Abstract
Meta-heuristics have been successfully applied to many complex optimization problems. One of the main reasons for its success is its ability to handle non-convex, nonlinear, multimodal, multi-variable, and multi-objective problems with easy implementation. However, the quality of the response of these algorithms to an optimization problem is highly susceptible to the control parameters, and few works aim to tune them or find tools that can improve the algorithms. The literature is rich in proposals for new algorithms, but not for improving existing ones. This paper presents different strategies for tuning and accelerating meta-heuristics using the first hybrid algorithm in the literature. The Lichtenberg algorithm is inspired by lightning and Lichtenberg figures and has been increasingly successfully applied to various optimization problems. However, a study of its best parameters has never been presented until now. After a discussion of the best tuning tools, its tuning parameters are performed using response surface methodology. Then, 14 versions are studied through 10 test functions using chaos theory and Lévy flights scenarios. After 13,500 simulations, the chaotic Lichtenberg algorithm equipped with the piecewise function and tuned parameters proved the best version with only 16% similarity to the original algorithm. Then, it was compared to the genetic algorithm, particle swarm optimization, gray wolf optimizer, salp swarm optimization, whale optimization algorithm, and dragonfly algorithm. The proposed algorithm had both the best average accuracy, lower computational cost, and the smallest standard deviation.
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Abbreviations
- CCD:
-
Central composite design
- CLA1:
-
Chaotic Lichtenberg algorithm with Chebyshev series
- CLA2:
-
Chaotic Lichtenberg algorithm with circle series
- CLA3:
-
Chaotic Lichtenberg algorithm with Gauss series
- CLA4:
-
Chaotic Lichtenberg algorithm with iterative series
- CLA5:
-
Chaotic Lichtenberg algorithm with logistic series
- CLA6:
-
Chaotic Lichtenberg algorithm with piecewise series
- CLA7:
-
Chaotic Lichtenberg algorithm with sine series
- CLA8:
-
Chaotic Lichtenberg algorithm with singer series
- CLA9:
-
Chaotic Lichtenberg algorithm with sinusoidal series
- CLA10:
-
Chaotic Lichtenberg algorithm with tent series
- DA:
-
Dragonfly algorithm
- DLA:
-
Diffusion limited aggregation
- DoE:
-
Design of experiments
- F opt :
-
Theoretical optimum
- GA:
-
Genetic algorithm
- GWO:
-
Grey wolf optimizer
- LA:
-
Lichtenberg algorithm
- LF:
-
Lévy flights
- LFG:
-
Lichtenberg figure
- LLA1:
-
Chaotic Lichtenberg algorithm with Lévy flights series (β = ½)
- LLA2:
-
Chaotic Lichtenberg algorithm with Lévy flights series (β = 1)
- M :
-
Figure switching parameter in LA
- n :
-
Dimension or number of design variables (of problems)
- N p :
-
Number of particles (DLA and LA)
- OLA:
-
Original Lichtenberg algorithm
- Pop:
-
Number of population used in LA
- PSO:
-
Particle swarm optimization
- R c :
-
Creation radius (DLA and LA)
- Ref:
-
LA refinement
- rand:
-
Random number between 0 and 1
- S :
-
Stickiness coefficient (DLA and LA)
- SSA:
-
Salp swarm algorithm
- TLA:
-
Tuned Lichtenberg algorithm
- WOA:
-
Whale optimization algorithm
- μ :
-
Mean
- σ :
-
Standard deviation
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Acknowledgements
The authors would like to acknowledge the financial support from the Brazilian agencies FAPESP (São Paulo Research Foundation, Grant 2022/10683-7), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico—Process Number 150117/2021-3), and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais—APQ-00385-18).
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Pereira, J.L.J., Francisco, M.B., de Almeida, F.A. et al. Enhanced Lichtenberg algorithm: a discussion on improving meta-heuristics. Soft Comput 27, 15619–15647 (2023). https://doi.org/10.1007/s00500-023-08782-w
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DOI: https://doi.org/10.1007/s00500-023-08782-w