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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.

Simulation-based optimization is a decision-making tool for identifying an optimal design of a system. Here, optimal design means a smart system with sensing, computing and control capabilities with improved efficiency. As compared to testing the physical prototype, computer-based simulation provides much cheaper, faster and lesser time-and resource-consuming solutions. In this work, a comparative analysis of heuristic simulation optimization methods (genetic algorithms, evolutionary strategies, simulated annealing, tabu search and simplex search) is performed.

In this work, a comparative analysis of heuristic simulation optimization methods (genertic algorithms, evolutionary strategies, simulated annealing, tabu search and simplex search) is performed. Further, a novel simulation annealing-based heuristic approach is proposed for critical infrastructure.

A small scale network of 50–100 nodes shows that genetic simulation optimization with multi-criteria and multi-dimensional features performs better as compared to other simulation optimization approaches. Further, a minimum of 3.4 percent and maximum of 16.2 percent improvement is observed in faster route identification for small scale Internet-of-things (IoT) networks with simulation optimization constraints integrated model as compared to the traditional method.

In this work, simulation optimization techniques are applied for identifying optimized Quality of service (QoS) parameters for critical infrastructure which in turn helps in improving the network performance. In order to identify optimized parameters, Tabu search and ant-inspired heuristic optimization techniques are applied over QoS parameters. These optimized values are compared with every monitoring sensor point in the network. This comparative analysis helps in identifying underperforming and outperforming monitoring points. Further, QoS of these points can be improved by identifying their local optimum values which in turn increases the performance of overall network. In continuation, a simulation model of bus transport is taken for analysis. Bus transport system is a critical infrastructure for Dehradun. In this work, feasibility of electric recharging units alongside roads under different traffic conditions is checked using simulation. The simulation study is performed over five bus routes in a small scale IoT network.

The purpose of this paper is to propose hybrid revised weighted fuzzy c-means (RWFCM) clustering and Nelder–Mead (NM) simplex algorithm, called as RWFCM-NM, for generalized multisource Weber problem (MWP).

Although the RWFCM claims that there is no obligation to sequentially use different methods together, NM’s local search advantage is investigated and performance of the proposed hybrid algorithm for generalized MWP is tested on well-known research data sets.

Test results state the outstanding performance of new hybrid RWFCM and NM simplex algorithm in terms of cost minimization and CPU times.

Proposed approach achieves better results in continuous facility location 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 proposes a hybrid biogeography‐based optimization (BBO) with simplex method (SM) algorithm (HSMBBO).

BBO is a new intelligent optimization algorithm. The global optimization ability of BBO is better than that of genetic algorithm (GA) and particle swarm optimization (PSO), but BBO also easily falls into local minimum. To improve BBO, HSMBBO combines BBO and SM, which makes full use of the high local search ability of SM. In HSMBBO, BBO is used firstly to obtain the current global solution. Then SM is searched to acquire the optimum solution based on that global solution. Due to the searching of SM, the search range is expanded and the speed of convergence is faster. Meanwhile, HSMBBO is applied to motion estimation of video coding.

In total, six benchmark functions with multimodal and high dimension are tested. Simulation results show that HSMBBO outperforms GA, PSO and BBO in converging speed and global search ability. Meanwhile, the application results show that HSMBBO performs better than GA, PSO and BBO in terms of both searching precision and time‐consumption.

The proposed algorithm improves the BBO algorithm and provides a new approach for motion estimation of video coding.

The purpose of this paper is to present an adaptive numerical algorithm for forward kinematics analysis of general Stewart platform.

Unlike the convention of developing a set of kinematic equations and then solving them, an alternative numerical algorithm is proposed in which the principal components of link lengths are used as a bridge to analyze the forward kinematics of a Stewart platform. The values of link lengths are firstly transformed to the values of principal components through principal component analysis. Then, the computation of the values of positional variables is transformed to a two‐dimensional nonlinear minimization problem by using the relationships between principal components and positional variables. A hybrid Nelder Mead‐particle swarm optimizer (NM‐PSO) algorithm and a modified NM algorithm are used to solve the two‐dimensional nonlinear minimization problem.

