Using Improved Particle Swarm Optimization to Compare Quadratic and Exact Penalty Methods for Nonlinear Programming Problem

Purpose of the study: Penalty method plays an important role in handling constraints of a Non-Linear Programming Problem (NLPP). There exist varieties in penalty applying procedures. Quadratic and exact penalty methods belong to that class. The present paper computationally compares the performance of quadratic and exact penalty methods when they are implemented on NLPP with inequality constraints. Methodology: We have used some benchmark functions. The constraints are applied arbitrarily to the test functions. An improved version of the metaheuristic Particle Swarm Optimization (PSO) is used to handle the unconstrained NLPP obtained from the constrained NLPP. Main Findings: The results obtained are compared under similar conditions when quadratic and exact penalty methods are used as constraints handling techniques. The computational results are also reported under different ways to use the inertia weight in improved PSO. The paper discusses the computational convergence of these two methods. The condition for the same is also discussed. Applications of this study: The research is applied on NLPP problem. Constrained NLPPs are applicable in industry. Novelty/Originality of this study: The research gives a way to handle constraint between the exact penalty and quadratic penalty methods while solving NLPP using an improved PSO method.