Reference

R. Storn, and K. Price. (1997). “Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces”. Journal of Global Optimization. 11: 341-359.

Pseudocode

1. Set algorithm parameters F, CR, mutation strategy, and recombination strategy
2. Initialize population $\mathbb{P}=\{\mathbf{p}_1,\ldots,\mathbf{p}_N\}$.
   1. For each $\mathbf{p} \in \mathbb{P}$:
      1. Initialize $\mathbf{p}=\{$x, v, u, f(x)$\}$
      2. Evaluate f(x)
3. While termination criterion is not fulfilled:
   1. For each $\mathbf{p} \in \mathbb{P}$:
      1. v $\gets$ mutate(F, x$_{r_1}$, x$_{r_2}$, x$_{r_3}$, …)
      2. u $\gets$ recombine(CR, x, v)
      3. Evaluate f(u)
      4. x $\gets$ select(x, f(x), u, f(u))
4. Output results

Class view

class Canonical_DE : public algorithm

Link: algorithm

Data member

Name	Type	Utility
m_pop	DE::population<DE::individual>>	The population

Member function

Name	Utility
intialize() ⊕	Set parameters; initialize and evaluate the population (Pseudocode 1., 2.)
run_() ⊕	The optimization process (Pseudocode 3.)
record() ⊕	Record the evluations and the error in GOPs. Record the evaluations and the number of optima found in MMOPs.

DE::population

Class view

template<typename Individual>
class DE::population : public population<Individual>

Links: population

Data member

Name	Type	Utility
m_F	real	The value of parameter F
m_CR	real	The value of parameter CR

Member function

Name	Utility
evolve() ⊕	Optimization operators in each iteration (Pseudocode 3.1.)

DE::individual

Class view

class DE::individual : public individual<variable_vector<real>, real>

Links: individual

Data member

Name	Type	Utility
m_pv	solution<>	The donor vector
m_pu	solution<>	The trial vector

Member function

Name	Utility
mutate(F, r1, r2, r3, r4, r5)	Pseudocode 3.1.1.
recombine(CR, rs)	Pseudocode 3.1.2.
select()	Pseudocode 3.1.4.

DE/rand/1

Command line arguments example

AN=DE-rand-1 PS=100

Mutation strategy

v = x$_{r_1}$ + F $\cdot$ (x$_{r_2}$ - x$_{r_3}$)

Class view

class DE_rand_1 : public Canonical_DE

Overridden member function

Name	Utility
initialize() ⊕	Set the mutation strategy to DE::mutation_strategy::rand_1

DE/best/2

Command line arguments example

AN=DE-best-2 PS=100

Mutation strategy

v = x$_{best}$ + F $\cdot$ (x$_{r_1}$ - x$_{r_2}$) + F $\cdot$ (x$_{r_3}$ - x$_{r_4}$)

Class view

class DE_best_2 : public Canonical_DE

Overridden member function

Name	Utility
initialize() ⊕	Set the mutation strategy to DE::mutation_strategy::best_2

DE/nrand/1

Command line arguments example

AN=DE-nrand-1 PS=100

Reference

Michael G. Epitropakis, Vassilis P. Plagianakos, and Michael N. Vrahatis. (2011). “Finding multiple global optima exploiting differential evolution’s niching capability”. IEEE Symposium on Differential Evolution (SDE)

Mutation strategy

v = x$_{nearest}$ + F $\cdot$ (x$_{r_1}$ - x$_{r_2}$)

Class view

class DE_nrand_1 : public Canonical_DE

Overridden member function

Name	Utility
initialize() ⊕	Set the mutation strategy to DE::mutation_strategy::nrand_1