Composite Differential Evolution for Constrained Evolutionary Optimization

Abstract

Abstract-When solving constrained optimization problems by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite differential evolution, the feasibility rule and the ε constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated constrained optimization problems. By assembling the above techniques together, a constrained composite differential evolution is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

Push and pull search for solving constrained multi-objective optimization problems

“…, H. 4 while FES ≤ MaxFES do 5 Calculate ε(G). 6 Divide P into top sub-population P t and bottom sub-population P b according to the SF constraint-handling method. 7 for i ← 1 to T do 8 For each target vector x i,G ∈ P t , use three DE strategies to generate three trial vectors u i1,G ,…”

“…The primary feature of the proposed PPS-DE lies in strengthening the DE algorithm and the constrainthandling method. PPS-DE is inspired from the following stateof-the-art DE variants, including CoDE [10], C 2 oDE [6], LSHADE44+IDE [35], UDE [36], IUDE [37] and AGA-PPS [38]. PPS-DE uses three different trial vector generation strategies, including modified DE/rand/1/bin, DE/current-to-pbest/1, and DE/current-torand/1, to generate three trial vectors.…”

“…• C 2 oDE -C 2 oDE [6] is an extension of CoDE [10] for solving CSOPs. It also adopts three different trial vector generation strategies, including DE/current-to-rand/1, DE/current-to-best/1, and modified DE/rand-to-best/1, to balance diversity and convergence of a working population.…”

“…The second reason is that the number of parameters in DE is few. It is very convenient for a novice to solve optimization problems by using DE [6]. In recent years, many different DE variants have been suggested, which include FADE [7], jDE [8], JADE [9], CoDE [10], SHADE [11], LSHADE [12], LSHADE44 [13] and so on.…”

What Determines EP Curve Shape?

“…As shown in [21,22], the DyHF and the CMODE algorithms are the two best no-adjustment-needed global optimization algorithms. Now that the C 2 oDE algorithm is better than these two [23], it would be desirable to see how it works on the GB2 fit problem. With a foolproof universally applicable global optimization algorithm, the ado with shape factor and their boundaries will no longer be needed, or be used merely as some validations; but before that time, the hard earned knowledge about shape factor through CAS is still indispensable.…”