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 of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems in large graphs. 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. GraphCombEx has previously or currently been tested in scenarios of exploring synthetic graph models, as well as real-world networks ranging from social network samples, biological networks, to very large networks from the SNAP network data repository. The tool has already been successfully used to support a number of recent studies and is particularly beneficial in exploring the combinatorial properties of previously unseen network data, before applying more sophisticated custom optimisation algorithms.
This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available. The application of unmanned aerial vehicle (UAV) in indoor environment is emerging nowadays due to the advancements in technology. UAV brings more space flexibility in an occupied or hardly accessible indoor environment, e.g. shop floor of manufacturing industry, greenhouse, and nuclear powerplant. UAV helps in creating an autonomous manufacturing system by executing tasks with less human intervention in a time-efficient manner. Consequently, a scheduler is an essential component to be focused on; yet the number of reported studies on UAV scheduling has been minimal. This work proposes a mathematical model of the problem and a heuristic-based methodology to solve it. To suit near real-time operations, a quick response towards uncertain events and a quick creation of new high-quality feasible schedule are needed. Hence, the proposed heuristic is incorporated with particle swarm optimization algorithm to find a near optimal schedule in a short computation time. This proposed methodology is implemented into a scheduler and tested on a few scales of datasets generated based on real flight demonstrations. Performance evaluation of scheduler is discussed in detail, and the best solution obtained from a selected set of parameters is reported.