Hybridization of Adaptive Differential Evolution with an Expensive Local Search Method

Table 1

CEC2005 test instances.

Test instance	Test instances definition		Initialization range	Value to reach
	Minimize ,			−450
	where and ,
	where is the dimension and is the shifted global optimum.
	Minimize ,			−450
	where and ,
	where is the dimension and is the shifted global optimum.
	Minimize ,			−450
	where and ,
	where is the dimension, is the shifted global optimum.
	is the orthogonal matrix.
	Minimize ,			−450
	where and ,
	where is the dimension and is the shifted global optimum.
	Minimize ,			−310
	where , , is the dimension,
	matrix, are random numbers ∈,
	, is the th row of , ,
	is an vector, and are random numbers ∈.
	Minimize ,			390
	where and ,
	where is the dimension and is the shifted global optimum.
	Minimize ,			−180
	where and ,
	where is the dimension and is the shifted global optimum.
	is the linear transformation matrix, .
	Minimize,			−140
	where , ,
	is the dimension, and is the shifted global optimum.
	M is the linear transformation matrix.
	Minimize ,			−330
	where and ,
	where is the dimension and is the shifted global optimum.
	Minimize ,			−330
	where and ,
	where is the dimension and is the shifted global optimum.
	M is the linear transformation matrix.
	Minimize , where			90
	, , , ,
	is the dimension, is the shifted global optimum,
	, and M is the linear transformation matrix.
	Minimize , where			−460
	,
	, ,
	, is the dimension,
	, and are random integers ∈.
	M is the linear transformation matrix.
	Minimize ,			−130
	Griewank’s function is as follows: .
	Rosenbrock’s function is as follows: , , .
	is the dimension. is the the shifted global optimum.
	Minimize .			−300
	is the expansion of ,
	, , and is the dimension.
	is the shifted global optimum.
	is the linear transformation matrix.