Visualisation of Multi-agent System Organisations Using a Self-organising Map of Pareto Solutions

The structure and performance of organisations – natural or manmade – are intricately linked, and these multifaceted interactions are increasingly being investigated using Multi Agent System concepts. This paper shows how a selection of generic structural metrics for organisations can be explored using a combination of Pareto Frontier exemplars, from extensive simulations of simple goal-orientated Multi Agent Systems, and exposé of organisational types through Self-Organising Map clusters can provide insights into desirable structures for such objectives as robustness and efficiency. 1 Background and Motivation The increasing trends for complexity in industry and the lack of explicit Multi Agent Systems (MAS) research into organisations outside of coordination techniques [1, 2] is the basis of our research programme. An organisation’s behaviour/performance is primarily a function of its environment, the composition of its individual agents and how they interact. In turn, how agents are connected determines an organisation’s structure [3]. Our underlying research questions include how to measure and visualise the relationships between structure and performance, and why organisational structures/attributes (e.g. centralised, hierarchical) are more suited specific performance requirements. To examine these research questions, an extendable simulation has been developed that can construct organisations of varying complexity and size to solve simple tasks. This is discussed in §3, proceeding an overview of our work to develop a method of graphing organisational structure and a set of generic metrics to quantify structural relationships. 2 Relating Organisational Structure to Performance Much work has been carried out in the MAS and Distributed Artificial Intelligence (DAI) community to formalise individual utterances between agents [4]. These ‘conversations’ have been retrospectively examined using methods developed for Social Network and Dooley Graphs, where nodes represent identities of particular agents as well as the state of information transferred [5]. In our simulation, we chart the conversations between agents and the type of information conveyed. The graphs can be described in matrix form, which lends itself to deeper analysis of organisational structure. Using this organisational structure matrix, we can quantify the type of structure based on a set of metrics. Below is an overview of some of these metrics. For a full description of how the network graphs are constructed, matrices developed and details of all metrics see [6]. • Centrality of communication – The overall cohesion of a network graph, indicating the extent to which a graph is organised around its most central point [7]. This metric has been adapted to cope with multiple connections afferent or efferent between two or more points. A measure of ‘1’ indicates a fully centralised network while ‘0’ indicates no communication or fully decentralised network where all communication is equal between nodes. • Degree hierarchy – Krackhardt [8] developed a measure of degree of hierarchy that indicates the extent to which relations among the nodes in a network are ordered and there is little, if any, reciprocity. A measure of ‘1’ indicates a fully hierarchical network while ‘0’ indicates a flat organisational structure. • Specialisation – In heterogeneous organisations, capabilities and skills will be unevenly distributed. For each particular capability, we measure the volatility of distribution in agents over the entire organisation. A measure of ‘1’ indicates a fully specialised skill, meaning only one agent has a particular skill. ‘0’ indicates that all agents have the said skill with equal degree. • Heterogeneity of capabilities – The heterogeneity of capabilities looks at how capabilities are distributed throughout an organisation while ‘0’ indicates that the sum of each capability throughout the group is equal. The greater the difference, the more this measure will tend towards ‘1’. Using these generic metrics, we can relate them to organisations and their specific performance metrics in an effort to understand how structure affects performance, and aid our understanding and design of organisations. 3 Organisational Metrics Concept Demonstrator The Java based Organisational Metrics Concept Demonstrator (OMCD) simulation is based on a two-dimensional grid which has no boundary conditions and where the agents have a simple “find and remove” objective. The agents move around the grid using a random walk searching for one or more ‘targets’. When a target appears within an agent’s search range, the agent communicates that a potential target has been found by placing a communication ‘signal’ around the target. The signal is strongest at the source, and tails off to zero at the edges. Agents that can remove targets and are within the signal’s region will travel up the signal gradient to the source. The communication is recorded in a relationship matrix outlined in §2. To summarise, an agent, j, will have one or more capabilities, i, defined as cij where , and Na is the total number of a j j N ∈ ∧ ≤ { } search, remove, communicate i = agents in the organisation. cij describes the range of capability i; if no capability is present, cij is zero. Validation of the model and further details about the simulation are covered in [6]. 3.1 Time taken to reach termination condition The termination condition of the simulation is defined as the removal of all targets in the environment. The time taken, τ, to remove all targets is the average time taken from a set of simulations, or epochs ε, based on a single scenario configuration, but with random start positions. The average time taken has an error margin determined through standard statistical methods. The normalised time taken which also includes the ‘cost of organisation’ dimensional parameter is defined as: