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Chapter and Conference Paper
Experimental Supplements to the Theoretical Analysis of EAs on Problems from Combinatorial Optimization
It is typical for the EA community that theory follows experiments. Most theoretical approaches use some model of the considered evolutionary algorithm (EA) but there is also some progress where the expected o...
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Chapter and Conference Paper
The Ising Model on the Ring: Mutation Versus Recombination
The investigation of genetic and evolutionary algorithms on Ising model problems gives much insight how these algorithms work as adaptation schemes. The Ising model on the ring has been considered as a typical...
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Chapter and Conference Paper
The Ising Model: Simple Evolutionary Algorithms as Adaptation Schemes
The investigation of evolutionary algorithms as adaptation schemes has a long history starting with Holland (1975). The Ising model from physics leads to a variety of different problem instances and it is inte...
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Chapter and Conference Paper
Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem
Randomized search heuristics, among them randomized local search and evolutionary algorithms, are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimizatio...
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Chapter and Conference Paper
Real Royal Road Functions for Constant Population Size
Evolutionary and genetic algorithms (EAs and GAs) are quite successful randomized function optimizers. This success is mainly based on the interaction of different operators like selection, mutation, and cross...
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Chapter and Conference Paper
On the Optimization of Monotone Polynomials by the (1+1) EA and Randomized Local Search
Randomized search heuristics like evolutionary algorithms and simulated annealing find many applications, especially in situations where no full information on the problem instance is available. In order to un...
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Chapter
Theory of Evolutionary Algorithms and Genetic Programming
Randomized search heuristics are an alternative to specialized and problem-specific algorithms. They are applied to NP-hard problems with the hope of being efficient in typical cases. They are an alternative i...
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Chapter and Conference Paper
Fitness Landscapes Based on Sorting and Shortest Paths Problems
The analysis of evolutionary algorithms is up to now limited to special classes of functions and fitness landscapes. It is not possible to describe those subproblems of NP-hard optimization problems where cert...
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Chapter and Conference Paper
Distributed Hybrid Genetic Programming for Learning Boolean Functions
When genetic programming (GP) is used to find programs with Boolean inputs and outputs, ordered binary decision diagrams (OB-DDs) are often used successfully. In all known OBDD-based GP-systems the variable or...
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Chapter and Conference Paper
On the Choice of the Mutation Probability for the (1+1) EA
When evolutionary algorithms are used for function optimization, they perform a heuristic search that is influenced by many parameters. Here, the choice of the mutation probability is investigated. It is shown...
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Chapter and Conference Paper
On the optimization of unimodal functions with the (1+1) evolutionary algorithm
We investigate the expected running time of the (1+1) EA, a very simple Evolutionary Algorithm, on the class of unimodal fitness functions with Boolean inputs. We analyze the behavior on a generalized version ...
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Chapter and Conference Paper
Optimal attribute-efficient learning of disjunction, parity, and threshold functions
Decision trees are a very general computation model. Here the problem is to identify a Boolean function f out of a given set of Boolean functions F by asking for the value of f at adaptively chosen inputs. For cl...
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Chapter and Conference Paper
Read-once projections and formal circuit verification with binary decision diagrams
Computational complexity is concerned with the complexity of solving problems and computing functions and not with the complexity of verifying circuit designs. The importance of formal verification is evident....
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Chapter and Conference Paper
The worst case complexity of MC Diarmid and Reed's variant of BOTTOM-UP-HEAT SORT is less than n log n+1.1n
BOTTOM-UP-HEAP SORT is a variant of HEAP SORT which beats on average even the clever variants of QUICK SORT, if n is not very small. Up to now, the worst case complexity of BOTTOM-UP-HEAP SORT can be estimated on...
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Chapter and Conference Paper
Symmetric functions in AC 0 can be computed in constant depth with very small size
It is well-known which symmetric Boolean functions can be computed by constant depth, polynomial size, unbounded fan-in circuits, i.e. which are contained in the complexity class AC 0. This result is sharpened. S...
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Chapter and Conference Paper
Bottom-up-heap sort, a new variant of heap sort beating on average quick sort (if n is not very small)
A new variant of HEAP SORT, called BOTTOM-UP-HEAP SORT, is presented. This new sequential sorting algorithm is easy to implement and beats QUICK SORT on average, if n ≥ 400, and the best-off-three version of QUIC...
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Chapter
The complexity of symmetric boolean functions
The class of symmetric Boolean functions contains many fundamental functions, among them all types of counting functions. Hence the efficient computation of symmetric functions is a fundamental problem in comp...
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Chapter and Conference Paper
The critical complexity of all (monotone) boolean functions and monotone graph properties
CREW-PRAM's build a powerful model of parallel computers. Cook/Dwork/Reischuk proved that the CREW-PRAM complexity of Boolean functions is bounded below by logbc(f) where b ≈ 4.79 and c(f) is the critical complex...
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Chapter and Conference Paper
Proving lower bounds on the monotone complexity of Boolean functions
The hardware of computers may be well modelled by Boolean networks computing Boolean functions f:{0, 1}n → {0, 1}m. Though by counting arguments it is easy to show that nearly all Boolean functions may be compute...
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Chapter and Conference Paper
Boolean functions whose monotone complexity is of size n2/log n
We construct a sequence of monotone Boolean functions hn:{0, 1}n→{0, 1}n, such that the monotone complexity of hn is of order n2/log n. This result includes the largest known lower bound of this kind. Previously ...