A binary tournament competition algorithm for solving partial differential equation constrained optimization via finite element method

Nirmal Kumar

doi:10.1016/j.asoc.2022.109394

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A binary tournament competition algorithm for solving partial differential equation constrained optimization via finite element method

2022-10-01

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Nirmal Kumar *

Sanat Kumar Mahato

Asoke Kumar Bhunia

DOI：10.1016/j.asoc.2022.109394

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Abstract

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Sometimes, in a tournament competition to form a single team from two teams, 50% players are selected from the union of both teams according to their performance (fitness). Considering this idea, the aim of this article is to design an algorithm based on binary tournament process using two different types of metaheuristic algorithms. Here, at first, four swarms of populations are considered. The first two swarms are updated by Gaussian quantum behaved particle swarm optimization (GQPSO) algorithm and other two swarms are updated by weighted quantum behaved particle swarm optimization (WQPSO) algorithm considering second strategy among six strategies of existing binary tournamenting process. Thereafter, a swarm is formed from the updated solutions found from GQPSO and also from WQPSO algorithms. Finally, an algorithm is selected randomly with equal probability to update the final swarm. To test the effectiveness of the proposed algorithm, it is applied on partial differential equation (PDE) constrained optimization problems transforming these into bound constrained optimization problems using finite element discretization method and the obtained results are compared with the parent algorithms, WQPSO and GQPSO numerically. Also, the results are compared with a number of existing metaheuristic algorithms. Finally, to check the significance of the results and also to draw the fruitful conclusion, nonparametric statistical tests are performed. (c) 2022 Elsevier B.V. All rights reserved.

Keywords:

PDE constrained optimization

WQPSO

GQPSO

Binary tournament competition algorithm (BTCA)