Talk given in: 2017 IEEE Congress on Evolutionary Computation (CEC), taking place at Donostia - San Sebastian, Spain, June 5-8, 2017. Associated special session at CEC: Associated with Competition on Bound Constrained Single Objective Numerical Optimization III (June 6, 14:30-16:30, Room 4).
Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b
Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 Constrained Real-Parameter Optimization
1. Adaptive Constraint Handling and Success
History Differential Evolution for CEC 2017
Constrained Real-Parameter Optimization
2017 IEEE Congress on Evolutionary Computation (CEC)
Donostia - San Sebasti´an, Spain
June 5–8, 2017
Session: Associated with Competition on Bound Constrained Single
Objective Numerical Optimization III (June 6, 14:30-16:30, Room 4),
Aleˇs Zamuda
University of Maribor
Aleˇs Zamuda University of Maribor
Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 1 / 22
3. Motivation
CEC 2017 Competition and Special Session on Constrained
Single Objective Real-Parameter Optimization
L-SHADE
Adaptive level of -violation
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5. CEC 2017 Constrained Single Objective Real-Parameter
Optimization Functions
The collection includes 28 functions.
Functions are instanced for dimensions D = {10, 30, 50, 100}.
Function evaluations (FEs) dependent on D: FEs = 20,000D.
25 independent runs of stochastic optimization algorithm.
New algorithm name: CAL-SHADE.
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Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 5 / 22
6. Differential Evolution and L-SHADE
DE: population-based floating-point encoding EA for global
optimization over continuos spaces
the evolutionary process, by generations improves
population of vectors,
for each new population vector, evolutionary operators are
executed.
L-SHADE – CEC 2014: c.p-best/1, p = 0.11, H = 6, rarc = 2.6, rNinit = 18
mutation:
vi,G+1 = xi,G + Fi × (xpbest,G − xi,G ) + Fi × (x1,G − xr2,G ),
crossover:
ui,j,G+1 =
vi,j,G+1 if rand(0, 1) ≤ CR ali j = jrand
xi,j,G otherwise
and
selection: xi,G+1 =
ui,G+1 if f (ui,G+1) ≤ f (xi,G )
xi,G otherwise
,
includes mechanisms:
F and CR self-adaptation using success history archive,
archive; a linear population size NP reduction mechanism.Aleˇs Zamuda University of Maribor
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8. CAL-SHADE: Outline
The proposed CAL-SHADE: constrained L-SHADE,
Constraint Handling with Success History Adaptive
Differential Evolution.
Based on L-SHADE.
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Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 8 / 22
9. CAL-SHADE: Constraint Handling, -level
CAL-SHADE uses constraints and adaptation of epsilon value,
i.e. epsilon level handling to adapt constraints comparisons.
Constraints violation and aggregation computation:
gi (x) ≤ 0, i = 1, ..., q, (1)
|hj (x)| − ≤ 0, j = q + 1, ..., m, (2)
ν =
( q
i=1 Gi (x) + m
j=q+1 Hj (x))
m
, (3)
Gi (x) =
gi (x), gi (x) > 0,
0, gi (x) ≤ 0,
(4)
Hj (x) =
|hj (x)|, |hj (x)| − > 0,
0, |hj (x)| − ≤ 0.
(5)
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Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 9 / 22
10. CAL-SHADE: Constraint Handling, -level
Then, in the individual vectors comparisons, the equation (6)
is used.
xi,g+1 =
xj,g if (νi,g > νj,g ),
xj,g else if (νj,g = 0) ∧ (f (xi,g ) > f (xj,g )),
xi,g otherwise,
(6)
Constraints take precedence:
When computing difference in success history adaptation and
when there are constraint violation improvements.
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Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 10 / 22
12. Experimental Setup for CAL-SHADE
CAL-SHADE uses an initial population size of NPinit = 2 × D
p value for current-to-pbest/1 mutation 0.11
historical memory size H = 5, and
external archive size |A| of Ninit multiplied by rarc = 2.
The initial level is set at Deb-rules ranked individual at 0.2
NP-th individual, and at θg = 0.8NP-th in later generations;
level is diminished to order of 5, and
after gc = 500 generations this level relaxation is omitted to
fully consider all the constraints.
Except the NPinit, θg , H, and rarc, the parameter settings are
therefore taken from the literature (Zamuda&Sosa&Adler:
2016 UGPP; Tanabe: 2014 L-SHADE)
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19. Function Values Achieved: FES = 2 × 106
, 100D, C19 – C24.
FEs C19 C20 C21 C22 C23 C24
Best 0.000066 6.311732 3.980643 122274.131508 0.800967 18.097334
Median 0.000088 7.342300 9.995811 259925.383174 0.810964 21.817367
c 1, 0, 0 0, 0, 0 0, 0, 0 1, 0, 0 0, 0, 1 0, 1, 0
ν 48646.342504 0.000000 0.000000 46.885568 0.000000 0.323019
2 × 106
Mean 8.82e-05 7.40385 14.9419 263043 0.814437 22.8996
Worst 0.000122 8.571167 31.578069 508308.160038 0.844395 31.156972
STD 1.3235e-05 5.5579e-01 7.3058e+00 9.7856e+04 1.0029e-02 2.8828e+00
SR 0% 100% 100% 0% 92% 8%
vio 48646.3 2e-07 3.2e-07 46.1771 3.684e-05 234.413
Function Values Achieved: FES = 2 × 106
, 100D, C25 – C28.
FEs C25 C26 C27 C28
Best 642.455558 1.097472 28172.148693 354.855690
Median 717.802821 1.099953 47450.441847 410.517414
c 0, 0, 1 1, 0, 1 2, 0, 0 1, 0, 0
ν 0.004779 50.500583 1106046245.109879 48875.776527
2 × 106
Mean 724.212 1.10092 47247.7 415.526
Worst 797.951458 1.125744 84021.726414 492.948144
STD 3.2369e+01 5.3132e-03 1.2565e+04 3.5785e+01
SR 24% 0% 0% 0%
vio 0.0295336 52.6093 1.37064e+09 48880.7
Definition of denotations:
c is the number of violated constraints at the median solution (the sequence of three numbers
indicate the number of violations — including inequalities and equalities — by more than 1.0, in
the range [0.01, 1.0], and in the range [0.0001, 0.01], respectively; the count can be non-zero for a
feasible solution; note qC9 = 1),
ν is the mean value of violations of all constraints at the median solution,
SR is the feasibility rate of the solutions obtained in 25 runs, and
vio is the mean constraint violation value of all the solutions of 25 runs.
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20. Conclusion
CAL-SHADE.
Algorithm for optimization of 28 challenges with 4 different
dimensions,
the set of challenges is as composed for Congress on
Evolutionary Computation (CEC) 2017 Constrained Single
Objective Real-Parameter Optimization.
The presented algorithm is based on L-SHADE algorithm,
extended with adaptive constraint handling.
The algorithm is successfully assessed on all benchmark
functions.
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Adaptive Constraint Handling and Success History Differential Evolution for CEC 2017 CRPO 20 / 22
21. Future Work
Improve performance for some functions,
more parameter tuning,
constraint handling improvements,
analysis of including other DE enhancements,
other application domains.
Acknowledgement: ARRS P2-0041; COST CA15140
Improving Applicability of Nature-inspired Optimisation by
Joining Theory and Practice (ImAppNIO)
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22. Thank you for your attention.
Questions?
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