MultistartOptimization.jl

Experimenting with multistart optimization methods in Julia.

WORK IN PROGRESS. Expect API changes, but SemVer 2 will of course be respected.

Documentation is very much WIP.

How to use this package

1. Define a minimization problem with the objective, lower- and upper bounds,

2. pick a local method for each multistart point (currently methods in NLopt.jl are supported),

3. pick a multistart method (currently we have TikTak from Arnoud, Guvenen, and Kleineberg (2019)).

Example:

using MultistartOptimization, NLopt
P = MinimizationProblem(x -> sum(abs2, x), -ones(10), ones(10))
local_method = NLoptLocalMethod(NLopt.LN_BOBYQA)
multistart_method = TikTak(100)
p = multistart_minimization(multistart_method, local_method, P)
p.location, p.value

Some benchmarks

Number of function evaluations for

• TikTak with 100 Sobol initial points,
• dimension 10,
• local search terminating with absolute tolerance 1e-8 in the position

	ShiftedQuadratic	Griewank	LevyMontalvo2	Rastrigin	Rosenbrock
LN_BOBYQA	569	2633	4235	FAIL	10995
LN_NELDERMEAD	15750	17108	33088	FAIL	42785
LN_NEWUOA_BOUND	580	2088	2253	FAIL	13409
LN_SBPLX	12329	11806	11447	FAIL	7020038
LN_COBYLA	16943	37414	32792	FAIL	985676
LN_PRAXIS	1850	9886	8548	FAIL	15436