3 research outputs found
When is it Beneficial to Reject Improvements?
We investigate two popular trajectory-based algorithms from biology and physics to answer a question of general significance: when is it beneficial to reject improvements? A distinguishing factor of SSWM (Strong Selection Weak Mutation), a popular model from population genetics, compared to the Metropolis algorithm (MA), is that the former can reject improvements, while the latter always accepts them. We investigate when one strategy outperforms the other. Since we prove that both algorithms converge to the same stationary distribution, we concentrate on identifying a class of functions inducing large mixing times, where the algorithms will outperform each other over a long period of time. The outcome of the analysis is the definition of a function where SSWM is efficient, while Metropolis requires at least exponential time
Memetic Algorithms Beat Evolutionary Algorithms on the Class of Hurdle Problems
Memetic algorithms are popular hybrid search heuristics that integrate
local search into the search process of an evolutionary algorithm
in order to combine the advantages of rapid exploitation and global
optimisation. However, these algorithms are not well understood and
the field is lacking a solid theoretical foundation that explains when
and why memetic algorithms are effective.
We provide a rigorous runtime analysis of a simple memetic algorithm,
the (1+1) MA, on the Hurdle problem class, a landscape class
of tuneable difficulty that shows a “big valley structure”, a characteristic
feature of many hard problems from combinatorial optimisation.
The only parameter of this class is the hurdle width w, which describes
the length of fitness valleys that have to be overcome. We show
that the (1+1) EA requires Θ(n
w) expected function evaluations to
find the optimum, whereas the (1+1) MA with best-improvement and
first-improvement local search can find the optimum in Θ(n
2 +n
3/w2
)
and Θ(n
3/w2
) function evaluations, respectively. Surprisingly, while
increasing the hurdle width makes the problem harder for evolutionary
algorithms, the problem becomes easier for memetic algorithms.
We discuss how these findings can explain and illustrate the success of
memetic algorithms for problems with big valley structures