of efficiently finding near-optimal decisions in multi-agent systems has become increasingly important because of the growing number of multi-agent applications with large numbers of agents operating in real-world environments. In these systems, agents are often subject to tight resource constraints and agents have only local views. When agents have non-global constraints, each of which is independent, the problem can be formalized as a distributed constraint optimization problem (DCOP). The DCOP is closely associated with the problem of inference on graphical models. Many approaches from inference literature have been adopted to solve DCOPs. We focus on the Max-Sum algorithm and the Action-GDL algorithm that are DCOP variants of the popular inference algorithm called the Max-Product algorithm and the Belief Propagation algorithm respectively. The Max-Sum algorithm and the Action-GDL algorithm are well-suited for multi-agent systems because it is distributed by nature and requires less communication than most DCOP algorithms. However, the resource requirements of these algorithms are still high for some multi-agent domains and various aspects of the algorithms have not been well studied for use in general multi-agent settings. This thesis is concerned with a variety of issues of applying the Max-Sum algorithms and the Action-GDL algorithm to general multi-agent settings. We develop a hybrid algorithm of ADOPT and Action-GDL in order to overcome the communication complexity of DCOPs. Secondly, we extend the Max-Sum algorithm to operate more efficiently in more general multi-agent settings in which computational complexity is high. We provide an algorithm that has a lower expected computational complexity for DCOPs even with n-ary constraints. Finally, In most DCOP literature, a one-to-one mapping between a variable and an agent is assumed. However, in real applications, many-to-one mappings are prevalent and can also be beneficial in terms of communication and hardware cost in situations where agents are acting as independent computing units. We consider how to exploit such mapping in order to increase efficiency

Coalition Formation For Distributed Constraint Optimization Problems

This dissertation presents our research on coalition formation for Distributed Constraint Optimization Problems (DCOP). In a DCOP, a problem is broken up into many disjoint sub-problems, each controlled by an autonomous agent and together the system of agents have a joint goal of maximizing a global utility function. In particular, we study the use of coalitions for solving distributed k-coloring problems using iterative approximate algorithms, which do not guarantee optimal results, but provide fast and economic solutions in resource constrained environments. The challenge in forming coalitions using iterative approximate algorithms is in identifying constraint dependencies between agents that allow for effective coalitions to form. We first present the Virtual Structure Reduction (VSR) Algorithm and its integration with a modified version of an iterative approximate solver. The VSR algorithm is the first distributed approach for finding structural relationships, called strict frozen pairs, between agents that allows for effective coalition formation. Using coalition structures allows for both more efficient search and higher overall utility in the solutions. Secondly, we relax the assumption of strict frozen pairs and allow coalitions to form under a probabilistic relationship. We identify probabilistic frozen pairs by calculating the propensity between two agents, or the joint probability of two agents in a k-coloring problem having the same value in all satisfiable instances. Using propensity, we form coalitions in sparse graphs where strict frozen pairs may not exist, but there is still benefit to forming coalitions. Lastly, we present a cooperative game theoretic approach where agents search for Nash stable coalitions under the conditions of additively separable and symmetric value functions

Constructing a unifying theory of dynamic programming DCOP algorithms via the generalized distributive law

In this paper we propose a novel message-passing algorithm, the so-called Action-GDL, as an extension to the generalized distributive law (GDL) to ef¿ciently solve DCOPs. Action-GDL provides a unifying perspective of several dynamic programming DCOP algorithms that are based on GDL, such as DPOP and DCPOP algorithms. We empirically show how Action-GDL using a novel distributed post-processing heuristic can outperform DCPOP, and by extension DPOP, even when the latter uses the best arrangement provided by multiple state-of-the-art heuristics.Work funded by IEA (TIN2006-15662-C02-01), AT (CONSOLIDER CSD2007-0022, INGENIO 2010) and EVE (TIN2009-14702-C02-01 and 02). Vinyals is supported by the Spanish Ministry of Education (FPU grant AP2006-04636)Peer Reviewe