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