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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.
Ant Colony Optimisation and Local Search for Bin Packing and Cutting Stock Problems
 Journal of the Operational Research Society. (forthcoming
, 2003
"... The Bin Packing Problem and the Cutting Stock Problem are two related classes of NPhard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for realworld problems we have to rely on heuristic methods. In recent years, researchers have started t ..."
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Cited by 11 (1 self)
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The Bin Packing Problem and the Cutting Stock Problem are two related classes of NPhard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for realworld problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimisation (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can outperform some existing solution methods, whereas the hybrid approach can compete with the best known solution methods. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.
Computing minimum cuts by randomized search heuristics
 Collaborative Research Center 531, Technical University of Dortmund
, 2008
"... We study the minimum stcut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many realworld optimization problems and have a variety of applicati ..."
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Cited by 9 (5 self)
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We study the minimum stcut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many realworld optimization problems and have a variety of applications in several different areas. We prove that there exist instances of the minimum stcut problem that cannot be solved by standard singleobjective evolutionary algorithms in reasonable time. On the other hand, we develop a bicriteria approach based on the famous maximumflow minimumcut theorem that enables evolutionary algorithms to find an optimum solution in expected polynomial time.
A New Approach for Analyzing Average Time Complexity of PopulationBased Evolutionary Algorithms on Unimodal Problems
, 2009
"... In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easytoapply approach designed particularly for populationbased EAs on unimodal problems. In this paper, we first g ..."
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Cited by 9 (5 self)
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In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easytoapply approach designed particularly for populationbased EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the socalled (N + N) EAs and we show that, on two wellknown unimodal problems, LEADINGONES and ONEMAX, the EAs with the bitwise mutation and two commonly used selection schemes both need O(n ln n + n2 /N) and O(n ln ln n + n ln n/N) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some populationbased EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problemspecific knowledge to get the tight bounds. It is the first time a general idea for analyzing populationbased EAs on unimodal problems is discussed theoretically.
Memetic Algorithm with Extended Neighborhood Search for Capacitated . . .
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 2009
"... The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NPhard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In t ..."
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Cited by 9 (4 self)
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The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NPhard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely MergeSplit (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of stateoftheart algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.
Ant Colony Optimisation for Bin Packing and Cutting Stock
 In Proceedings of the UK Workshop on Computational Intelligence
, 2001
"... The Bin Packing and Cutting Stock Problems are wellknown NPhard combinatorial optimisation problems with many applications. A number of evolutionary computation techniques have been applied to these problems, including genetic algorithms and evolutionary strategies. In this work, we investigate the ..."
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Cited by 5 (1 self)
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The Bin Packing and Cutting Stock Problems are wellknown NPhard combinatorial optimisation problems with many applications. A number of evolutionary computation techniques have been applied to these problems, including genetic algorithms and evolutionary strategies. In this work, we investigate the use of Dorigo's Ant Colony Optimisation metaheuristic to solve Bin Packing and Cutting Stock Problems. We show that the technique works well and can outperform other EC techniques. It is also shown to be quite sensitive to the relative weighing of the heuristic ( rst t decreasing) as opposed to pheromone trail information. 1
Maximum cardinality matching by evolutionary algorithms
 Proc. of 2002 U.K. Workshop on Computational Intelligence (UKCI’02
, 2002
"... The analysis of time complexity of evolutionary algorithms has always focused on some artificial binary problems. This paper considers the average time complexity of an evolutionary algorithm for maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce matchin ..."
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Cited by 1 (1 self)
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The analysis of time complexity of evolutionary algorithms has always focused on some artificial binary problems. This paper considers the average time complexity of an evolutionary algorithm for maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce matchings with nearly maximum cardinality in average polynomial time. I.
Solving the Cutting Stock Problem in the Steel Industry
, 2002
"... The purpose of this research is to improve an optimization model of a twodimensional cutting stock problem in the steel industry. The improvements address the functionality of the model and solution times of the optimization problem. The research problem is important, since even small improveme ..."
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The purpose of this research is to improve an optimization model of a twodimensional cutting stock problem in the steel industry. The improvements address the functionality of the model and solution times of the optimization problem. The research problem is important, since even small improvements in the cutting layouts result in large savings of raw material and energy when the amount of produced material is huge. The research methods consist of benchmarking the improved model against the current one. Although numerous
Intelligence, ” at the Technische Universität Dortmund and was printed with financial support of the Deutsche Forschungsgemeinschaft. Computing Minimum Cuts by Randomized Search Heuristics ∗
, 2008
"... We study the minimum stcut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many realworld optimization problems and have a variety of applicati ..."
Abstract
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We study the minimum stcut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many realworld optimization problems and have a variety of applications in several different areas. We prove that there exist instances of the minimum stcut problem that cannot be solved by standard singleobjective evolutionary algorithms in reasonable time. On the other hand, we develop a bicriteria approach based on the famous MaxFlowMinCut Theorem that enables evolutionary algorithms to find an optimum solution in expected polynomial time.