International Journal of Mathematical Modelling and Numerical Optimisation (5 papers in press)

Regular Issues

• Numerical approximation of Duffing equationusing Hermite wavelet method  
  by Jay Kishore Sahani, Pappu Kumar, Arvind Kumar, Satyendra Kumar 
  Abstract: This article presents an efficient technique based on Hermite wavelet for the numerical approximation of Duffing equation with and without damping force . The given equations are converted into a set of nonlinear algebraic equations with the help of truncated Hermite wavelet expansions and then find the values of the unknown vectors using Newton-Raphson method. The comparison has been made with analytical solution (if possible) and existing numerical solution to validate the Hermite wavelet solution(HWS). The HWS of Duffing equation in absence of damping force shows excellent agreement with analytical solution and desired level of accuracy can be achieved by increasing number of collocation points. The HWS solution of Duffing equation in presence of damping force has also been compared with existing solution like Taylor wavelet method, RK45 and others and found more suitable, easy to implement and greater degree of accuracy with same number of grid points.
  Keywords: Hermite wavelet; operational matrix of integration; Duffing equation; nonlinearity.
  DOI: 10.1504/IJMMNO.2025.10070634
   
  
• Bioeconomic modelling for the sustainable exploitation of three key marine species in Morocco  
  by Ilham Ait El Harch , Khalid Outaaoui, Y. El Foutayeni  
  Abstract: This study aims to deepen the understanding and optimize fishing activity in Morocco by holistically integrating biological and economic aspects. We develop a biological equilibrium model in which these competing species present their natural growth by logistic equations, taking into account density and competition between them. The integration of human intervention adds a realistic dimension to our model. A company specifically targeting the three species, thus influencing population dynamics according to their fishing activities. The aim of this work is to determine the fishing effort that maximizes fishing’s profit, taking into account the constraints associated with conserving ecosystem equilibrium.
  Keywords: bioeconomical modelling; optimisation techniques; linear complementarity problem; LCP; biological equilibrium; maximising profits.
  DOI: 10.1504/IJMMNO.2025.10070678
   
  
• Transmission network expansion planning: best so far solution using hermit crab shell exchange algorithm  
  by Divya Rajoria, Ajay Sharma, Nirmala Sharma 
  Abstract: In this research, a recently developed meta-heuristic technique in the field of nature inspired algorithms (NIAs), namely, the hermit crab shell exchange (HCSE) algorithm is applied on the transmission network expansion planning (TNEP) problem. In this work, HCSE is applied with contingency based security constrained TNEP (SeTNEP) with DCOPF for standard Graver’s six bus test system and Brazilian 46 bus test system. Also TNEP with ACOPF for standard Graver’s six bus test system and IEEE 24 bus test system is considered. The outcomes were evaluated against other renowned algorithms and deterministic methods that are available in the literature. The results reveal that the HCSE algorithm has accurately and proficiently solved the TNEP problem in these test scenarios.
  Keywords: DC optimal power flow; DCOPF; AC optimal power flow; ACOPF; meta-heuristic; hermit crab shell exchange algorithm; nature-inspired algorithms; NIAs; transmission network expansion planning; TNEP.
  DOI: 10.1504/IJMMNO.2025.10070730
   
  
• Modelling cancer data using a new generalised type II Topp-Leone heavy-tailed type II exponentiated half logistic-G family of distributions  
  by Peter T. Chinofunga, Broderick Oluyede, Fastel Chipepa 
  Abstract: In this paper, a novel generalised family of distributions (FoD), the Type II Topp-Leone Heavy-Tailed Type II Exponentiated Half Logistic-G (TIITL-HT-TIIEHL-G) distribution is developed. Some statistical properties of this new FoD which include the quantile function, order statistics, Rényi entropy, stochastic ordering, moment of residual and reversed residual life are derived. Through Monte Carlo simulations, the maximum likelihood estimation method outperforms alternative techniques namely weighted least squares, least squares, Cramér-von Mises, and Anderson Darling in estimating the Type II-Topp-Leone Heavy-Tailed Type II-Exponentiated-Half-Logistic-Weibull (TIITL-HT-TIIEHL-W) distribution, a special case of the TIITL-HT-TIIEHL-G FoD, parameters. The distribution is used to illustrate the flexibility of this new FoD using two real life datasets.
  Keywords: type II Topp-Leone distribution; heavy-tailed distribution; type II exponentiated half logistic distribution; moments; maximum likelihood estimation.
  DOI: 10.1504/IJMMNO.2025.10070897
   
  
• Measuring role of penalty constant on nonlinear programming problem through computational experiments on benchmark functions  
  by Raju Prajapati, Jayantika Pal, Om Prakash Dubey 
  Abstract: This paper focuses on the nonlinear programming problem (NLPP) consisting of inequality constraints. We use an improved version of particle swarm optimisation (PSO) method for handling the unconstrained NLPP obtained from the constrained NLPP. A constrained NLPP could be converted to an unconstrained NLPP using a quadratic penalty function. An unconstrained NLPP could be solved by various available methods. In this paper, an improved version of PSO is used to solve the converted unconstrained NLPP. We chose some testing problems available in literature for illustration. We apply randomly chosen constraints with these testing problems. The improved PSO is successfully able to solve the corresponding unconstrained NLPPs and obtain the optimal solution to these testing problems. The paper focuses on the values of penalty constants. For this, we took different values of penalty constants and compared the solution obtained using the improved PSO approach. Also, the paper proves that by increasing the penalty constants, we find an improvement in results under similar experimental setups. The higher penalty constants give better results.
  Keywords: penalty method; particle swarm optimisation; nonlinear programming problem; inequality constraints.