An adaptive fuzzy penalty method for constrained evolutionary optimization

A two-stage adaptive penalty method based on co-evolution for constrained evolutionary optimization

“…, q, where f (x) is the objective function, x i ∈ [L i , U i ] is the ith dimension of a decision vector/solution (denoted as x), S = D i=1 [L i , U i ] denotes the decision space, and g j (x) and h j (x) represent an inequality constraint and an equality constraint, respectively. For a decision vector (i.e., x), the violation of the jth constraint is calculated as follows [6]:…”

“…Constraint handling techniques (CHTs), which provide a basis for the environment selection of a COEA, are designed to address this issue [13]. In general, there are four cases in CHTs, namely those based on penalty function [6,14], separation of constraints and objective function [15][16][17], multiobjective optimization [18][19][20], and hybrid methods [21,22], respectively. Additionaly, some researchers have designed non-penalty-based CHTs by using supervised learning technology [23] or special operators [24].…”

“…Among the aforementioned CHTs, the penalty function method has attracted increasing attention [6,12,14]. In this kind of CHTs, a penalty factor is used to balance the satisfaction of all constraints and the search for global optimum.…”

“…-CHTs based on static penalty factor [25], -CHTs based on dynamic penalty factor [26], and -CHTs based on adaptive penalty factor [6,22].…”

“…Michalewicz et al [27] pointed out that adaptive penalty function methods have better performance in solving COPs. Thus, most existing penalty function methods adopt adaptive strategies [6].…”