This algorithm combines modules and operators of standard GAs with specilized routines aimed at archieving enhanched performance on istances with specific types of constraints, in particular linear.

1. A Modular Genetic
Algorithm Specialized
for Linear Constraints
Stefano Costanzo, Lorenzo Castelli,
Alessandro Turco

2. Genetic Algorithms
Genetic Algorithms are popular stochastic
optimization methods inspired by the evolutionist
theory on the origin of species and natural selection.
GAs are particularly suitable for solving complex
single and multi-objective problems and finding
reasonably good trade-off solutions.
2

3. How it works
GAs are designed to simulate processes in natural
systems necessary for evolution, following the
“Survival of the fittest“ by Charles Darwin.
GA initializes a population and improves it through
iteration of the selection, genetic operators and
evaluation phases.
3

4. Genetic Algorithm Process
4

5. Target
Effectively tackle problems with specific characteristics
and maintain at least the performance of state-of-the-
art Genetic Algorithms.
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6. Problem characteristics
• Linear constraints
• Nonlinear constraints
• Equality constraints
• Variable Bounds
• Single-objective problems
• Multi-objective problems
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7. Modularity
• Each phase is well defined and independent
• New valid phases are simple to design
• Multiple alternatives can co-exist
• Wide variety of specialized GA phases in literature
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8. Genetic Algorithm Process
8

9. Modularity Exploitation - Selection 9

10. Modularity Exploitation – Genetic Operators 10

11. Modularity Exploitation – Before optimization 11

12. Before Optimization - Linear Constraints Logic
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13. Pre-processing
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14. MOGASI
Multi-Objective Genetic Algorithm for Structured Inputs

15. MOGASI - Complete Initialization Phase 15

16. MOGASI - Main Loop 16

17. Benchmarking
Three different categories of tests are performed:
• Constrained single-objective problem
• Unconstrained multi-objective problem
• Constrainted multi-objective problem
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18. Benchmarking
For each category multiple tests are chosen:
• Constrained single-objective problem
from Michalewicz Library: t01, t02, t06, t12, t13, t17, t26
• Unconstrained multi-objective problem
from NSGA-II tests: SCH, POL, KUR, ZDT1, ZDT2, ZDT4
• Constrained multi-objective problem
from NSGA-II tests: DEB, SRN, TNK, WATER
18

19. Competitors – State of the Art GAs
• GENOCOP III
• Non-dominated Sorting Genetic Algorithm, NSGA-II
• Multi-Objective Genetic Algorithm, MOGA-II
Z. Michalewicz and G. Nazhiyath - Genocop III: co-evolutionary algorithm for numerical
optimization problems with nonlinear constraints
K. Deb – A fast and elitist multiobjective genetic algorithm: NSGA-II
C. Poloni, V. Pediroda - GA coupled with computationally expensive simulations: tools
to improve efficiency 19

20. Single Objective Problems
Test name t13
Objective Function:
Constraint:
Bounds:
Average Optimal Solution
Percentage Deviation
GENOCOP 0.1422 %
MOGASI 0.0000 %
NSGA-II 43.704 %
MOGA-II 40.527 %
GENOCOP 24.9644
MOGASI 25.0000
NSGA-II 14.0738
MOGA-II 14.8680
10,00
12,00
14,00
16,00
18,00
20,00
22,00
24,00
26,00
Genocop
MOGASI
NSGA-II
MOGA-II
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21. Medal Table – Single-Objective Problems
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1st
2nd
3rd
4th

22. Multi-Objective Problems
Test Name: SRN Optimization progress with IGD:
Objective Function:
Constraint:
Bounds:
Evaluation MOGA-II NSGA-II MOGASI
1 000 0.883843 1.640582 1.094851
2 000 0.521967 0.92367 0.541842
5 000 0.305973 0.607951 0.232426
10 000 0.209635 0.531319 0.128108
15 000 0.16975 0.419232 0.092720
20 000 0.147247 0.338228 0.069383
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23. Medal Table - Multi-Objective Problems
23
1st
2nd
3rd

24. Conclusions
• Problem meta-type defined by characteristics
• Exploited specific characteristics knowledge
• Kept standard GAs performance
• Good results in Benchmarks
• Easy case study expansion
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25. Thank you for your
attention