Title: Analysing augmented objective function values in nonlinear programming problems computationally using an improved particle swarm optimisation

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: A mixed constrained nonlinear programming problem (NLPP) contains equality as well as inequality constraints. Solution of the same is the goal of this paper. We use penalty method for this purpose. A version of penalty method is quadratic penalty method, which is effective on mixed constrained NLPPs. The quadratic penalty method is used for the general constrained NLPP for converting it to an unconstrained NLPP. An improved version of PSO is applied to solve the converted unconstrained NLPP. We consider the improved PSO with constant inertia weight and constriction factor with parameters/values as suggested in literature. Further, we also use a single random number and boundary handling conditions. The augmented objective function values and objective function values are reported in limited number of iterations. The paper also certifies that on increasing the penalty constants, the computational objective values decrease significantly.

Keywords: penalty method; nonlinear programming problems; particle swarm optimisation; mixed-constrained optimisation; test problem.

DOI: 10.1504/IJAISC.2026.153145

International Journal of Artificial Intelligence and Soft Computing, 2026 Vol.10 No.1, pp.90 - 109

Received: 06 Jun 2025
Accepted: 07 Jan 2026
Published online: 23 Apr 2026 *

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