Simulation experiments have been conducted to validate the numerical algorithm and experimental results show that the numerical algorithm is valid and can achieve good accuracy and high efficiency.

This paper proposes an adaptive numerical algorithm for forward kinematics analysis of general Stewart platform.

This study aims to improve the bat algorithm (BA) performance for solving optimization problems in electrical engineering.

For this task, two strategies were investigated. The first one is based on including the crossover technique into classical BA, in the same manner as in the genetic algorithm method. Therefore, the newly generated version of BA is called the crossover–bat algorithm (C-BA). In the second strategy, a hybridization of the BA with the Nelder–Mead (NM) simplex method was performed; it gives the NM-BA algorithm.

First, the proposed strategies were applied to solve a set of two standard benchmark problems; then, they were applied to solve the TEAM workshop problem 25, where an electromagnetic field was computed by use of the 2D non-linear finite element method. Both optimization algorithms and finite element computation tool were implemented under MATLAB.

The two proposed optimization strategies, C-BA and NM-BA, have allowed good improvements of classical BA, generally known for its poor solution quality and slow convergence rate.

The purpose of this paper is computer-aided engineering analysis of the recently proposed side-vent-channel concept for mitigation of the blast-loads resulting from a shallow-buried mine detonated underneath a light tactical vehicle. The concept involves the use of side-vent-channels attached to the V-shaped vehicle underbody, and was motivated by the concepts and principles of operation of the so-called “pulse detonation” rocket engines. By proper shaping of the V-hull and side-vent-channels, venting of supersonically expanding gaseous detonation products is promoted in order to generate a downward thrust on the targeted vehicle.

The utility and the blast-mitigation capacity of this concept were examined in the prior work using computational methods and tools which suffered from some deficiencies related to the proper representation of the mine, soil, and vehicle materials, as well as air/gaseous detonation products. In the present work, an attempt is made to remove some of these deficiencies, and to carry out a bi-objective engineering-optimization analysis of the V-hull and side-vent-channel shape and size for maximum reduction of the momentum transferred to and the maximum acceleration acquired by the targeted vehicle.

Due to the conflicting nature of the two objectives, a set of the Pareto designs was identified, which provide the optimal levels of the trade-off between the two objectives.

To the authors’ knowledge, the present work is the first public-domain report of the side-vent-channel blast-mitigation concept.

The awareness for protecting the environment has resulted in remanufacturing and recycling policies in manufacturing industries. Carbon emission is one of the most important elements affecting the environment. Carbon emission due to production and transportation creates complicated situations for the manufacturing firms by affecting the manufacturer's carbon quota. The ecological consequences posed in a reverse logistic model are the subject of this study.

The present study explores the fuzzy model of economic production for both remanufacturing and recycling with uncertain cost parameters under the cap-and-trade rule to control the carbon emission due to different modes of transportation. Due to imprecise cost parameters, the hexagonal fuzzy numbers are set to fuzzify the overall cost, which leads to correct decisions in a more confident way. The result is defuzzified by using graded mean integration.

This study offers an explicit condition to control the carbon emission of the manufacturer and reduce the optimum cost. The findings indicate that the collection of used goods that can be remanufactured must be increased. The model is validated numerically. Sensitivity analysis explores the various aspects of different parameters on net cost to accomplish the fuzzy production model.

Under fuzzy inference, the research offers a relevant contribution in the field of recycling with controlling carbon emission by using the cap-and-trade policy. This study provides a trading strategy for a manufacturer's decision to avoid losses.

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing simple, exact and efficient techniques. Here, an efficient, fast and exact technique is proposed for solving integer‐programming problems that normally arise in optimal reliability design problems. The algorithm presented is superior to any of the earlier methods available so far, being based on functional evaluations and a limited systematic search close to the boundary of resources. Thus it can quickly solve even very large system problems. It can also be effectively used with other operations research problems involving integer‐programming formulations.