Article: Measuring the role of penalty constant on nonlinear programming problem through computational experiments on benchmark functions Journal: International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO) 2025 Vol.15 No.2 pp.119 - 136 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. Inderscience Publishers - linking academia, business and industry through research

Title: Measuring the role of penalty constant on nonlinear programming problem through computational experiments on benchmark functions

Authors: Raju Prajapati; Jayantika Pal; Om Prakash Dubey

Addresses: Department of Mathematics, Usha Martin University, Ranchi, Jharkhand, India ' Department of Mathematics, Usha Martin University, Ranchi, Jharkhand, India ' Department of Mathematics, J.J. College, Veer Kunwar Singh University, Ara, Bhojpur, Bihar, India

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; PSO; nonlinear programming problem; NLPP; inequality constraints.

DOI: 10.1504/IJMMNO.2025.146323

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.2, pp.119 - 136

Received: 24 Oct 2024
Accepted: 08 Mar 2025
Published online: 21 May 2025 *

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Title: Measuring the role of penalty constant on nonlinear programming problem through computational experiments on benchmark functions

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