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Differential evolution with multi-constraint consensus methods for constrained optimization

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Abstract

Constrained optimization is an important research topic that assists in quality planning and decision making. To solve such problems, one of the important aspects is to improve upon any constraint violation, and thus bring infeasible individuals to the feasible region. To achieve this goal, different constraint consensus methods have been introduced, but no single method performs well for all types of problems. Hence, in this research, for solving constrained optimization problems, we introduce different variants of the Differential Evolution algorithm, with multiple constraint consensus methods. The proposed algorithms are tested and analyzed by solving a set of well-known bench mark problems. For further improvements, a local search is applied to the best variant. We have compared our algorithms among themselves, as well as with other state of the art algorithms. Those comparisons show similar, if not better performance, while also using significantly lower computational time.

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Abbreviations

X :

Decision vector

D :

Number of decision variables

f (X):

Objective function

g c (X):

cth inequality constraint

h e (X):

eth equality constraint

L j :

Lower limit of x j

U j :

Upper limit of x j

PS :

Population Size

Cr :

Crossover rate

F :

Amplification factor

WS :

Window size parameter

Ni :

Number of individuals assigned to the ith group

\({\varepsilon}\) :

Epsilon parameter for the equality constraints

P :

Number of infeasible points that follow the CC methods

\({\vec{V}_{i,t}}\) :

Mutant vector

α :

Feasibility distance tolerance

β :

Movement tolerance

μ :

Number of generations

\({Vio_{i,t}^{\rm best}}\) :

Constraint violation of the best individual in subpopulation i

FR i,t :

Feasibility ratio of operator i at generation t

MSS :

Minimum subpopulation size

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Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Australian Defense Force Academy, Canberra, ACT, 2600, Australia

    Noha M. Hamza, Ruhul A. Sarker & Daryl L. Essam

Authors
  1. Noha M. Hamza
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  2. Ruhul A. Sarker
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  3. Daryl L. Essam
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Correspondence to Noha M. Hamza.

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Hamza, N.M., Sarker, R.A. & Essam, D.L. Differential evolution with multi-constraint consensus methods for constrained optimization. J Glob Optim 57, 583–611 (2013). https://doi.org/10.1007/s10898-012-9987-z

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