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The purpose of this paper is to present a degenerated simplex search method to optimize neural network error function. By repeatedly reflecting and expanding a simplex, the centroid property of the simplex changes the location of the simplex vertices. The proposed algorithm selects the location of the centroid of a simplex as the possible minimum point of an artificial neural network (ANN) error function. The algorithm continually changes the shape of the simplex to move multiple directions in error function space. Each movement of the simplex in search space generates local minimum. Simulating the simplex geometry, the algorithm generates random vertices to train ANN error function. It is easy to solve problems in lower dimension. The algorithm is reliable and locates minimum function value at the early stage of training. It is appropriate for classification, forecasting and optimization problems.

Adding more neurons in ANN structure, the terrain of the error function becomes complex and the Hessian matrix of the error function tends to be positive semi‐definite. As a result, derivative based training method faces convergence difficulty. If the error function contains several local minimum or if the error surface is almost flat, then the algorithm faces convergence difficulty. The proposed algorithm is an alternate method in such case. This paper presents a non‐degenerate simplex training algorithm. It improves convergence by maintaining irregular shape of the simplex geometry during degenerated stage. A randomized simplex geometry is introduced to maintain irregular contour of a degenerated simplex during training.

Simulation results show that the new search is efficient and improves the function convergence. Classification and statistical time series problems in higher dimensions are solved. Experimental results show that the new algorithm (degenerated simplex algorithm, DSA) works better than the random simplex algorithm (RSM) and back propagation training method (BPM). Experimental results confirm algorithm's robust performance.

The algorithm is expected to face convergence complexity for optimization problems in higher dimensions. Good quality suboptimal solution is available at the early stage of training and the locally optimized function value is not far off the global optimal solution, determined by the algorithm.

Traditional simplex faces convergence difficulty to train ANN error function since during training simplex can't maintain irregular shape to avoid degeneracy. Simplex size becomes extremely small. Hence convergence difficulty is common. Steps are taken to redefine simplex so that the algorithm avoids the local minimum. The proposed ANN training method is derivative free. There is no demand for first order or second order derivative information hence making it simple to train ANN error function.

The algorithm optimizes ANN error function, when the Hessian matrix of error function is ill conditioned. Since no derivative information is necessary, the algorithm is appealing for instances where it is hard to find derivative information. It is robust and is considered a benchmark algorithm for unknown optimization problems.

Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

This paper introduces a new hybrid evolutionary algorithm (EA) for continuous global optimization problems, called estimation of distribution algorithm with local search (EDA/L). Like other EAs, EDA/L maintains and improves a population of solutions in the feasible region. Initial candidate solutions are generated by uniform design, these solutions evenly scatter over the feasible solution region. To generate a new population, a marginal histogram model is built based on the global statistical information extracted from the current population and then new solutions are sampled from the model thus built. The incomplete simplex method applies to every new solution generated by uniform design or sampled from the histogram model. Unconstrained optimization by diagonal quadratic approximation applies to several selected resultant solutions of the incomplete simplex method at each generation. We study the effectiveness of main components of EDA/L. The experimental results demonstrate that EDA/L is better than four other recent EAs in terms of the solution quality and the computational cost.

Transverse flux induction heating (TFH) is a process advantageously applied for the heat treatment of thin non‐ferrous metal strips. In comparison with the better known longitudinal flux heating the design of TFH inductors is more complex. In fact both the prediction of power density distribution in the strip and the calculation of the thermal transient during the heating process require a solution of 3D electromagnetic and thermal problems. Moreover the requirements for a good inductor design are in conflict with each other. In the paper a code for the solution of 3D electromagnetic and thermal problems suitable for the design of TFH systems is presented. The analytical‐numerical approach (analytical for the electromagnetic problem, numerical for the thermal one) is suitable for coupling with optimisation algorithms. Both evolutionary strategy and simplex methods and their combination have been used in order to obtain an optimal design for a particular application of TFH.

The purpose of this paper is to study the patterns of formation of anti-corrosion properties, the development of compositions for pigments by using the method of co-precipitation and subsequent heat treatment.

To obtain co-precipitated hydroxides, aqueous solutions of salts were used. The conditions of synthesis varied according to the following parameters: the nature of the starting salts of metals; and the ratio of metal cations. The anticorrosive activity of the pigments was evaluated by the potentiodynamic method, by comparing the anodic and cathodic polarization curves, and calculated potentials and corrosion currents on the basis of regions of Tafel on curves. Polarization curves were obtained by using Potentiostat/Galvanostat/ZRA Gamry, which connected to the PC, and by using the program Gamry Framework. The measurement results were processed by using the method of simplex-lattice planning. X-ray diffractograms of pigments were recorded on a DRON – 2.0 diffractometer (monochromatic copper radiation with a nickel filter).

The paper deals with the results of research the dependence of colour characteristics and anticorrosion properties of synthesized compositions on their nature and composition. The presence of aluminium cations leads to the formation of solid solutions of ferrum and aluminium oxyhydroxides.

The main technological properties of pigments are determined by the anionic and cationic composition. Colour characteristics are determined by the cation-chromophore. The anti-corrosive properties of non-calcined pigments are determined to a greater extent by the presence of the formed hydroxyl ions and the composition of the compounds. The greatest protective effect is observed when using double compounds of metals, the dissociation constants of which differ significantly. The protective effect is mainly determined by the slowdown of the anode process. Anions containing aluminium atoms accelerate the corrosion processes.

