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An Analysis of the (µ+1) EA on Simple PseudoBoolean Functions (Extended Abstract)
"... Carsten Witt FB Informatik, LS 2 Univ. Dortmund 44221 Dortmund, Germany carsten.witt@cs.unidortmund.de Abstract. Evolutionary Algorithms (EAs) are successfully applied for optimization in discrete search spaces, but theory is still weak in particular for populationbased EAs. Here, a first r ..."
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Carsten Witt FB Informatik, LS 2 Univ. Dortmund 44221 Dortmund, Germany carsten.witt@cs.unidortmund.de Abstract. Evolutionary Algorithms (EAs) are successfully applied for optimization in discrete search spaces, but theory is still weak in particular for populationbased EAs. Here, a first rigorous analysis of the (+1) EA on pseudoBoolean functions is presented. For three example functions wellknown from the analysis of the (1+1) EA, bounds on the expected runtime and success probability are derived. For two of these functions, upper and lower bounds on the expected runtime are tight, and the (+1) EA is never more e#cient than the (1+1) EA. Moreover, all lower bounds grow with . On a more complicated function, however, a small increase of provably decreases the expected runtime drastically.
Lower Bounds for Local Search by Quantum Arguments
"... The problem of finding a local minimum of a blackbox function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1} n (, we show a lower bound of Ω 2 n/4) /n on the number of queries needed by a quantum computer to solve this ..."
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The problem of finding a local minimum of a blackbox function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1} n (, we show a lower bound of Ω 2 n/4) /n on the number of queries needed by a quantum computer to solve this problem. More surprisingly, our approach, based on Ambainis’s quantum ( adversary method, also yields a lower bound of Ω 2 n/2 /n 2 on the problem’s classical randomized query complexity. This improves and simplifies a 1983 result of Aldous. Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension d ≥ 3. 1.
Theoretical runtime analyses of search algorithms on the test data generation for the triangle classification problem
, 2008
"... Software Testing plays an important role in the life cycle of software development. Because software testing is very costly and tedious, many techniques have been proposed to automate it. One technique that has achieved good results is the use of Search Algorithms. Because most previous work on sear ..."
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Cited by 12 (9 self)
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Software Testing plays an important role in the life cycle of software development. Because software testing is very costly and tedious, many techniques have been proposed to automate it. One technique that has achieved good results is the use of Search Algorithms. Because most previous work on search algorithms has been of an empirical nature, there is a need for theoretical results that confirm the feasibility of search algorithms applied to software testing. Such theoretical results might shed light on the limitations and benefits of search algorithms applied in this context. In this paper, we formally analyse the expected runtime of three different search algorithms on the problem of Test Data Generation for an instance of the Triangle Classification program. The search algorithms that we analyse are Random Search, Hill Climbing and Alternating Variable Method. We believe that this is a necessary first step that will lead and help the Software Engineering community to better understand the role of Search Based Techniques applied to software testing.
Analysis of Computational Time of Simple Estimation of Distribution Algorithms
, 2010
"... Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well ED ..."
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Estimation of distribution algorithms (EDAs) are widely used in stochastic optimization. Impressive experimental results have been reported in the literature. However, little work has been done on analyzing the computation time of EDAs in relation to the problem size. It is still unclear how well EDAs (with a finite population size larger than two) will scale up when the dimension of the optimization problem (problem size) goes up. This paper studies the computational time complexity of a simple EDA, i.e., the univariate marginal distribution algorithm (UMDA), in order to gain more insight into EDAs complexity. First, we discuss how to measure the computational time complexity of EDAs. A classification of problem hardness based on our discussions is then given. Second, we prove a theorem related to problem hardness and the probability conditions of
Automatic software generation and improvement through search based techniques
, 2009
"... etheses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. ..."
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Cited by 10 (0 self)
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etheses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission Writing software is a difficult and expensive task. Its automation is hence very valuable. Search algorithms have been successfully used to tackle many software engineering problems. Unfortunately, for some problems the traditional techniques have been of only limited scope, and search algorithms have not been used yet. We hence propose a novel framework that is based on a coevolution of programs and test cases to tackle these difficult problems. This framework can be used to tackle software engineering tasks such as Automatic Refinement, Fault Correction and Improving Nonfunctional Criteria. These tasks are very difficult, and their automation in literature has been limited. To get a better understanding of how search algorithms work, there is the need of a theoretical foundation. That would help to get better insight of search based software engineering. We provide first theoretical analyses for search based software testing, which is one of the main components of our coevolutionary framework. This thesis gives the important contribution of presenting a novel framework, and we then study its application to three difficult software engineering problems. In this thesis we also give the important contribution of defining a first theoretical foundation. Acknowledgements
Full theoretical runtime analysis of alternating variable method on the triangle classification problem
 In International Symposium on Search Based Software Engineering (SSBSE
, 2009
"... Runtime Analysis is a type of theoretical investigation that aims to determine, via rigorous mathematical proofs, the time a search algorithm needs to find an optimal solution. This type of investigation is useful to understand why a search algorithm could be successful, and it gives insight of how ..."
