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151
Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem
 IN PROC. OF GECCO ’04
, 2004
"... 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 optimization. The analysis ..."
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Cited by 66 (29 self)
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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 optimization. The analysis
Evolutionary Algorithms and the Maximum Matching Problem
, 2002
"... Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically wellfounded analyses exist. Such a ..."
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Cited by 65 (10 self)
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Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically wellfounded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the wellknown maximum matching problem. It is
Worstcase and Averagecase Approximations by Simple Randomized Search Heuristics
 In Proc. of STACS ’05, volume 3404 of LNCS
, 2005
"... Abstract. In recent years, probabilistic analyses of algorithms have received increasing attention. Despite results on the averagecase complexity and smoothed complexity of exact deterministic algorithms, little is known about the averagecase behavior of randomized search heuristics (RSHs). In thi ..."
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Cited by 47 (12 self)
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Abstract. In recent years, probabilistic analyses of algorithms have received increasing attention. Despite results on the averagecase complexity and smoothed complexity of exact deterministic algorithms, little is known about the averagecase behavior of randomized search heuristics (RSHs). In this paper, two simple RSHs are studied on a simple scheduling problem. While it turns out that in the worst case, both RSHs need exponential time to create solutions being significantly better than 4/3approximate, an averagecase analysis for two input distributions reveals that one RSH is convergent to optimality in polynomial time. Moreover, it is shown that for both RSHs, parallel runs yield a PRAS. 1
Running Time Analysis of a MultiObjective Evolutionary Algorithm on a Simple Discrete Optimization Problem
, 2002
"... For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the ..."
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Cited by 44 (7 self)
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For the first time, a running time analysis of a multiobjective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudoBoolean problem (Lotz: leading ones  trailing zeroes) is defined and a populationbased optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in #(n 2 log n) function evaluations where n is the number of binary decision variables. 1
Upper and Lower Bounds for Randomized Search Heuristics . . .
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY (ECCC
, 2004
"... Randomized search heuristics like local search, tabu search, simulated annealing or all kinds of evolutionary algorithms have many applications. However, for most problems the best worstcase expected run times are achieved by more problemspecific algorithms. This raises ..."
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Cited by 42 (6 self)
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Randomized search heuristics like local search, tabu search, simulated annealing or all kinds of evolutionary algorithms have many applications. However, for most problems the best worstcase expected run times are achieved by more problemspecific algorithms. This raises
A Tutorial on Evolutionary Multiobjective Optimization
 In Metaheuristics for Multiobjective Optimisation
, 2003
"... Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. ..."
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Cited by 41 (0 self)
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Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1
A Study of Drift Analysis for Estimating Computation Time of Evolutionary Algorithms
"... This paper introduces drift analysis and its applications in estimating average computation time of evolutionary algorithms. Firstly, drift conditions for estimating upper and lower bounds of the mean first hitting times of evolutionary algorithms are presented. Then drift analysis is applied to two ..."
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Cited by 39 (14 self)
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This paper introduces drift analysis and its applications in estimating average computation time of evolutionary algorithms. Firstly, drift conditions for estimating upper and lower bounds of the mean first hitting times of evolutionary algorithms are presented. Then drift analysis is applied to two specific evolutionary algorithms and problems. Finally, a general classification of easy and hard problems for evolutionary algorithms is given based on the analysis.
From an individual to a population: An analysis of the first hitting time of populationbased evolutionary algorithms
 IEEE Transactions on Evolutionary Computation
, 2002
"... Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1+1) EAs only. Theoretical results on the average computation time of populationbased EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The u ..."
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Cited by 38 (12 self)
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Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1+1) EAs only. Theoretical results on the average computation time of populationbased EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The use of population has been regarded as one of the key features of EAs. It is important to understand in depth what the real utility of population is in terms of the time complexity of EAs, when EAs are applied to combinatorial optimization problems. This paper compares (1 + 1) EAs and (N + N) EAs theoretically by deriving their first hitting time on the same problems. It is shown that a population can have a drastic impact on an EA’s average computation time, changing an exponential time to a polynomial time (in the input size) in some cases. It is also shown that the first hitting probability can be improved by introducing a population. However, the results presented in this paper do not imply that populationbased EAs will always be better than (1 + 1) EAs for all possible problems. I.
Towards an analytic framework for analysing the computation time of evolutionary algorithms
 Artificial Intelligence
, 2003
"... In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optim ..."
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Cited by 36 (13 self)
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In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise. This paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms. The framework is built on the absorbing Markov chain model of evolutionary algorithms. The first step towards a systematic comparative study among different EAs and their first hitting times has been made in the paper.
Theoretical aspects of evolutionary algorithms
 PROC. OF 28TH INT. COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), LNCS 2076
, 2001
"... Randomized search heuristics like simulated annealing and evolutionary algorithms are applied successfully in many different situations. However, the theory on these algorithms is still in its infancy. Here it is discussed how and why such a theory should be developed. Afterwards, some fundamental r ..."
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Cited by 34 (16 self)
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Randomized search heuristics like simulated annealing and evolutionary algorithms are applied successfully in many different situations. However, the theory on these algorithms is still in its infancy. Here it is discussed how and why such a theory should be developed. Afterwards, some fundamental results on evolutionary algorithms are presented in order to show how theoretical results on randomized search heuristics can be proved and how they contribute to the understanding of evolutionary algorithms.