ChengCheng-Qin / mosa-ea

This repository includes the C++ source code of MOSA-EA.

MOSA-EA

Multi-Objective Self-Adaptive EA (MOSA-EA) (Lehre and Qin, 2022), was proposed to optimise single-objective Pseudo-Boolean functions, which treats parameter control from multi-objectivisation. The algorithm maximises the fitness and the mutation rates simultaneously, allowing individuals in "dense" fitness valleys and on "sparse" local optima to co-exist on a non-dominated Pareto front.

Please find more in the publication below.

• Publication:

  GECCO '22: https://research.birmingham.ac.uk/en/publications/self-adaptation-via-multi-objectivisation-a-theoretical-study

  PPSN '22: https://research.birmingham.ac.uk/en/publications/self-adaptation-via-multi-objectivisation-an-empirical-study

Example - Python Version

First install IOHprofiler via pip. IOHprofiler is a benchmarking platform for evaluating the performance of iterative optimisation heuristics.

pip install ioh

The arguments the python code:

-n is problem size.
-f is id of fitness function (A int value from 1 to 25. Here we use PBO problem set in IOHprofiler, for information of function ids please see IOHproblem).
-A is A in MOSA-EA (A float value greater than 1; we recommend to set as 1.01).
-p is p_inc in MOSA-EA (A float value between 0 and 1; we recommend to set as 0.4).
-c is minimal mutation rate parameter χ_min in MOSA-EA (A float value greater than 0; we recommend to set as 0.5/log(n) under noise).
-l is population size (λ) in MOSA-EA (A int value greater than 1; we recommend to set as 5000 log(n)).
-m is μ in (μ,λ) selection in MOSA-EA (A int value greater than 1 and less than λ; we recommend to set as λ/8).
-e is the maximum of the number of evaluations.
-r is the number of runs.
-log is to turn on logger to record optimisation progress via IOHprofiler (1 is on and 0 is off).

To run it:

cd mosaea-python-version
python mosa-ea.py -n 50 -f 2 -A 1.01 -p 0.4 -c 0.1 -l 5000 -m 625 -e 100000000 -r 1 -log 0

If you turn logger on, you can upload the data to IOHanalyzer to analyse the performance of MOSA-EA. The guide of IOHanalyzer is available here.

To use customised fitness function, please read here.

Example - C++ Version

To compile it:

cd mosaea-cpp-version
make

The arguments in the C++ code:

-n is problem size.
-f is id of fitness function (1 is OneMax, and 2 is LeadingOnes).
-A is A in MOSA-EA (A float value greater than 1; we recommend to set as 1.01).
-p is p_inc in MOSA-EA (A float value between 0 and 1; we recommend to set as 0.4).
-c is minimal mutation rate parameter χ_min in MOSA-EA (A float value greater than 0; we recommend to set as 0.5/log(n)).
-l is population size (λ) in MOSA-EA (A int value greater than 1; we recommend to set as 5000 log(n)).
-m is μ in (μ,λ) selection in MOSA-EA (A int value greater than 1 and less than λ; we recommend to set as λ/8).
-e is the maximum of the number of evaluations.

To run it:

./mosa-ea -n 50 -f 2 -A 1.01 -p 0.4 -c 0.1 -l 5000 -m 625 -e 100000000

which is to optimise LeadingOnes (n=100) in 100000000 evaluations by using the recommanded parameter setting.

You also can add a customised fitness function by adding a global function and giving an id in Class Evaluation. Please follow examples of OneMax and LeadingOnes in the code.

Contact

If you have any questions, comments or suggestions, please don't hesitate to contact us:

• Xiaoyu Qin, School of Computer Science, University of Birmingham.
• Per Kristian Lehre, School of Computer Science, University of Birmingham,

When using MOSA-EA and parts thereof, please kindly cite this work as

@inproceedings{mosa-ea-theory,
	title = {Self-adaptation to Multi-objectivisation: A Theoretical Study},
	booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference},
	publisher = {ACM},
	author = {Lehre, Per Kristian and Qin, Xiaoyu},
	year = {2022},
}

@inproceedings{mosa-ea-empirical,
	title = {Self-adaptation to Multi-objectivisation: An Empirical Study},
	booktitle = {Proceedings of the Parallel Problem Solving from Nature},
	publisher = {Springer},
	author = {Qin, Xiaoyu and Lehre, Per Kristian},
	year = {2022},
}

License

MOSA-EA is released under the MIT license. See LICENSE for additional details about it.