GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

Hybrid STAN: Identifying and managing combinatorial optimisation sub-problems in planning

It is well-known that planning is hard but it is less well-known how to approach the hard parts of a problem instance effectively. Using static domain analysis techniques we can identify and abstract certain combinatorial sub-problems from a planning instance, and deploy specialised technology to solve these sub-problems in a way that is integrated with the broader planning activities. We have developed a hybrid planning system (STAN4) which brings together alternative planning strategies and specialised algorithms and selects them according to the structure of the planning domain. STAN4 participated successfully in the AIPS-2000 planning competition. We describe how sub-problem abstraction is done, with particular reference to route-planning abstraction, and present some of the competition data to demonstrate the potential power of the hybrid approach

Multiagent resource allocation with k-additive utility functions

We briefly review previous work on the welfare engineering framework where autonomous software agents negotiate on the allocation of a number of discrete resources, and point out connections to combinatorial optimisation problems, including combinatorial auctions, that shed light on the computational complexity of the framework. We give particular consideration to scenarios where the preferences of agents are modelled in terms of k-additive utility functions, i.e. scenarios where synergies between different resources are restricted to bundles of at most k items. Key words: negotiation, representation of utility functions, social welfare, combinatorial optimisation, bidding languages for combinatorial auctions

On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks

Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed

CAMELOT - computational-analytical multi-fidelity low-thrust optimisation toolbox

CAMELOT (Computational-Analytical Multi-fidelity Low-thrust Optimisation Toolbox) is a toolbox for the fast preliminary design and optimisation of low-thrust trajectories. It solves highly complex combinatorial problems to plan multi-target missions characterised by long spirals including different perturbations. In order to do so, CAMELOT implements a novel multi-fidelity approach combining analytical surrogate modelling and accurate computational estimations of the mission cost. Decisions are then made by using two pptimisation engines included in the toolbox, a single objective global optimiser and a combinatorial optimisation algorithm. CAMELOT has been applied to a variety of applications: from the design of interplanetary trajectories to the optimal deorbiting of space debris, from the deployment of constellations to on-orbit servicing. In this paper the main elements of CAMELOT are described and two space mission design problems solved using the toolbox are described