An alternative formulation for the fuzzy assignment problem

The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method. © 2012 Operational Research Society Ltd. All rights reserved.

On the k-anonymization of time-varying and multi-layer social graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users’ privacy. In order to deal with malicious attacks, k -anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes’ identity. In this paper, we study the problem of ensuring k anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

Optimization of physical distribution problem in logistics management

Physical distribution plays an imporant role in contemporary logistics management. Both satisfaction level of of customer and competitiveness of company can be enhanced if the distribution problem is solved optimally. The multi-depot vehicle routing problem (MDVRP) belongs to a practical logistics distribution problem, which consists of three critical issues: customer assignment, customer routing, and vehicle sequencing. According to the literatures, the solution approaches for the MDVRP are not satisfactory because some unrealistic assumptions were made on the first sub-problem of the MDVRP, ot the customer assignment problem. To refine the approaches, the focus of this paper is confined to this problem only. This paper formulates the customer assignment problem as a minimax-type integer linear programming model with the objective of minimizing the cycle time of the depots where setup times are explicitly considered. Since the model is proven to be MP-complete, a genetic algorithm is developed for solving the problem. The efficiency and effectiveness of the genetic algorithm are illustrated by a numerical example.

PCB assembly line assignment:a genetic algorithm approach

Purpose – This paper sets out to study a production-planning problem for printed circuit board (PCB) assembly. A PCB assembly company may have a number of assembly lines for production of several product types in large volume. Design/methodology/approach – Pure integer linear programming models are formulated for assigning the product types to assembly lines, which is the line assignment problem, with the objective of minimizing the total production cost. In this approach, unrealistic assignment, which was suffered by previous researchers, is avoided by incorporating several constraints into the model. In this paper, a genetic algorithm is developed to solve the line assignment problem. Findings – The procedure of the genetic algorithm to the problem and a numerical example for illustrating the models are provided. It is also proved that the algorithm is effective and efficient in dealing with the problem. Originality/value – This paper studies the line assignment problem arising in a PCB manufacturing company in which the production volume is high.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Optimal production planning for PCB assembly

It is indisputable that printed circuit boards (PCBs) play a vital role in our daily lives. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB manufacturer’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly lines’ efficiency. This is done by: • integrating the component sequencing and the feeder arrangement problems together for both the pick-and-place machine and the chip shooter machine; • constructing mathematical models and developing an efficient and effective heuristic solution approach for the integrated problems for both types of placement machines, the line assignment problem, and the component allocation problem; and • developing a prototype of the PCB assembly planning system. The techniques proposed in Optimal Production Planning for PCB Assembly will enable process planners in the electronics manufacturing industry to improve the assembly line’s efficiency in their companies. Graduate students in operations research can familiarise themselves with the techniques and the applications of mathematical modeling after reading this advanced introduction to optimal production planning for PCB assembly.

Petrographic image analysis and understanding

This study considers the application of image analysis in petrography and investigates the possibilities for advancing existing techniques by introducing feature extraction and analysis capabilities of a higher level than those currently employed. The aim is to construct relevant, useful descriptions of crystal form and inter-crystal relations in polycrystalline igneous rock sections. Such descriptions cannot be derived until the `ownership' of boundaries between adjacent crystals has been established: this is the fundamental problem of crystal boundary assignment. An analysis of this problem establishes key image features which reveal boundary ownership; a set of explicit analysis rules is presented. A petrographic image analysis scheme based on these principles is outlined and the implementation of key components of the scheme considered. An algorithm for the extraction and symbolic representation of image structural information is developed. A new multiscale analysis algorithm which produces a hierarchical description of the linear and near-linear structure on a contour is presented in detail. Novel techniques for symmetry analysis are developed. The analyses considered contribute both to the solution of the boundary assignment problem and to the construction of geologically useful descriptions of crystal form. The analysis scheme which is developed employs grouping principles such as collinearity, parallelism, symmetry and continuity, so providing a link between this study and more general work in perceptual grouping and intermediate level computer vision. Consequently, the techniques developed in this study may be expected to find wider application beyond the petrographic domain.

An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

A multi-depot travelling salesman problem and its iterative and integrated approaches

This paper formulates a logistics distribution problem as the multi-depot travelling salesman problem (MDTSP). The decision makers not only have to determine the travelling sequence of the salesman for delivering finished products from a warehouse or depot to a customer, but also need to determine which depot stores which type of products so that the total travelling distance is minimised. The MDTSP is similar to the combination of the travelling salesman and quadratic assignment problems. In this paper, the two individual hard problems or models are formulated first. Then, the problems are integrated together, that is, the MDTSP. The MDTSP is constructed as both integer nonlinear and linear programming models. After formulating the models, we verify the integrated models using commercial packages, and most importantly, investigate whether an iterative approach, that is, solving the individual models repeatedly, can generate an optimal solution to the MDTSP. Copyright © 2006 Inderscience Enterprises Ltd.

Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

The influence of memory in a threshold model for distributed task assignment

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task selection in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without a priori knowledge of the available mail at the cities or inter-agent communication. In order to process a different mail type than the previous one, agents must undergo a change-over during which it remains inactive. We propose a threshold based algorithm in order to maximise the overall efficiency (the average amount of mail collected). We show that memory, i.e. the possibility for agents to develop preferences for certain cities, not only leads to emergent cooperation between agents, but also to a significant increase in efficiency (above the theoretical upper limit for any memoryless algorithm), and we systematically investigate the influence of the various model parameters. Finally, we demonstrate the flexibility of the algorithm to changes in circumstances, and its excellent scalability.

Generalized mean field approximation for parallel dynamics of the Ising model

The dynamics of the non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The proposed method shows significant improvement in predicting local system properties compared to other mean field approximation techniques, particularly in systems with symmetric interactions. Results are also evaluated against those obtained from Monte Carlo simulations. The method is also employed to obtain parameter values for the kinetic inverse Ising modeling problem, where couplings and local field values of a fully connected spin system are inferred from data. © 2014 IOP Publishing Ltd and SISSA Medialab srl.