start [COmparing Continuous Optimisers: COCO]

COCO (COmparing Continuous Optimizers) is a platform for systematic and sound comparisons of real-parameter global optimizers. COCO provides benchmark function testbeds, experimentation templates which are easy to parallelize, and tools for processing and visualizing data generated by one or several optimizers. The COCO platform has been used for the Black-Box-Optimization-Benchmarking (BBOB) workshops that took place during the GECCO conference in 2009, 2010, 2012, 2013, and in 2015-2019 (and that will take place again in 2021). It was also used at the IEEE Congress on Evolutionary Computation (CEC'2015) in Sendai, Japan.

The COCO experiment source code has been rewritten in the years 2014-2015 and the current production code is available on our COCO github page. The old code is still available at the downloads page and shall be used for experiments on the noisy test suite until this test suite will be available in the new code as well.

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Internal wiki: https://gforge.inria.fr/plugins/mediawiki/wiki/coco

Selected Results

The figures show selected results from BBOB 2009. The empirical runtime distribution is shown for six subgroups of the BBOB functions. Click on the respective figures for more details. (At the top of this page the aggregated results over all functions are shown). More plots (for all supported COCO test suites) can be found in the http://coco.gforge.inria.fr/ppdata-archive/ppdata-archive.

Current BBOB Functions

The current 24 noiseless test functions are

1 Separable Functions
f1	Sphere Function
f2	Ellipsoidal Function
f3	Rastrigin Function
f4	Büche-Rastrigin Function
f5	Linear Slope
2 Functions with low or moderate conditioning
f6	Attractive Sector Function
f7	Step Ellipsoidal Function
f8	Rosenbrock Function, original
f9	Rosenbrock Function, rotated
3 Functions with high conditioning and unimodal
f10	Ellipsoidal Function
f11	Discus Function
f12	Bent Cigar Function
f13	Sharp Ridge Function
f14	Different Powers Function
4 Multi-modal functions with adequate global structure
f15	Rastrigin Function
f16	Weierstrass Function
f17	Schaffers F7 Function
f18	Schaffers F7 Functions, moderately ill-conditioned
f19	Composite Griewank-Rosenbrock Function F8F2
5 Multi-modal functions with weak global structure
f20	Schwefel Function
f21	Gallagher's Gaussian 101-me Peaks Function
f22	Gallagher's Gaussian 21-hi Peaks Function
f23	Katsuura Function
f24	Lunacek bi-Rastrigin Function

Only f1 and f5 are purely quadratic or linear respectively.

See also N. Hansen et al (2010): Comparing Results of 31 Algorithms from the Black-Box Optimization Benchmarking BBOB-2009. Workshop Proceedings of the GECCO Genetic and Evolutionary Computation Conference 2010, ACM. ¹⁾

The current 30 noisy test functions are

1 Functions with moderate noise
1.1	f101 Sphere with moderate Gaussian noise
	f102 Sphere with moderate uniform noise
	f103 Sphere with moderate seldom Cauchy noise
1.2	f104 Rosenbrock with moderate Gaussian noise
	f105 Rosenbrock with moderate uniform noise
	f106 Rosenbrock with moderate seldom Cauchy noise
2 Functions with severe noise
2.1	f107 Sphere with Gaussian noise
	f108 Sphere with uniform noise
	f109 Sphere with seldom Cauchy noise
2.2	f110 Rosenbrock with Gaussian noise
	f111 Rosenbrock with uniform noise
	f112 Rosenbrock with seldom Cauchy noise
2.3	f113 Step ellipsoid with Gaussian noise
	f114 Step ellipsoid with uniform noise
	f115 Step ellipsoid with seldom Cauchy noise
2.4	f116 Ellipsoid with Gaussian noise
	f117 Ellipsoid with uniform noise
	f118 Ellipsoid with seldom Cauchy noise
2.5	f119 Different Powers with Gaussian noise
	f120 Different Powers with uniform noise
	f121 Different Powers with seldom Cauchy noise
3 Highly multi-modal functions with severe noise
3.1	f122 Schaffer's F7 with Gaussian noise
	f123 Schaffer's F7 with uniform noise
	f124 Schaffer's F7 with seldom Cauchy noise
3.2	f125 Composite Griewank-Rosenbrock with Gaussian noise
	f126 Composite Griewank-Rosenbrock with uniform noise
	f127 Composite Griewank-Rosenbrock with seldom Cauchy noise
3.3	f128 Gallagher's Gaussian Peaks 101-me with Gaussian noise
	f129 Gallagher's Gaussian Peaks 101-me with uniform noise
	f130 Gallagher's Gaussian Peaks 101-me with seldom Cauchy noise

²⁾

¹⁾ This work was partially funded by FUI of System@tic Paris-Region ICT cluster through contract DGT 117 407 Complex Systems Design Lab (CSDL), and by the ANR-2010-COSI-002 grant (SIMINOLE) of the French National Research Agency.

²⁾ Work on Coco has been funded to a great extend via the ANR project NumBBO and in the context of the PGMO project AESOP. We also acknowledge support via Inria's ADT funding.

Selected Results

Current BBOB Functions

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