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Runtime Analysis is a type of theoretical investigation that aims to determine, via rigorous mathematical proofs, the time a search algorithm needs to find an optimal solution. This type of investigation is useful to understand why a search algorithm could be successful, and it gives insight of how search algorithms work. In previous work, we proved the runtimes of different search algorithms on the test data generation for the Triangle Classification (TC) problem. We theoretically proved that Alternating Variable Method (AVM) has the best performance on the coverage of the most difficult branch in our empirical study. In this paper, we prove that the runtime of AVM on all the branches of TC is O((log n) 2). That is necessary and sufficient to prove that AVM has a better runtime on TC compared to the other search algorithms we previously analysed. The theorems in this paper are useful for future analyses. In fact, to state that a search algorithm has worse runtime compared to AVM, it will be just sufficient to prove that its lower bound is higher than Ω((log n) 2) on the coverage of at least one branch of TC.
On the Impact of Objective Function Transformations on Evolutionary and BlackBox Algorithms
, 2005
"... Different fitness functions describe different problems. Hence, certain fitness transformations can lead to easier problems although they are still a model of the considered problem. In this paper, the class of neutral transformations for a simple rankbased evolutionary algorithm (EA) is described ..."
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Different fitness functions describe different problems. Hence, certain fitness transformations can lead to easier problems although they are still a model of the considered problem. In this paper, the class of neutral transformations for a simple rankbased evolutionary algorithm (EA) is described completely, i.e., the class of functions that transfers easy problems for this EA in easy ones and difficult problems in difficult ones. Moreover, the class of neutral transformations for this populationbased EA is equal to the blackbox neutral transformations. Hence, it is a proper superset of the corresponding class for an EA based on fitnessproportional selection, but it is a proper subset of the class for random search. Furthermore, the minimal and maximal class of neutral transformations is investigated in detail.
Design and Analysis of an Asymmetric Mutation Operator
, 2007
"... Evolutionary algorithms are general randomized search heuristics and typically perform an unbiased random search that is guided only by the fitness of the search points encountered. However, in practical applications there is often problemspecific knowledge that suggests some additional bias. The u ..."
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Cited by 7 (1 self)
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Evolutionary algorithms are general randomized search heuristics and typically perform an unbiased random search that is guided only by the fitness of the search points encountered. However, in practical applications there is often problemspecific knowledge that suggests some additional bias. The use of appropriately biased variation operators may speedup the search considerably. Problems defined over bit strings of finite length often have the property that good solutions have only very few 1bits or very few 0bits. A specific mutation operator tailored towards such situations is studied under different perspectives and in a rigorous way discussing its assets and drawbacks. This is done by considering illustrative example functions as well as function classes. The main focus is on theoretical run time analysis yielding asymptotic results. These findings are accompanied by the results of empirical investigations that deliver additional insights.
How Randomized Search Heuristics Find Maximum Cliques in Planar Graphs
, 2006
"... Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple randomized optimizers on the maximum clique problem on planar graphs is investigated rigorously. The focus is on the wor ..."
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Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple randomized optimizers on the maximum clique problem on planar graphs is investigated rigorously. The focus is on the worst, average, and semiaveragecase behaviors. In semirandom planar graph models an adversary is allowed to modify moderately a random planar graph, where a graph is chosen uniformly at random among all planar graphs. With regard to the heuristics particular interest is given to the influences of the following four popular strategies to overcome local optima: local vs. globalsearch, single vs. multistart, small vs. large population, and elitism vs. nonelitism selection. Finally, the blackbox complexities of the planar graph models are analyzed.
Running Time Analysis of Ant Colony Optimization for Shortest Path Problems
, 2011
"... Ant Colony Optimization (ACO) is a modern and very popular optimization paradigm inspired by the ability of ant colonies to find shortest paths between their nest and a food source. Despite its popularity, the theory of ACO is still in its infancy and a solid theoretical foundation is needed. We pre ..."
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Cited by 5 (4 self)
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Ant Colony Optimization (ACO) is a modern and very popular optimization paradigm inspired by the ability of ant colonies to find shortest paths between their nest and a food source. Despite its popularity, the theory of ACO is still in its infancy and a solid theoretical foundation is needed. We present bounds on the running time of different ACO systems for shortest path problems. First, we improve previous results by Attiratanasunthron and Fakcharoenphol [Information Processing Letters, 105(3):88–92, 2008] for singledestination shortest paths and extend their results from DAGs to arbitrary directed graphs. Our upper bound is asymptotically tight for large evaporation factors, holds with high probability, and transfers to the allpairs shortest paths problem. There, a simple mechanism for exchanging information between ants with different destinations yields a significant improvement. A comparison with evolutionary and genetic approaches indicates that ACO is among the best known metaheuristics for the allpairs shortest paths problem.