A comparisation of methods for the optimisation of a non-linear function subject to non-linear constraints

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A non-linear encoder using a binary counterfor pulse-code modulation

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A fuzzy AHP based integer linear programming model for the multi-criteria transshipment problem

Purpose – The purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments. Design/methodology/approach – This paper proposes a fuzzy-based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi-criteria transshipment problem. Findings – This paper provides several novel insights about how to transform a company from a cost-based model to a service-dominated model by using an integrated MCDM method. It suggests that the contemporary customer-driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously. Research limitations/implications – This research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output. Practical implications – The paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network. Originality/value – The major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.

Challenges of developing non-linear devices to achieve the linear Shannon limit

To achieve the Shannon Capacity Limit, we need to develop practical, effective and deployable non-linear devices to invert the non-linear effects of the transmission line. In this work, we will summarise the progress we are making to realise these, specifically looking at optical phase conjugation and phase regenerators as methods to improve non-linear tolerances. © 2014 IEEE.

High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats

We demonstrate a simple method to experimentally evaluate nonlinear transmission performance of high order modulation formats using a low number of channels and channel-like ASE. We verify it's behaviour is consistent with the AWGN model of transmission.

Travelling-wave model of semiconductor optical amplifier based non-linear loop mirror

A travelling-wave model of a semiconductor optical amplifier based non-linear loop mirror is developed to investigate the importance of travelling-wave effects and gain/phase dynamics in predicting device behaviour. A constant effective carrier recovery lifetime approximation is found to be reasonably accurate (±10%) within a wide range of control pulse energies. Based on this approximation, a heuristic model is developed for maximum computational efficiency. The models are applied to a particular configuration involving feedback.

Approaching the non-linear Shannon limit

We review the recent progress of information theory in optical communications, and describe the current experimental results and associated advances in various individual technologies which increase the information capacity. We confirm the widely held belief that the reported capacities are approaching the fundamental limits imposed by signal-to-noise ratio and the distributed non-linearity of conventional optical fibres, resulting in the reduction in the growth rate of communication capacity. We also discuss the techniques which are promising to increase and/or approach the information capacity limit.

Non-linear temperature response of Bragg gratings in doped and un-doped holey polymer optical fibre

We present measurements on the non-linear temperature response of fibre Bragg gratings recorded in pure and trans-4-stilbenemethanol-doped polymethyl methacrylate (PMMA) holey fibres.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Multi-threaded parallel simulation of non-local non-linear problems in ultrashort laser pulse propagation in the presence of plasma

We describe a parallel multi-threaded approach for high performance modelling of wide class of phenomena in ultrafast nonlinear optics. Specific implementation has been performed using the highly parallel capabilities of a programmable graphics processor. © 2011 SPIE.

On the solution of a class of capital investment problems

In this work the solution of a class of capital investment problems is considered within the framework of mathematical programming. Upon the basis of the net present value criterion, the problems in question are mainly characterized by the fact that the cost of capital is defined as a non-decreasing function of the investment requirements. Capital rationing and some cases of technological dependence are also included, this approach leading to zero-one non-linear programming problems, for which specifically designed solution procedures supported by a general branch and bound development are presented. In the context of both this development and the relevant mathematical properties of the previously mentioned zero-one programs, a generalized zero-one model is also discussed. Finally,a variant of the scheme, connected with the search sequencing of optimal solutions, is presented as an alternative in which reduced storage limitations are encountered.

SAS/OWA:ordered weighted averaging in SAS optimization

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weight averaging (OWA) operators of decision-making units (DMUs). OWA was originally introduced by Yager (IEEE Trans Syst Man Cybern 18(1):183-190, 1988) has gained much interest among researchers, hence many applications such as in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. On the other hand, the SAS is powerful software and it is capable of running various optimization tools such as linear and non-linear programming with all type of constraints. To facilitate the use of OWA operator by SAS users, a code was implemented. The SAS macro developed in this paper selects the criteria and alternatives from a SAS dataset and calculates a set of OWA weights. An example is given to illustrate the features of SAS/OWA software. © Springer-Verlag 2009.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.