The Quadratic Shortest Path Problem and its Genetic Algorithm

The quadratic shortest path (QSP) problem is to find a path from a node to another node in a given network such that the total cost includes two kinds of costs, say direct cost and interactive cost, is minimum. The direct cost is the cost associated with each arc and the interactive cost occurs when two arcs appear simultaneously in the shortest path. In this paper, the concept of the quadratic shortest path is initialized firstly. Then a spanning tree-based genetic algorithm is designed for solving the quadratic shortest path problem. Finally, a numerical example is given

Low Cost Quality of Service Multicast Routing in High Speed Networks

Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.

Multi-criteria Evolution of Neural Network Topologies: Balancing Experience and Performance in Autonomous Systems

Majority of Artificial Neural Network (ANN) implementations in autonomous systems use a fixed/user-prescribed network topology, leading to sub-optimal performance and low portability. The existing neuro-evolution of augmenting topology or NEAT paradigm offers a powerful alternative by allowing the network topology and the connection weights to be simultaneously optimized through an evolutionary process. However, most NEAT implementations allow the consideration of only a single objective. There also persists the question of how to tractably introduce topological diversification that mitigates overfitting to training scenarios. To address these gaps, this paper develops a multi-objective neuro-evolution algorithm. While adopting the basic elements of NEAT, important modifications are made to the selection, speciation, and mutation processes. With the backdrop of small-robot path-planning applications, an experience-gain criterion is derived to encapsulate the amount of diverse local environment encountered by the system. This criterion facilitates the evolution of genes that support exploration, thereby seeking to generalize from a smaller set of mission scenarios than possible with performance maximization alone. The effectiveness of the single-objective (optimizing performance) and the multi-objective (optimizing performance and experience-gain) neuro-evolution approaches are evaluated on two different small-robot cases, with ANNs obtained by the multi-objective optimization observed to provide superior performance in unseen scenarios

ECARDM: Energy Consumption Aware Route Discovery for Multicasting in Mobile Ad hoc Networks

Consideration of energy consumption in the case of wireless ad hoc networks leads to effective reduction of energy consumption by the nodes and increases the lifetime of the batteries for nodes. It is imperative from the existing models that there is significant scope for improvement in the energy-consumption based route discovery models. A model of Fuzzy based marginal energy disbursed multicast route discovery model for MANETs can support in reducing the power consumption has been proposed in our earlier research paper. In the present paper, a contemporary solution termed 201C;Energy Consumption Aware Route Discovery for Multicasting for MANETs201D; has been proposed, which is profoundly a fuzzy reasoning and genetic algorithm based model that focus on both the energy consumption and also the element of end-to-end delay whilst discovering the route. The experimental study of the model in comparison to BWDCMR and GAEEQMR models depicted that the proposed algorithm is very effective and can certainly be result oriented

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

When the path is never shortest: a reality check on shortest path biocomputation

Shortest path problems are a touchstone for evaluating the computing performance and functional range of novel computing substrates. Much has been published in recent years regarding the use of biocomputers to solve minimal path problems such as route optimisation and labyrinth navigation, but their outputs are typically difficult to reproduce and somewhat abstract in nature, suggesting that both experimental design and analysis in the field require standardising. This chapter details laboratory experimental data which probe the path finding process in two single-celled protistic model organisms, Physarum polycephalum and Paramecium caudatum, comprising a shortest path problem and labyrinth navigation, respectively. The results presented illustrate several of the key difficulties that are encountered in categorising biological behaviours in the language of computing, including biological variability, non-halting operations and adverse reactions to experimental stimuli. It is concluded that neither organism examined are able to efficiently or reproducibly solve shortest path problems in the specific experimental conditions that were tested. Data presented are contextualised with biological theory and design principles for maximising the usefulness of experimental biocomputer prototypes.Comment: To appear in: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

An Oriented Convergent Mutation Operator for Solving a Scalable Convergent Demand Responsive Transport Problem

International audienceThis paper presents a method for solving the convergence demand responsive transport problem, by using a stochastic approach based on a steady state genetic algorithm for enumerating a set of optimizing sprawling spanning trees, which constitute the best solutions to this problem. Specifically designed to speed up the convergence to optimal solutions, we introduce an oriented convergent mutation operator, allowing multi-objective considerations. So this solution lays the first stakes for considering real-time solving of such a problem. Led by computer science and geography laboratories, this study is provided with a set of experimental results evaluating the approach

A genetic algorithm for shortest path with real constraints in computer networks

The shortest path problem has many different versions. In this manuscript, we proposed a muti-constrained optimization method to find the shortest path in a computer network. In general, a genetic algorithm is one of the common heuristic algorithms. In this paper, we employed the genetic algorithm to find the solution of the shortest path multi-constrained problem. The proposed algorithm finds the best route for network packets with minimum total cost, delay, and hop count constrained with limited bandwidth. The new algorithm was implemented on four different capacity networks with random network parameters, the results showed that the shortest path under constraints can be found in a reasonable time. The experimental results showed that the algorithm always found the shortest path with minimal constraints

Topological Design of Multiple Virtual Private Networks UTILIZING SINK-TREE PATHS

With the deployment of MultiProtocol Label Switching (MPLS) over a core backbone networks, it is possible for a service provider to built Virtual Private Networks (VPNs) supporting various classes of services with QoS guarantees. Efficiently mapping the logical layout of multiple VPNs over a service provider network is a challenging traffic engineering problem. The use of sink-tree (multipoint-to-point) routing paths in a MPLS network makes the VPN design problem different from traditional design approaches where a full-mesh of point-to-point paths is often the choice. The clear benefits of using sink-tree paths are the reduction in the number of label switch paths and bandwidth savings due to larger granularities of bandwidth aggregation within the network. In this thesis, the design of multiple VPNs over a MPLS-like infrastructure network, using sink-tree routing, is formulated as a mixed integer programming problem to simultaneously find a set of VPN logical topologies and their dimensions to carry multi-service, multi-hour traffic from various customers. Such a problem formulation yields a NP-hard complexity. A heuristic path selection algorithm is proposed here to scale the VPN design problem by choosing a small-but-good candidate set of feasible sink-tree paths over which the optimal routes and capacity assignments are determined. The proposed heuristic has clearly shown to speed up the optimization process and the solution can be obtained within a reasonable time for a realistic-size network. Nevertheless, when a large number of VPNs are being layout simultaneously, a standard optimization approach has a limited scalability. Here, the heuristics termed the Minimum-Capacity Sink-Tree Assignment (MCSTA) algorithm proposed to approximate the optimal bandwidth and sink-tree route assignment for multiple VPNs within a polynomial computational time. Numerical results demonstrate the MCSTA algorithm yields a good solution within a small error and sometimes yields the exact solution. Lastly, the proposed VPN design models and solution algorithms are extended for multipoint traffic demand including multipoint-to-point and broadcasting connections