The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Pro

The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Problems

Ahmet Cinar1 and Mustafa Kiran2

1Department of Computer Engineering, Selçuk University, Turkey

2Department of Computer Engineering, Konya Technical University, Turkey

Abstract: The constraints are the most important part of many optimization problems. The metaheuristic algorithms are designed for solving continuous unconstrained optimization problems initially. The constraint handling methods are integrated into these algorithms for solving constrained optimization problems. Penalty approaches are not only the simplest way but also as effective as other constraint handling techniques. In literature, there are many penalty approaches and these are grouped as static, dynamic and adaptive. In this study, we collect them and discuss the key benefits and drawbacks of these techniques. Tree-Seed Algorithm (TSA) is a recently developed metaheuristic algorithm, and in this study, nine different penalty approaches are integrated with the TSA. The performance of these approaches is analyzed on well-known thirteen constrained benchmark functions. The obtained results are compared with state-of-art algorithms like Differential Evolution (DE), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Genetic Algorithm (GA). The experimental results and comparisons show that TSA outperformed all of them on these benchmark functions.

Keywords: Constrained optimization, penalty functions, penalty approaches, tree-seed algorithm.

Received January 3, 2019; accepted February 26, 2020

https://doi.org/10.34028/iajit/17/5/13

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