113 research outputs found
Local search in memetic algorithms
Memetic algorithms are popular randomized search heuristics combining evolutionary algorithms and local search. Their efficiency has been demonstrated in countless applications covering a wide area of practical problems. However, theory of memetic algorithms is still in its infancy and there is a strong need for a rigorous theoretical foundation to better understand these heuristics. Here, we attack one of the fundamental issues in the design of memetic algorithms from a theoretical perspective, namely the choice of the frequency with which local search is applied. Since no guidelines are known for the choice of this parameter, we care about its impact on memetic algorithm performance. We present worst-case problems where the choice of the local search frequency has an enormous impact on the performance of a simple memetic algorithm. A rigorous theoretical analysis shows that on these problems, with overwhelming probability, even a small factor of 2 decides about polynomial versus exponential optimization times
Self-stablizing cuts in synchronous networks
Consider a synchronized distributed system where each node can only observe the state of its neighbors. Such a system is called self-stabilizing if it reaches a stable global state in a finite number of rounds. Allowing two different states for each node induces a cut in the network graph. In each round, every node decides whether it is (locally) satisfied with the current cut. Afterwards all unsatisfied nodes change sides independently with a fixed probability p. Using different notions of satisfaction enables the computation of maximal and minimal cuts, respectively. We analyze the expected time until such cuts are reached on several graph classes and consider the impact of the parameter p and the initial cut
Runtime Analysis of Quality Diversity Algorithms
Quality diversity~(QD) is a branch of evolutionary computation that gained
increasing interest in recent years. The Map-Elites QD approach defines a
feature space, i.e., a partition of the search space, and stores the best
solution for each cell of this space. We study a simple QD algorithm in the
context of pseudo-Boolean optimisation on the ``number of ones'' feature space,
where the th cell stores the best solution amongst those with a number of
ones in . Here is a granularity parameter . We give a tight bound on the expected time until all cells are covered
for arbitrary fitness functions and for all and analyse the expected
optimisation time of QD on \textsc{OneMax} and other problems whose structure
aligns favourably with the feature space. On combinatorial problems we show
that QD finds a -approximation when maximising any monotone
sub-modular function with a single uniform cardinality constraint efficiently.
Defining the feature space as the number of connected components of a connected
graph, we show that QD finds a minimum spanning tree in expected polynomial
time
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