Computing Near-Optimal Solutions to the Steiner Problem in a Graph Using a Genetic Algorithm

A new Genetic Algorithm (GA) for the Steiner Problem in a Graph (SPG) is presented. The algorithm is based on a bitstring encoding. A bitstring specifies selected Steiner vertices and the corresponding Steiner tree is computed using the Distance Network Heuristic. This scheme ensures that every bitstring correspond to a valid Steiner tree and thus eliminates the need for penalty terms in the cost function. The GA is tested on all SPG instances from the OR-Library of which the largest graphs have 2,500 vertices and 62,500 edges. When executed 10 times on each of 58 graph examples, the GA finds the global optimum at least once for 55 graphs and every time for 43 graphs. In total the GA finds the global optimum in 77 % of all program executions and is within 1 % from the global optimum in more than 92 % of all executions. The performance is compared to that of two branch-and-cut algorithms and one of the very best deterministic heuristics, an iterated version of the Shortest Path Heuristic (SPH-I). For all test examples but one, even the worst result ever found by the GA is equal to or better than the result of SPH-I and in many cases the average error ratio of the GA is an order of magnitude better than that of SPH-I. The runtime of the GA is moderate for all test examples. This is in contrast to SPH-I as well as the branch-and-cut algorithms, for which the runtime in some cases are extremely high

A parallel genetic algorithm for the Steiner Problem in Networks

This paper presents a parallel genetic algorithm to the Steiner Problem in Networks. Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the characteristics of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to build a comparison term for validating deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. On the other hand, the large dimensions of our sample networks require the adoption of a parallel implementation of the Steiner GA, which is able to deal with such large problem instances

QoS multicast tree construction in IP/DWDM optical internet by bio-inspired algorithms

Copyright @ Elsevier Ltd. All rights reserved.In this paper, two bio-inspired Quality of Service (QoS) multicast algorithms are proposed in IP over dense wavelength division multiplexing (DWDM) optical Internet. Given a QoS multicast request and the delay interval required by the application, both algorithms are able to find a flexible QoS-based cost suboptimal routing tree. They first construct the multicast trees based on ant colony optimization and artificial immune algorithm, respectively. Then a dedicated wavelength assignment algorithm is proposed to assign wavelengths to the trees aiming to minimize the delay of the wavelength conversion. In both algorithms, multicast routing and wavelength assignment are integrated into a single process. Therefore, they can find the multicast trees on which the least wavelength conversion delay is achieved. Load balance is also considered in both algorithms. Simulation results show that these two bio-inspired algorithms can construct high performance QoS routing trees for multicast applications in IP/DWDM optical Internet.This work was supported in part ny the Program for New Century Excellent Talents in University, the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant no. 60673159 and 70671020, the National High-Tech Reasearch and Development Plan of China under Grant no. 2007AA041201, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant no. 20070145017

Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP where 1 stands for a node being selected to construct the multicast tree while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on GA, ACO, and PSO

RoboTSP - A Fast Solution to the Robotic Task Sequencing Problem

In many industrial robotics applications, such as spot-welding, spray-painting or drilling, the robot is required to visit successively multiple targets. The robot travel time among the targets is a significant component of the overall execution time. This travel time is in turn greatly affected by the order of visit of the targets, and by the robot configurations used to reach each target. Therefore, it is crucial to optimize these two elements, a problem known in the literature as the Robotic Task Sequencing Problem (RTSP). Our contribution in this paper is two-fold. First, we propose a fast, near-optimal, algorithm to solve RTSP. The key to our approach is to exploit the classical distinction between task space and configuration space, which, surprisingly, has been so far overlooked in the RTSP literature. Second, we provide an open-source implementation of the above algorithm, which has been carefully benchmarked to yield an efficient, ready-to-use, software solution. We discuss the relationship between RTSP and other Traveling Salesman Problem (TSP) variants, such as the Generalized Traveling Salesman Problem (GTSP), and show experimentally that our method finds motion sequences of the same quality but using several orders of magnitude less computation time than existing approaches.Comment: 6 pages, 7 figures, 1 tabl

Inference of single-cell phylogenies from lineage tracing data using Cassiopeia.

The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia