Influence of Different Deviations Allowed for Equality Constraints on Particle Swarm Optimization and Differential Evolution

Differential evolution in constrained numerical optimization: An empirical study

“…On the other hand, there is a tendency to combine different variants in one single approach by adding self-adaptive mechanisms [3] sub-populations [57] or mathematical-programming methods [21]. Finally, the most popular combination is DE/rand/1/bin with Deb's feasibility rules [20,25,38,42,[73][74][75] or DE/rand/1/ bin with a slightly variant of Deb's rules [22,24].…”

“…They also conducted a study on termination conditions for DE/rand/1/bin in constrained optimization [74]. These two authors also analyzed the effect of the dynamic tolerance for equality constraints on DE/rand/1/bin [75].…”

“…From the summary of the state-of-the-art presented in Section 4 it is clear that DE/rand/1/bin is used in more than half of the proposed approaches [15,19,20,22,24,25,38,42,70,[73][74][75], while similar variants such as DE/best/1/bin, are barely preferred [30]. The most popular constraint-handling mechanism used with DE is the set of feasibility rules proposed by Deb [3,[20][21][22]24,25,38,42,45,[73][74][75], while penalty functions [19,57] and multiobjective concepts [15,30] are sparingly utilized.…”

“…The most popular constraint-handling mechanism used with DE is the set of feasibility rules proposed by Deb [3,[20][21][22]24,25,38,42,45,[73][74][75], while penalty functions [19,57] and multiobjective concepts [15,30] are sparingly utilized. There are several approaches which use local search (Gradient-base mutation, Sequential Quadratic Programming, NelderMead Simplex among others) [15,20,21,30,[54][55][56].…”

“…3. Novel bio-inspired approaches: Other nature-inspired algorithms have been used to solve numerical constrained problems, such as artificial immune systems (AIS) [8], particle swarm optimization (PSO) [4,39], and differential evolution (DE) [22,24,38,45,[54][55][56][57][73][74][75]. 4.…”