Lévy flights, non-local search and simulated annealing

By Ilya Pavlyukevich. Journal of Computational Physics, 2007

656 citations recorded by the source corpus.

We solve a problem of non-convex stochastic optimisation with help of simulated annealing of Levy flights of a variable stability index. The search of the ground state of an unknown potential is non-local due to big jumps of the Levy flights process. The convergence to the ground state is fast due to a polynomial decrease rate of the temperature.

Subfields: Mathematical Physics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/df3ba6786f1d804f5c25d690eca8e7550ff00af8

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Citations in the corpus

Firefly Algorithm, Lévy Flights and Global Optimization (2010, background): “On the other hand, various studies have shown that flight behaviour of many animals and insects has demonstrated the typical characteristics of Lévy flights [4, 13, 11, 12].”
Levy Flight Algorithm for Optimization Problems - A Literature Review (2013, methodology): “Ilya Pavlyukevich (2007) has used Levy flight in his research to present and theoretically justify a new stochastic algorithm for global optimization.”
Optimum design of reinforced concrete retaining walls with the flower pollination algorithm (2019, background): “The travel behaviour of pollinators can be well reproduced by Lévy flights (Pavlyukevich 2007).”
Flower Pollination Algorithm for Global Optimization (2012, methodology): “In addition, bees and birds may behave as Lévy flight behaviour [13], with jump or fly distance steps obey a Lévy distribution.”
Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques (2019, neutral): “6 Meta-heuristic optimization algorithm Cuckoo search (CS) is a meta-heuristic algorithm developed based on the obligate brood parasitic behavior of some cuckoo species along with the Lévy flight behavior [35] of fruit flies and some birds [36].”
Lévy Flight Trajectory-Based Whale Optimization Algorithm for Global Optimization (2017, methodology): “been used for optimization and optimal search, and preliminary results show that it has promising capability [17], [19], [21], [22].”
Cuckoo Search via Lévy flights (2009, background): “On the other hand, various studies have shown that flight behaviour of many animals and insects has demonstrated the typical characteristics of Lévy flights [4, 15, 13, 14].”
Flower pollination algorithm: A novel approach for multiobjective optimization (2014, methodology): “with jumping or flying distance steps obeying a Lévy distribution (Pavlyukevich 2007).”
Nature-Inspired Optimization Algorithms: Challenges and Open Problems (2020, background): “The mean distance covered by the L´evy ﬂights after N steps is This power-law feature is typically for super-diﬀusion phenomena [Pavlyukevich(2007)].”
Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems (2016, methodology): “Subsequently, Lévy-flight have been applied to optimization and optimal search, and preliminary results show its promising capability [22, 25].”
Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems (2011, background): “For example, various studies have shown that the flight behavior of many animals and insects has demonstrated the typical characteristics of Le ´vy flights [6, 7 ].”