An improved immune algorithm with parallel mutation and its application

Lulu Liu; Shuaiqun Wang; Lulu Liu; Shuaiqun Wang

doi:10.3934/mbe.2023544

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12211-12239. doi: 10.3934/mbe.2023544

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An improved immune algorithm with parallel mutation and its application

Lulu Liu ^,,
Shuaiqun Wang

College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China

Academic Editor: Shangce Gao

Received: 28 February 2023 Revised: 10 April 2023 Accepted: 08 May 2023 Published: 17 May 2023

The objective of this paper is to design a fast and efficient immune algorithm for solving various optimization problems. The immune algorithm (IA), which simulates the principle of the biological immune system, is one of the nature-inspired algorithms and its many advantages have been revealed. Although IA has shown its superiority over the traditional algorithms in many fields, it still suffers from the drawbacks of slow convergence and local minima trapping problems due to its inherent stochastic search property. Many efforts have been done to improve the search performance of immune algorithms, such as adaptive parameter setting and population diversity maintenance. In this paper, an improved immune algorithm (IIA) which utilizes a parallel mutation mechanism (PM) is proposed to solve the Lennard-Jones potential problem (LJPP). In IIA, three distinct mutation operators involving cauchy mutation (CM), gaussian mutation (GM) and lateral mutation (LM) are conditionally selected to be implemented. It is expected that IIA can effectively balance the exploration and exploitation of the search and thus speed up the convergence. To illustrate its validity, IIA is tested on a two-dimension function and some benchmark functions. Then IIA is applied to solve the LJPP to exhibit its applicability to the real-world problems. Experimental results demonstrate the effectiveness of IIA in terms of the convergence speed and the solution quality.
- immune algorithm,
- mutation operators,
- Cauchy mutation,
- Gaussian mutation,
- lateral mutation,
- Lennard-Jones potential problem
Citation: Lulu Liu, Shuaiqun Wang. An improved immune algorithm with parallel mutation and its application[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12211-12239. doi: 10.3934/mbe.2023544

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Abstract

The objective of this paper is to design a fast and efficient immune algorithm for solving various optimization problems. The immune algorithm (IA), which simulates the principle of the biological immune system, is one of the nature-inspired algorithms and its many advantages have been revealed. Although IA has shown its superiority over the traditional algorithms in many fields, it still suffers from the drawbacks of slow convergence and local minima trapping problems due to its inherent stochastic search property. Many efforts have been done to improve the search performance of immune algorithms, such as adaptive parameter setting and population diversity maintenance. In this paper, an improved immune algorithm (IIA) which utilizes a parallel mutation mechanism (PM) is proposed to solve the Lennard-Jones potential problem (LJPP). In IIA, three distinct mutation operators involving cauchy mutation (CM), gaussian mutation (GM) and lateral mutation (LM) are conditionally selected to be implemented. It is expected that IIA can effectively balance the exploration and exploitation of the search and thus speed up the convergence. To illustrate its validity, IIA is tested on a two-dimension function and some benchmark functions. Then IIA is applied to solve the LJPP to exhibit its applicability to the real-world problems. Experimental results demonstrate the effectiveness of IIA in terms of the convergence speed and the solution quality.

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