Forthcoming and Online First Articles

International Journal of Mathematical Modelling and Numerical Optimisation

International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO)

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International Journal of Mathematical Modelling and Numerical Optimisation (13 papers in press)

Regular Issues

  •   Free full-text access Open AccessSeparation correction by speed-adjustment for aircraft on air routes to a congested airport
    ( Free Full-text Access ) CC-BY-NC-ND
    by Hirohide Matsunaga 
    Abstract: Currently, a minimum separation between aircraft (ACFT) is ensured for safety with time management primarily achieved using two-dimensional (2D) detour coordination. This result in a requirement to balance trade-offs between safety separation, delay times and fuel consumption. This study introduces ACFT speed adjustments in response to the stochastic processes and uncertain factors affecting ACFT separation, including meteorological conditions, instructions on the part of air-traffic control (ATC) and actions on the part of the pilot. In particular, we focus on speed adjustments in one-dimensional (1D) merge routes to improve ACFT separation, delay and fuel consumption. A novel social-welfare (SW) function model is established; subsequently, the relationships amongst the safety value, efficiency and other exchangeable values are confirmed, in addition to determining the optimal point of merging, which was shown to be closer to the alternative merging (zipper) process than the first-come-first-served (FCFS) process.
    Keywords: air route; speed adjustment; separation correction; alternative merging process; zipper; first-come-first-served process; FCFS; exchangeable value; social welfare; total optimisation.

  • Improvement in Estimation of Population Variance utilizing Known Auxiliary Parameters for Decision Making Model   Order a copy of this article
    by Dinesh Sharma, S.K. Yadav, Hari Sharma 
    Abstract: There is variation in similar things, whether natural or artificial. It is therefore in our best interest to estimate this variation. In this article, we suggest a Searls ratio type estimator for the main variable using the available information on the tri-mean and the third quartile of the auxiliary variable for an enhanced population variance estimation. The bias and mean squared error (MSE) of the proposed estimator are derived up to the first-degree approximation. The optimal value of the characterizing scalar is obtained and, for this optimal value, the least MSE is achieved. The suggested estimator is compared with the competing estimators by their MSEs, both theoretically and empirically. The calculation of biases and MSEs of suggested and competing estimators is accomplished by using R programming. The study's outcome is evidenced in the least MSE of the proposed model compared to competing estimators used in the study for business decision-making.
    Keywords: Population Variance; Searls Type Estimator; Auxiliary variable; Bias; MSE; PRE.

  • Modelling the Transmission Dynamics of Coronavirus disease 2019 with Treatment as a Control Strategy: The Case of India   Order a copy of this article
    by Sonam Gyeltshen, Thinley Tobgay 
    Abstract: This paper model the transmission dynamics of coronavirus disease 2019 (COVID-19) and its treatment based on the cases in India, by extending the classic SIR model to include exposed, asymptomatic, and treatment classes with a special focus to investigate the effect of ineffective treatment on the transmissibility of the infection with variation in the treatment initiation. The basic reproduction number was computed to understand the relative effect of early treatment initiation from the delayed treatment initiation on the transmissibility of the infection. With the estimated parameters obtained by faithfully fitting the simulation to the observed data, a global sensitivity analysis carried out indicated that the treatment initiation to be one of the most influential parameters to infection control. With this concept, a further analysis resulted that an early treatment initiation can be a helpful control strategy on the transmissibility of the infection. However, for it to happen the intervention such as proactively doing case finding is deemed important.
    Keywords: coronavirus; transmission dynamics; treatment initiation; ineffective treatment; SIR; susceptible; infectious and recovery; global sensitivity analysis; basic reproduction number; symptom onset; control strategy; asymptomatic.

  • Stability analysis of an eco-epidemiological SIN model with impulsive control strategy for integrated pest management considering stage-structure in predator   Order a copy of this article
    by Preety Kalra, Maninderjit Kaur 
    Abstract: Pest outbreak is a major threat to agricultural resources and livestock.rnIntegrated pest management is widely being used nowadays to control the pestrnpopulation. Natural enemies are immensely beneficial to control the outbreak of pests. To achieve the same, in this paper, microbial and biological pest control techniques are applied simultaneously by impulsively releasing natural enemies and infected pests. Therefore a SIN (prey-predator) model considering infection in prey with two classes (susceptible-infected) and stage structure in predator is investigated for the cause of integrated pest management. Prey acts as pest and predator plays the role of a natural enemy. Firstly, local and global stability of pest extinction periodic solution is carried out, then condition for the permanencernof system is derived using Stroboscopic map, comparison analysis technique, and Floquet theory of impulsive differential equations. Further, it is observed that there exists a threshold value of the impulsive period which plays an important role in the dynamics of the system. Finally, for validating the established results, numerical simulation is done using MATLAB.
    Keywords: biological control; impulsive control strategy; pest management; stage-structure.

