Lichtenberg algorithm: A novel hybrid physics-based meta-heuristic for global optimization

• Published in: Expert systems with applications 2021-05, Vol.170, p.114522, Article 114522
• Main Authors: Pereira, João Luiz Junho, Francisco, Matheus Brendon, Diniz, Camila Aparecida, Antônio Oliver, Guilherme, Cunha, Sebastião Simões, Gomes, Guilherme Ferreira
• Format: Article
• Language: English
• Subjects: Algorithms; Energy costs; Global optimization; Heuristic methods; Lichtenberg Algorithm; Lichtenberg Figures; Lightning; Limited Diffusion Aggregation; Metaheuristics; Optimization
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2020.114522

•A new optimization algorithm based on Lichtenberg figure pattern is presented.•Difussion Limited Aggregation is formulated to create new agents in search space.•Lichtenberg figure pattern presents exploration–exploitation balance.•Tested on complex functions and problems and compared with renowned metaheuristics. This paper proposes a novel global optimization algorithm called Lichtenberg Algorithm (LA), inspired by the Lichtenberg figures patterns. Optimization is an essential tool to minimize or maximize functions, obtaining optimal results on costs, mass, energy, gains, among others. Actual problems may be multimodal, nonlinear, and discontinuous and may not be minimized by classical analytical methods that depend on the gradient. In this context there are metaheuristics algorithms inspired by natural phenomena to optimize real problems. There is no algorithm that is the worst or the best, but more efficient for a given type of problem. Thus, an unprecedented metaheuristic algorithm was created inspired by the physical phenomenon of radial intra-cloud lightning and Lichtenberg figures, successfully exploiting the fractal power and it is different from many in the literature as it is a hybrid algorithm composed of methods of search based on population and trajectory. Several test functions, including a design problem in a welded beam, were used to verify the robustness and to validate the Lichtenberg Algorithm. In all cases, the results were satisfactory when compared to those in the literature. LA shown to be a powerful optimization tool for both unconstraint optimizations and real problems with linear and nonlinear constraints.