In order to make a thorough inquiry into the criterion of optimal product structure in the micro‐economic system (enterprise), this paper has proposed and demonstrated the benefit‐type linear programming model, and based on it, the concepts of enterprise's product structure, feasible structure and optimal structure have been discussed and the criterion of optimal structure has been revealed. In this paper, the methods of simplex iteration and sensitivity analysis are both used to approach necessarily the adjustment of product structure under the circumstances of varied or invaried environment inside and outside the system, and as a final, it has come to a conclusion that the variation of resource price vector P would not affect the optimal product structure in enterprise, but the variation of resource‐constrained vector b will cause negative effects both on optimal product structure in enterprise and on determination of criterion for optimal structure.

This paper aims to calibrate the mounted parameters between the LIDAR and the motor in a low-cost 3D LIDAR device. It proposes the model of the aimed 3D LIDAR device and analyzes the influence of all mounted parameters. The study aims to find a way more accurate and simple to calibrate those mounted parameters.

This method minimizes the coplanarity and area of the plane scanned to estimate the mounted parameters. Within the method, the authors build different cost function for rotation parameters and translation parameters; thus, the parameter estimation problem of 4-degree-of-freedom (DOF) is decoupled into 2-DOF estimation problem, achieving the calibration of these two types of parameters.

This paper proposes a calibration method for accurately estimating the mounted parameters between a 2D LIDAR and rotating platform, which realizes the estimation of 2-DOF rotation parameters and 2-DOF translation parameters without additional hardware.

Unlike previous plane-based calibration techniques, the main advantage of the proposed method is that the algorithm can estimate the most and more accurate parameters with no more hardware.

Discusses the use of optimizing techniques such as linear programming (LP) in managerial decision making. Argues that while LP has always offered a powerful tool for solving allocation type problems, the technique was rarely used except in large organizations. Lack of use has often been due, not to the limitations or assumptions associated with the technique, but to the need to use expensive and unintuitive application software which required extensive knowledge and training. Argues that new advances in spreadsheet software now offer the decision‐maker a powerful yet easy‐to‐use way of applying linear programming which can greatly enhance decision‐making effectiveness. Uses a simple example to contrast different approaches to solving allocation type problems and concludes that linear programming should now become an essential tool within the decision‐makers’ portfolio of problem‐solving techniques.

The purpose of this study is to develop a novel and practical series-parallel inventory-redundancy allocation system in a green supply chain including a single manufacturer and multiple retailers operating in several positions without any conflict of interests. The manufacturer first produces multi-product and then dispatches them to the retailers at different wholesale prices based on a common replenishment cycle policy. In contrast, the retailers sell the purchased products to customers at different retail prices. In this way, the manufacturer encounters a redundancy allocation problem (RAP), in which the solution subsequently enhances system production reliability. Furthermore, to emphasize on global warming and human health concerns, this paper pays attention both the tax cost of industrial greenhouse gas (GHG) emissions of all produced products and the limitation for total GHG emissions.

The manufacturer intends not only to maximize the total net profit but also to minimize the mean time to failure of his production system using a RAP. To achieve these objectives, the max-min approach associated with the solution method known as the interior point method is utilized to maximize the minimum (the worst) value of the objective functions. Finally, numerical experiments are presented to further demonstrate the applicability of the proposed methodology. Sensitivity analysis on the green supply chain approach is also performed to obtain more insight.

The computational results showed that increasing the number of products and retailers might lead into a substantial increase in the total net profit. This indicated that the manufacturer would feel adding a new retailer to the green supply chain strongly. Moreover, an increase in the number of machines provides significant improvement in the reliability of the production system. Furthermore, the results of the performed sensitivity analysis on the green approach indicated that increasing the number of machines has a substantial impact on both the total net profit and the total tax cost. In addition, not only the proposed green supply chain was more efficient than the supply chain without green but also the proposed green supply chain was very sensitive to the tax cost of GHG emission rather than the number of machines.

In summary, the motivations are as follows: the development of a bi-objective series-parallel inventory-RAP in a green supply chain; proposing a hybrid inventory-RAP; and considering the interior point solution method. The novel method comes from both theoretical and experimental techniques. The paper also has industrial applications. The advantage of using the proposed approach is to generate additional opportunities and cost effectiveness for businesses and companies that operate utilizing the green supply chain under an inventory model.

This paper aims to focus on applications of stochastic linear programming (SLP) to managerial accounting issues by providing a theoretical foundation and practical examples. SLP models may have more implications – and broader ones – in industry practice than deterministic linear programming (DLP) models do.

This paper introduces both DLP and SLP methods. In addition, continuous and discrete SLP models are explained. Applications are demonstrated using practical examples and simulations.

This research work extends the current knowledge of SLP, especially concerning managerial accounting issues. Through numerical examples, SLP demonstrates its great ability of hedging against all scenarios.

This study serves as an addition to building a cumulative tradition of research on SLP in managerial accounting. Only a few SLP studies in managerial accounting have focused on the development of such an instrument. Thus, the measurement scales in this research can be used as the starting point for further refining the instrument of optimization in managerial accounting.