Default boundary handling on bbob discus

[nikohansen]

Triggered by the results from Brockhoff 2023 found via

import cocopp
print(cocopp.archives.all('cma-b'))
dsl = cocopp.main('cma-b*')

['bbob/2023/cma-bp-bbob_Brockhoff.tgz', 'bbob/2023/cma-bt-bbob_Brockhoff.tgz', 'sbox-cost/2023/cma-bp-sboxcost-Brockhoff.tgz', 'sbox-cost/2023/cma-bt-sboxcost-Brockhoff.tgz']

(where bp and bt stand for penalty and transformation boundary handling, respectively) the following experiment reveals that the default boundary handling leads sometimes (here in about 5%) to undesirable behavior as in the lower figure below, compared to upper without boundary handling. Values below 1 are reached from iteration 400 without boundary handling but from iteration 1000 (and usually 550) with boundary handling.

Code:

import cocoex
import cma

suite = cocoex.Suite('bbob', '', '')
fun = suite.get_problem_by_function_dimension_instance(11, 20, 1)

print(cma.CMAOptions('disp'))  # checking
es = cma.CMA(20 * [0], 2,
    {'termination_callback': lambda _: fun.final_target_hit,
     'verb_disp_overwrite': 200,
     'bounds': [-5, 5],
     })
es.optimize(fun)
es.result_pretty();
es.plot();

This behaviour may be unavoidable as the boundary transformation can make the landscape significantly nonquadratic, hence a local adaptation to the curvature may not be the final necessary. It should be much less of an issue when the level sets are not purely ellipsoidal in the first place.

Reference: Brockhoff 2023.