MODIFIED PARTICLE SWARM OPTIMIZATION INCORPORATED AN INTEGRATED APPROACH FOR SOLUTION OF QUADRATIC PROGRAMMING PROBLEMS USING PENALTY METHOD
By
Priyavada and V. V. Singh
Department of Mathematics, Lingayas Vidyapeeth, Faridabad (Delhi NCR) Haryana, India- 121002.
Email: priyavada.parihar@gmail.com,singh vijayvir@yahoo.com
(Received: November 18, 2023; In format: December 09, 2023; Revised: July 04, 2024; Accepted: November 15, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54209
Abstract
The Quadratic Programming problem QPP is a special type of Non-linear linear programming problem in which the objective function is a multivariate quadratic function subject to linear constraints. Constraints can be equalities and inequalities. Many classical methods such as the graphical method, Beale’s method, Wolfe’s method, Karush-Kuhn Tucker conditions, etc. solve the QPP problem. Several non- traditional techniques like, Genetic algorithm, Particle swarm optimization, and Artificial bee colony algorithms have been introduced for the solution of different optimization problems. We used the Penalty method with Modified Particle swarm optimization (MPSO) incorporated integrated constriction factor and inertia weight to solve quadratic programming problems. Several computations have performed using the software MATLAB and the computational outcomes are compared with different variants such as Inertia and constriction factor, integrated inertia weight and constriction, Factor PSO-1 and integrated inertia weight and constriction Factor PSO-II approach. Only one random variable is used, r2 is used in terms of r1. Different modified parameters are used and the result of QPP.
2020 Mathematical Sciences Classification: 90C26, 90C30
Keywords: Evolutionary computation, Inertia weight, Penalty method, Constriction factor, and Particle Swarm Optimization.