  • Mathematical Model for a Compressed Air System That Couples Demand and Supply   Order a copy of this article
    by Mohamad Thabet, David Sanders, Giles Tewkesbury 
    Abstract: This paper presents a mathematical model for a compressed air system (CAS) that couples system supply and demand. The supply side contains components responsible for production, treatment and storage of compressed air, while the demand side contains components that deliver and consume compressed air. Components considered include: compressor, cooler, storage tank, linear actuators and an air blower. Simulations were performed to study the impact of pressure regulation and storage tank size on system energy consumption. Results showed that pressure regulation reduced air and energy consumption and a properly sized tank volume reduced energy consumption while maintaining good system pressure stability.
    Keywords: compressed; air; systems; modelling; simulation;.

  • Solution of an Integer Linear Programming Problem via a Primal Dual Method Combined with a Heuristic   Order a copy of this article
    by Mohand Ouamer Bibi, Houria Boussouira, Abdelhek Laouar 
    Abstract: In this paper, we propose an algorithm for solving Integer Linear Programming (ILP) problem with upper and lower bounded variables where we combined a cutting plane method with a heuristic. At each iteration, a relaxed problem is solved by the adaptive method and its optimal solution is submitted to a judicious rounding procedure. The concept of $beta$-optimality is used to indicate the quality of the approximate solution obtained by this heuristic. In order to compare our method with the intlinprog method of the Matlab optimization toolbox, numerical experiments on randomly generated test problems are presented.
    Keywords: Integer Linear Programming; Cutting Planes; AdaptivernMethod; Heuristic Method; Approximate Solution; $beta$-optimality.

  • Finite Element Tearing and Interconnecting-1 method for the solution of the topology optimization problem   Order a copy of this article
    by Ouafaa Raibi, Abdelilah Makrizi 
    Abstract: The algebraic system derived from the descritization of problems arising in physical field and engineering science appears to be challenging to solve due to the strong nonlinearity and the large size of such problems. Parallel processing is shown to be an efficient technique to handle the computational complexity associated with solving large linear systems and this is readily obtained by using one of the most popular methods which is known to be suitable for parallelization, namely, domain decomposition methods. In this work we apply Finite Element Tearing and Interconnecting method within the framework of topology optimization, we describe a methodology that brings together existing fast algorithms for topology optimization and FETI for solving the resulting large-scale linear systems.
    Keywords: Domain decomposition; FETI-1 method; minimum compliance; Topology optimization.

  • A virtual class of nonconforming finite elements and its applications to Poisson\'s equation   Order a copy of this article
    by Hammou El-Otmany 
    Abstract: In this paper, we develop and analyze the virtual class of nonconforming Finite Element inspired from the classical Crouzeix-Raviart element in two and three-dimensions. We focus on Poisson\'s equation for theoretical and numerical results. We show that the discrete problem is stable and the a priori error estimates are optimal. Two numerical tests are presented to demonstrate the theoretical results.
    Keywords: Nonconforming finite element; element of Crouzeix-Raviart; interpolation error; consistency error; a priori error estimates.

