Multi-layer Explosion Based Fireworks Algorithm


We propose a new multi-layer explosion strategy inspired by various explosion patterns of real reworks to accelerate reworks algorithm (FWA). Each rework individual conducts multiple explosions to explore a local fitness landscape carefully instead of a single layer explosion used in canonical FWA. In the proposal, each firework individual generates a small number of sparks in the first layer randomly, and then the generated sparks conduct the second layer explosions to generate new diverse sparks. These new sparks repeat the above operations until the number of this iteration reaches the predefined maximum layer number. Theoretically, the number of explosion layers can be set to any positive integer, and the proposed strategy expects to generate various potential sparks using the multi-layer explosion strategy without changing the total number of generated sparks. The proposed strategy can combine with not only basic FWA but also other versions of FWA algorithms easily and replace their corresponding explosion operations to develop a new version, multi-layer explosion-based FWA.

Fireworks Algorithm

In real world, a firework is launched into the sky then many sparks are generated around it. A firework explosion can be abstracted as a local search model around a specific point. FWA simulates the explosion process iteratively to find the optimal candidate solution.


Conventional FWA has two types of fireworks, better rework and poor firework. A better firework may close to an optimum so that many sparks are generated around it within a smaller range, while a poor firework may far from the optimum so less sparks are generated, and search range should be larger. Algorithm 1 shows the general own of FWA mainly consisting of three operations: explosion, mutation and selection


Algorithm 1


  • Be general framework of FWA.
  • Initialize n fireworks randomly.
  • Evaluate the fitness of each firework.
  • While termination condition is not satisfied do
  • Generate sparks for each firework.
  • Generate Gaussian mutation sparks.
  • If sparks are generated outside search area, then
  • Use a mapping rule to bring it back to search space.
  • End if
  • Evaluate the fitness of generated sparks.
  • Select n new fireworks for next generation.
  • End while
  • Output found feasible solution.


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