Bifurcation analysis on a discrete-time tabu learning model

In this paper, we consider a discrete-time tabu learning single neuron model. After investigating the stability of the given system, we demonstrate that Pichfork bifurcation, Flip bifurcation and Neimark–Sacker bifurcation will occur when the bifurcation parameter exceed a critical value, respectively. A formula is given for determining the direction and stability of Neimark–Sacker bifurcation by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.     

The Mathematics of Internet Search Engines

This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.     

Scatter search for the single source capacitated facility location problem

This paper considers the Single Source Capacitated Facility Location Problem (SSCFLP). We propose a Scatter Search approach to provide upper bounds for the optimal solution of the problem. The proposed approach uses GRASP to initialize the Reference Set. Solutions of the Reference Set are combined using a procedure that consists of two phases: (1) the initialization phase and (2) the improvement phase. During the initialization phase each client is assigned to an open facility to obtain a solution that is then improved with the improvement phase. Also, a tabu search algorithm is applied. In order to evaluate the proposed approach we use different sets of test problems. According to the results obtained we observe that the method provides good quality solutions with reasonable computational effort.     

Heuristic and exact methods for the cutting sequencing problem

Cutting stock problems deal with the generation of a set of cutting patterns that minimizes waste. Sometimes it is also important to find the processing sequence of this set of patterns to minimize the maximum queue of partially cut orders. In such instances a cutting sequencing problem has to be solved. This paper presents a new mathematical model and a three-phase approach for the cutting sequencing problem. In the first phase, a greedy algorithm produces a good starting solution that is improved in the second phase by a tabu search, or a generalized local search procedure, while, in the last phase, the problem is optimally solved by an implicit enumeration procedure that uses the best solution previously found as an upper bound. Computing experience, based on 300 randomly generated problems, shows the good performance of the heuristic methods presented.     

A tabu search scheme for abstract problems, with applications to the computation of fixed points

We present a general tabu search iterative algorithm to solve abstract problems on metric spaces. At each iteration, if the current solution turns out to be unacceptable then a neighborhood of unacceptable solutions is determined and excluded for further exploration, in such a way that, under mild assumptions, an acceptable solution is asymptotically reached. Thus our algorithm makes a crucial use of memory to avoid visiting unacceptable solutions more than once. We also present a specialization of our general method to the computation of fixed points.     

Trend of laser research developments in global level

An up-to-date progress of the international laser research and development is given in this article. The number of scientific publications and filed patents are considered as a figure of merit and based on these numbers the growth pace and important aspects are investigated. We have used the Science Finder Scholar search engine, which indexes more than 4000 journals, in different languages, and represents most significant published materials in laser science and engineering. The growth of the laser and related fields are described in terms of resulting scientific publications for the period of 1990–2003. The share of top nations in scientific publications, and in particular laser publications in terms of their gross domestic product (GDP) is presented. It is noted that the four countries including the USA, Japan, Germany and China have a laser publication contribution of 58.9% while the rest of the world including 189 countries contribute 41.1%. However, for the case of patent, which is a more important factor, these four countries hold a share of 90.1% while the remaining nations have a small share of 9.9%. The USA heads all the nations in the number of scientific publications, citations, and laser publications, however, in terms of accepted laser patents Japan shows a big lead. Scientific scopes of the laser systems are presented and some requirements to be met in each field are described. The key points in this field of research, which might be helpful in the future development of the laser technology are discussed.     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

Grasp Embedded Scatter Search for the Multicommodity Capacitated Network Design Problem

A GRASP embedded Scatter Search is developed for the multicommodity capacitated network design problem. Difficulty for this problem arises from the fact that selection of the optimal network design is an NP-complete combinatorial problem. There exist no polynomial exact algorithms which can solve this problem in a reasonable period of time for realistically sized instances. In such cases, heuristic procedures are commonly used. Two strategies were designed for GRASP: a traditional approach and a memory based technique. As for Scatter Search, 5 different strategies were used to update the reference set. Computational results on a large set of randomly generated instances show the convenience of the proposed procedures.     

Designing Least-Cost Survivable Wireless Backhaul Networks

This paper presents a new heuristic algorithm for designing least-cost telecommunications networks to carry cell site traffic to wireless switches while meeting survivability, capacity, and technical compatibility constraints. This requires solving the following combinatorial optimization problems simultaneously: (1) Select a least-cost subset of locations (network nodes) as hubs where traffic is to be aggregated and switched, and choose the type of hub (high-capacity DS3 vs. lower-capacity DS1 hub) for each location; (2) Optimally assign traffic from other nodes to these hubs, so that the traffic entering the network at these nodes is routed to the assigned hubs while respecting capacity constraints on the links and routing-diversity constraints on the hubs to assure survivability; and (3) Optimally choose the types of links to be used in interconnecting the nodes and hubs based on the capacities and costs associated with each link type. Each of these optimization problems must be solved while accounting for its impacts on the other two. This paper introduces a short term Tabu Search (STTS) meta-heuristic, with embedded knapsack and network flow sub-problems, that has proved highly effective in designing such backhaul networks for carrying personal communications services (PCS) traffic. It solves problems that are challenging for conventional branch-and-bound solvers in minutes instead of hours and finds lower-cost solutions. Applied to real-world network design problems, the heuristic has successfully identified designs that save over 20% compared to the best previously known designs.