  • Workload control with shifting bottlenecks: norms optimisation through design of experiments   Order a copy of this article
    by Francesco Zammori, Camilla Ferretti, Piero Ganugi, Davide Mezzogori 
    Abstract: Workload control is a production planning and control system designed to overcome the trade-off between high throughput and short and stable lead time. Specifically, work-in-process is continuously monitored, and new jobs are not admitted in the shop floor until work-in-process drops below predefined threshold values or norms. To exploit performance, norms should be fine-tuned to minimise queues, without generating starvation at the bottleneck machines. The optimisation process is straightforward for a perfectly balanced system, but much harder in case of shifting bottlenecks. The paper focuses on this issue and presents an innovative procedure, based on the response surfaces method, which allows one to optimise the norms in a precise way, keeping unaltered the maximal or desired throughput of the manufacturing system. A comprehensive simulation analysis demonstrated the quality of the proposed approach and showed the importance of using different norms to boost the overall performance of the manufacturing system.
    Keywords: bottleneck shiftiness; design of experiments; flow-shop; response surfaces; simulation; workload control; WLC.
    DOI: 10.1504/IJMMNO.2021.10041059
  • New redundant constraints for Klee-Minty problem   Order a copy of this article
    by Bib Paruhum Silalahi 
    Abstract: Interior-point method (IPM) is a class of methods which has polynomial time for iteration complexity in solving linear optimisation problems. The iteration complexity upper bound of IPM can be stated as O(√N ln N), where N is the number of inequalities. In this paper, we prove that the new redundant constraints of the form: −ρyk-1ykdk may cause the central path visits small neighbourhood of the vertices of the Klee-Minty cube. Our case has smaller number of redundant inequalities compared to best previous results, but of the same order: O(n22n ). In our case the central path goes to at least 2n−1 + 1 of the vertices (half of the vertices + 1).
    Keywords: interior-point method; IPM; Klee-Minty problem; lower bound; new redundant constraints.
    DOI: 10.1504/IJMMNO.2021.10041061
  • Numerical and experimental determination of the heat transfer coefficient at the casting-mould interface   Order a copy of this article
    by Murat Can Nişancı, Ali Yurddaş 
    Abstract: Sanitary tapware faucet that can drain hot and cold water from the plumbing systems in the desired proportions by mixing are called faucets. The raw material of faucets used today is generally brass alloy (CuZn39Pb1Al-C) and their production is carried out through the method of low-pressure die casting. In this study, K type thermocouple was placed in such a way that there was a distance of 3 mm to the casting surface of the mould, and temperature changes during the production were obtained by the measurement and recording device. Interfacial heat transfer coefficient was calculated numerically in Ansys Fluent program with the combination created by 1,283, 1,263, 1,243, 1,223, 1,203, 1,183, 1,163 K values of casting temperature and mould temperatures of 413, 473, 533, 593, 653 K. Numerically calculated heat transfer coefficients are entered by creating casting simulation in the Magma program, and they were analysed by making comparison between experimental temperature curves and simulation temperature curves.
    Keywords: interface heat transfer coefficient; IHTC; computational fluid dynamics; CFD; low-pressure die casting; CuCoNiBe; finite volume method.
    DOI: 10.1504/IJMMNO.2021.10041062
  • An improved ACO-based decision tree algorithm for imbalanced datasets   Order a copy of this article
    by Muhamad Hasbullah Mohd Razali, Rizauddin Saian, Yap Bee Wah, Ku Ruhana Ku-Mahamud 
    Abstract: Prediction of the minority class is challenging for classification of datasets with skewed class distribution. Bio-inspired classifier such as ant colony optimisation (ACO) decision tree could not provide effective decision boundaries since its entropy-based heuristics is affected by the strong presence of the majority class. Consequently, the developed trees were dominated by the likelihood of the majority class while the rare class being inadequately represented. This study proposes an improved algorithm called Hellinger-ant-tree-miner (HATM) which is inspired by the ant colony optimisation (ACO) meta heuristic for imbalanced learning using decision tree classification algorithm. The proposed algorithm was compared to the existing algorithm with entropy-based heuristics, ant-tree-miner (ATM) using nine publicly available imbalanced datasets and a simulation study. Simulation procedure reveals the superiority of HATM under imbalanced class environment as the sample size increased. Experimental results show that the performance of the existing algorithm evaluated via minority class prediction (MCP) and F-measure has improved due to the class skew-insensitiveness of Hellinger distance. The statistical significance test shows that HATM has higher mean in both performance measures than ATM, indicating a potential improvement of ACO decision tree structure for imbalanced class domain.
    Keywords: ant colony optimisation; ACO; decision tree; classification; Hellinger distance; imbalanced learning; skew-insensitive; heuristics.
    DOI: 10.1504/IJMMNO.2021.10041068
  • Generation of new knowledge and optimisation of systems and processes through meaningful interpretation of algebraic inequalities   Order a copy of this article
    by Michael Todinov 
    Abstract: The paper introduces a method for increasing the impact of additive quantities by meaningful interpretation of multivariate sub-additive and super-additive functions. The paper demonstrates that the segmentation of additive quantities through sub-additive and super-additive functions can be used to generate new knowledge and optimise systems and processes and the presented algebraic inequalities are applicable to any area of science and technology. The meaningful interpretation of the modified Cauchy-Schwarz inequality, led to a method for increasing of the power output from a voltage source and to a method for increasing the capacity for absorbing strain energy of loaded mechanical components. It was found that the existence of asymmetry is essential to increasing the strain energy absorbing capacity and the power output. Loaded elements experiencing the same displacement do not yield an increase of the absorbed strain energy. Similarly, loaded resistances experiencing the same current do not yield an increase of the power output. Finally, the meaningful interpretation of an algebraic inequality in terms of potential energy resulted in a general necessary condition for minimising the sum of powers of distances to a fixed number of points in space.
    Keywords: algebraic inequalities; sub-additive multivariate functions; super-additive multivariate functions; extensive quantities; segmentation.
    DOI: 10.1504/IJMMNO.2021.10041069