The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks

It is challenging to design large and low-cost communication networks. In this paper, we formulate this challenge as the prize-collecting Steiner Tree Problem (PCSTP). The objective is to minimize the costs of transmission routes and the disconnected monetary or informational profits. Initially, we note that the PCSTP is MAX SNP-hard. Then, we propose some post-processing techniques to improve suboptimal solutions to PCSTP. Based on these techniques, we propose two fast heuristic algorithms: the first one is a quasilinear time heuristic algorithm that is faster and consumes less memory than other algorithms; and the second one is an improvement of a stateof-the-art polynomial time heuristic algorithm that can find high-quality solutions at a speed that is only inferior to the first one. We demonstrate the competitiveness of our heuristic algorithms by comparing them with the state-of-the-art ones on the largest existing benchmark instances (169 800 vertices and 338 551 edges). Moreover, we generate new instances that are even larger (1 000 000 vertices and 10 000 000 edges) to further demonstrate their advantages in large networks. The state-ofthe-art algorithms are too slow to find high-quality solutions for instances of this size, whereas our new heuristic algorithms can do this in around 6 to 45s on a personal computer. Ultimately, we apply our post-processing techniques to update the bestknown solution for a notoriously difficult benchmark instance to show that they can improve near-optimal solutions to PCSTP. In conclusion, we demonstrate the usefulness of our heuristic algorithms and post-processing techniques for designing large and low-cost communication networks

Optimally locating a junction point for an underground mine to maximise the net present value

A review of the relevant literature identified an opportunity to develop algorithms for designing the access and construction schedule for an underground mine to maximise the net present value (NPV). The methods currently available perform the optimisation separately. However, this article focuses on optimising the access design and construction schedule simultaneously to yield a higher NPV. Underground mine access design was previously studied with the objective of minimising the haulage and development costs. However, when scheduling is included, time value of money has a crucial effect on locating the junction points (Steiner points) in the access network for maximum value. This article proposes an efficient algorithm to optimally locate a single junction, given a surface portal and two ore bodies, for maximum NPV where NPV includes the value of the ore bodies and the construction costs. We describe the variation in the location of the junction for a range of discount rates. References K. F. Lane, The economic definition of ore---cutoff grade in theory and practice. Mining Journal Books Limited, London 1988. F. K. Hwang, D. S. Richards and P. Winter, The Steiner tree problem. Elsevier, 1992. http://www.elsevier.com/books/the-steiner-tree-problem/hwang/978-0-444-89098-6 M. Brazil and D. A. Thomas, Network optimisation for the design of underground mines. Networks 49:40–50, 2007. doi:10.1002/net.20140 M. Brazil, J. H. Rubinstein, D. A. Thomas, J. F. Weng and N. C. Wormald, Gradient-constrained minimum networks (I). Fundamentals. J. Global Optim. 21:139–155, 2001. doi:10.1023/A:101190321029