Academic literature on the topic 'Heuristic Bisection Algorithm'

The graph bisection problem is an important problem in printed circuit board layout and communication networks. Since it is known to be NP-complete, approximation algorithm have been considered. In this paper, we propose a so-called two-state ant colony algorithm for efficiently solving the problem. In the proposed algorithm two kinds of pheromone and two kinds of heuristic information are introduced to reinforce the search ability. The proposed algorithm is tested on a large number of instances and is compared with a heuristic algorithm and a genetic algorithm. The experimental results show that the proposed approach is superior to its competitors.

A type II line balancing problem with multiple workers in workstations (mALBP-II) is considered given a total number of workers, group workers, and tasks into workstations so as to minimize cycle time. Different from the manufacturing environment where the traditional assembly line balancing problem (ALBP) rises, manual or semimanual manufacturing enjoys much higher flexibility allowing multiple workers to perform the same set of tasks on workpieces in the same workstation in parallel. The freedom of specifying the number of workers in workstations makes the classic NP-hard ALBP even harder to solve. A heuristic-mixed genetic algorithm (hGA) is therefore proposed to solve the problem. The algorithm minimizes cycle time as its first objective and balances workload among workstations as its second objective. A maximum-utilization heuristic and a bisection search are integrated into the decoding process of hGA so that the optimization of task assignment and worker allocation is accomplished simultaneously. Numerical results and a real-life application demonstrate the efficiency and effectiveness of hGA.

Visible light communications (VLC) is gaining interest as one of the enablers of short-distance, high-data-rate applications, in future beyond 5G networks. Moreover, non-orthogonal multiple-access (NOMA)-enabled schemes have recently emerged as a promising multiple-access scheme for these networks that would allow realization of the target spectral efficiency and user fairness requirements. The integration of NOMA in the widely adopted orthogonal frequency-division multiplexing (OFDM)-based VLC networks would require an optimal resource allocation for the pair or the cluster of users sharing the same subcarrier(s). In this paper, the max-min rate of a multi-cell indoor centralized VLC network is maximized through optimizing user pairing, subcarrier allocation, and power allocation. The joint complex optimization problem is tackled using a low-complexity solution. At first, the user pairing is assumed to follow the divide-and-next-largest-difference user-pairing algorithm (D-NLUPA) that can ensure fairness among the different clusters. Then, subcarrier allocation and power allocation are solved iteratively through both the Simulated Annealing (SA) meta-heuristic algorithm and the bisection method. The obtained results quantify the achievable max-min user rates for the different relevant variants of NOMA-enabled schemes and shed new light on both the performance and design of multi-user multi-carrier NOMA-enabled centralized VLC networks.

The loss of dispersal connections between habitat patches may destabilize populations in a patched ecological network. This work studies the stability of populations when one or more communication links is removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modelled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between habitat patches. A reaction–diffusion system on the graph models the dynamics of the predator–prey system over the patched ecological network. The graph Laplacian's Fiedler value, which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that, when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses the criterion for both the local and global stability of populations in partitioned networks. A heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and is illustrated with examples.

The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given a set ofngoals/targets andmagents, the objective is to findmround trips, such that each target is visited only once and by only one agent, and the total distance of these round trips is minimal. In this paper we describe the Multiagent Planning Problem, a variant of the classical Multiple Traveling Salesmen Problem: given a set ofngoals/targets and a team ofmagents,msubtours (simple paths) are sought such that each target is visited only once and by only one agent. We optimize for minimum time rather than minimum total distance; therefore the objective is to find the Team Plan in which the longest subtour is as short as possible (a min–max problem). We propose an easy to implement Genetic Algorithm Inspired Descent (GAID) method which evolves a set of subtours using genetic operators. We benchmarked GAID against other evolutionary algorithms and heuristics. GAID outperformed the Ant Colony Optimization and the Modified Genetic Algorithm. Even though the heuristics specifically developed for Multiple Traveling Salesmen Problem (e.g.,k-split, bisection) outperformed GAID, these methods cannot solve the Multiagent Planning Problem. GAID proved to be much better than an open-source Matlab Multiple Traveling Salesmen Problem solver.

<p>We design a system for generating newspaper layout proposals. The input to the system consists of editorial information (text, pictures, etc) and style information (non-editorial information that specifies the aesthetic appearance of a layout). We consider the automation of layout construction to pose two main problems. One problem consists in optimizing the layout with respect to the constraints and preferences specified in the style information. Another problem consists in finding a representation of the style information that both supports its use in the combinatorial optimization and supports its modification through high level user interaction and automatic inference from a database of examples.</p><p> </p><p>We propose a solution that combines <em> heuristic search, randomization </em> and <em> neural networks.</em> We have implemented a first version based on the <var> bisection </var> strategy -- a page is bisected recursively until the number of sub-divisions matches the number of articles to be placed.</p>

AbstractWe present a novel approach to the system inversion problem for linear, scalar (i.e. single-input, single-output, or SISO) plants. The problem is formulated as a constrained optimization program, whose objective function is the transition time between the initial and the final values of the system’s output, and the constraints are (i) a threshold on the input intensity and (ii) the requirement that the system’s output interpolates a given set of points. The system’s input is assumed to be a piecewise constant signal. It is formally proved that, in this frame, the input intensity is a decreasing function of the transition time. This result lets us to propose an algorithm that, by a bisection search, finds the optimal transition time for the given constraints. The algorithm is purely algebraic, and it does not require the system to be minimum phase or nonhyperbolic. It can deal with time-varying systems too, although in this case it has to be viewed as a heuristic technique, and it can be used as well in a model-free approach. Numerical simulations are reported that illustrate its performance. Finally, an application to a mobile robotics problem is presented, where, using a linearizing pre-controller, we show that the proposed approach can be applied also to nonlinear problems.

