Fireworks algorithm

The Fireworks Algorithm (FWA) is a swarm intelligence algorithm that explores a very large solution space by choosing a set of random points confined by some distance metric in the hopes that one or more of them will yield promising results, allowing for a more concentrated search nearby.

## Algorithm Description

The algorithm is implemented and described in terms of the explosion process of fireworks: explosions occur at specific points, and "sparks" fan out from the explosion. Each spark location is considered until an adequately optimal point is found. In terms of optimization, when finding an [math]\displaystyle{ x_j }[/math] satisfying [math]\displaystyle{ f(x_j)=y }[/math], the algorithm continues until a spark is sufficiently near [math]\displaystyle{ x_j }[/math].[1] The algorithm begins with selecting [math]\displaystyle{ n }[/math] initial locations where the fireworks will explode. Then the amount of sparks and their locations are determined based on the proximity of the firework to the optimal location. After each spark location is evaluated, the algorithm terminates if an optimal location was found, or it repeats with [math]\displaystyle{ n }[/math] new firework locations if an optimal location was not found.

## References

1. ↑ Tan, T; Zhu, Y (2010), Fireworks algorithm for optimization, International Conference in Swarm Intelligence, https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=bf2c921d75705ba8e74df025953d7643cb8e0af4

## External links

* Fireworks Algorithm
* Computational Intelligence Laboratory, Peking University

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Optimization: Algorithms, methods, and heuristics

Unconstrained nonlinear

| … functions|

* Golden-section search
* Interpolation methods
* Line search
* Nelder–Mead method
* Successive parabolic interpolation

|

… and gradients|

| Convergence|

* Trust region
* Wolfe conditions

|

Quasi–Newton|

* Berndt–Hall–Hall–Hausman
* Broyden–Fletcher–Goldfarb–Shanno and L-BFGS
* Davidon–Fletcher–Powell
* Symmetric rank-one (SR1)

Other methods|

* Gauss–Newton
* Gradient
* Levenberg–Marquardt
* Conjugate gradient
* Truncated Newton

… and Hessians|

* Newton's method

Constrained nonlinear

| General|

* Barrier methods
* Penalty methods

|

Differentiable|

* Augmented Lagrangian methods
* Sequential quadratic programming
* Successive linear programming

Convex optimization

| Convex
minimization|

* Cutting-plane method
* Reduced gradient (Frank–Wolfe)
* Subgradient method

|

Linear and
quadratic|

| Interior point|

* Affine scaling
* Ellipsoid algorithm of Khachiyan
* Projective algorithm of Karmarkar

|

Basis-exchange|

* Simplex algorithm of Dantzig
* Revised simplex algorithm
* Criss-cross algorithm
* Principal pivoting algorithm of Lemke

Combinatorial

| Paradigms|

* Approximation algorithm
* Dynamic programming
* Greedy algorithm
* Integer programming
* Branch and bound/cut

|

Graph
algorithms|

| Minimum
spanning tree|

* Borůvka
* Prim
* Kruskal

|

* Bellman–Ford
* Dijkstra
* Floyd–Warshall

Network flows|

* Dinic
* Edmonds–Karp
* Ford–Fulkerson
* Push–relabel maximum flow

Metaheuristics

* Evolutionary algorithm
* Hill climbing
* Local search
* Simulated annealing
* Tabu search

* Software

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