AbstractWireless sensor networks with mobile sinks enable a mobile device to move into the sensing area for the purpose of collecting the sensing data. Mobile sinks increase the flexibility and convenience of data gathering in such systems. Taking the energy consumption of the mobile sink into account, the moving distance of the mobile sink must be reduced efficiently. Hence, it is important and necessary to develop an efficient path planning scheme for mobile sinks in large-scale wireless sensor network systems. According to several greedy-based algorithms, we adopt an angle bisector concept to create the moving path for the mobile sink. In this paper, a novel and efficient data collection path planning scheme is proposed to reduce the moving distances and to prolong the lifetimes of mobile sinks in wireless sensor networks. Considering the communication range limitations of sensor nodes and the obstacles within sensing areas, we design an inner center path planning algorithm to reduce the moving distance for the mobile sink. A back-routing avoidance method is included to address the moving path backpropagation problem. We account for the obstacles in sensing area. The reference point of obstacle avoidance is employed to address the obstacle problem. The proposed scheme makes an adaptive decision for creating the moving path of the mobile sink. A suitable moving path planning scheme can be achieved, and the moving distance of the mobile sink can be reduced. The proposed scheme is promising in large-scale wireless sensor networks. When the number of sensor nodes in the sensing area is increased by 50, the proposed scheme yields an average moving distance that is 1.1 km shorter than that of the heuristic tour-planning algorithm, where the sensing area is 5 km × 5 km. Simulation results demonstrate that the proposed data collection path planning scheme outperforms the previously developed greedy-based scheme in terms of the moving paths and moving distances of mobile sinks in wireless sensor networks.

Reaction-Diffusion complex networks are ubiquitous in many pragmatic models of network of interacting nodes with individual dynamics, such as social interactions, neuronal functions, transportation models, ecological systems and metabolic reactions. In particular case of reaction-diffusion network, with two different agents interacting together by specifi ed inter-node dynamics, coupling between nodes and uniform rate of di usion, under type I instability the network is stable only, Fiedler value(second smallest eigenvalue of Laplacian operator) is greater than certain threshold. Given stable complex network along with dynamics, we want to fi nd partition such that dynamics on the resultant daughter networks are sustainable. These partitions are of practical interest in many real life situations. For example, consider meta-population dynamics of species on ecological network in population habitats. Too often habitats are fragmented by artifi cial invasion (industrial corridors, road and railway networks) of human activities or due to stochastic reasons(genetic, environmental and demographic conditions) which results in extinction of even dominant species. Thus deserving study of existence of minimal cut partition and stability on the resultant networks while preserving the population of species on the partitioned networks. It is well-known in the literature that balanced graph partition problem is NP-complete. Various approximation algorithms and heuristics are used to generate sufficiently good quality local optimum solutions. In this work, we propose a theoretical model of reaction-diffusion network with two different species and study properties of linearized stability and co-existential equilibrium. We argue, pre-existing graph (static) bisection algorithms cannot be used to partition live complex network, such that resultant components have sustainable dynamics. Thus, we design a iterative heuristic algorithm of O(jV j3) time complexity based on Weyl's perturbation theorem, to partition the network into stable components. Throughout the experiments, our test bed for various algorithms are DIMACS10 graph datasets. We exploit, the spectral properties of Laplacian operator(specially algebraic connectivity or Fiedler value) and dynamics of the network topology. Since calculation of eigenvalues are expensive and prone to perturbation in every iteration, we search for further alternatives by looking at the parallels of heuristic graph bisection algorithms. We study various existing global partition algorithms(spectral bisection, multilevel recursive methods etc.) for graph bisection and incorporate results in our algorithm to increase quality of the partitions. Further down the line, we explore various meta-heuristic local search methods such as Kerninghan-Lin, Fiduccia-Mattheyses etc., and incorporate data structures for constant time retrieval of gain of vertices in our algorithm. Simulated annealing is well-known idea in statistical mechanics and motivated by motion of high degrees of freedom of system in presence of heat sink. Due to similarities between combinatorial optimization problem with exponential search space and physical system with high degree of freedom, we propose an adaptation of simulated annealing algorithm to our stability preserving bisection objective. Our empirical results shows that, although the algorithms converges in reasonable time for small graphs but su ers from polynomial growth of execution time with respect to size of graph. In the second part, we present two important theorems regarding the stability of reaction-diffusion network and characterize it completely in terms of external and internal costs, thus avoiding the need for calculation for eigenvalues. Using these theorems and above experimental results, we design a linear time heuristic of O(jV j + jEj) time complexity for stability preserving partition which shows signi cant improvement in partition quality.