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## Approximating the nondominated front using the Pareto Archived Evolution Strategy (2000)

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Venue: | EVOLUTIONARY COMPUTATION |

Citations: | 319 - 19 self |

### Citations

10039 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...S performs consistently well on a range of multiobjective optimisation tasks. 1 Introduction Multiobjective optimisation using genetic algorithms has been investigated by many authors in recent years =-=[2, 6, 7, 10, 11, 17, 19, 20]-=-. However, in some real-world optimisation problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu search, either when a single o... |

1162 | Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Agorithms - Bäck - 1996 |

612 | Uniform crossover in genetic algorithms, - Syswerda - 1989 |

520 | Multiobjective optimization using nondominated sorting in genetic algorithms
- Srinivas, Deb
- 1993
(Show Context)
Citation Context ...ms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; Fonseca and Fleming, 1995; Horn et al., 1994; Horn and Nafpliotis, 1994; Parks and Miller, 1998; Schaffer, 1985; =-=Srinivas and Deb, 1994-=-). However, in some real-world optimization problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu search, either when a single ... |

485 | An Overview of Evolutionary Algorithms in Multiobjective Optimization
- Fonseca, Fleming
- 1995
(Show Context)
Citation Context ...ns, multiobjective performance assessment. 1 Introduction Multiobjective optimization using evolutionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; =-=Fonseca and Fleming, 1995-=-; Horn et al., 1994; Horn and Nafpliotis, 1994; Parks and Miller, 1998; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algori... |

464 |
Multiple objective optimization with vector evaluated genetic algorithms. In Genetic algorithms and their applications
- Schaffer
- 1985
(Show Context)
Citation Context ...tionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; Fonseca and Fleming, 1995; Horn et al., 1994; Horn and Nafpliotis, 1994; Parks and Miller, 1998; =-=Schaffer, 1985-=-; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu searc... |

392 | A niched Pareto genetic algorithm for multiobjective optimization
- Horn, Nafploitis, et al.
- 1994
(Show Context)
Citation Context ...nce assessment. 1 Introduction Multiobjective optimization using evolutionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; Fonseca and Fleming, 1995; =-=Horn et al., 1994-=-; Horn and Nafpliotis, 1994; Parks and Miller, 1998; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algorithm is overshadowed... |

376 | Quad Trees: A Data Structure for Retrieval on Composite Keys. - Finkel, Bentley - 1974 |

249 |
Finding the k shortest loopless paths in a network
- Yen
- 1971
(Show Context)
Citation Context ...ed these values throughout in our experiments. Summary of Heuristics Following [14], we pre-calculate the K-shortest paths between each pair of nodes in the network, using a fast algorithm due to Yen =-=[22]-=-. A candidate solution vector (genotype) is then formulated so as to contain j K-ary elements i.e for each of the j communications, one of the K shortest paths associated with the source-destination p... |

161 |
The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation
- Knowles, Corne
- 1999
(Show Context)
Citation Context ...de in Section 7. 2 The PAES Algorithm 2.1 Motivations PAES was initially developed as a multiobjective local search method for finding solutions to the off-line routing problem (Mann and Smith, 1996; =-=Knowles and Corne, 1999-=-), which is an important problem in the area of telecommunications routing optimization. Previous work on this problem used single-objective (penalty-function) methods, and it was found that local sea... |

160 | Cybernetic solution path of an experimental problem - Rechenberg - 1965 |

141 | Multiobjective optimization using the niched pareto genetic algorithm
- Horn, Goldberg
- 1993
(Show Context)
Citation Context ...ntroduction Multiobjective optimization using evolutionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; Fonseca and Fleming, 1995; Horn et al., 1994; =-=Horn and Nafpliotis, 1994-=-; Parks and Miller, 1998; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algorithm is overshadowed by local search methods su... |

133 |
Introduction to probability and statistics
- Mendenhall
- 1998
(Show Context)
Citation Context ...al techniques can then be used to summarise the distributions or to compare the distributions produced by two competing optimisers. We compare pairs of optimisers using the Mann-Whitney rank sum test =-=[15]-=- as our statistical comparator. 1.1 Overview of the Paper The remainder of the paper is organised as follows. In Section 2 we introduce PAES and its components. First we describe the general archiving... |

103 | On the performance assessment and comparison of stochastic multiobjective optimizers
- Fonseca, Fleming
- 1996
(Show Context)
Citation Context ...ns, multiobjective performance assessment. 1 Introduction Multiobjective optimization using evolutionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; =-=Fonseca and Fleming, 1995-=-; Horn et al., 1994; Horn and Nafpliotis, 1994; Parks and Miller, 1998; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algori... |

73 |
Pareto simulated annealing - a metaheuristic tecnhique for multiple objective combinatorial optimization
- Czyzak, Jaskiewicz
- 1998
(Show Context)
Citation Context ...sts that multiobjective optimizers which employ local search strategies would be promising to investigate and compare with population-based methods. Good results have been obtained with such methods (=-=Czyzak and Jaszkiewicz, 1998-=-; Gandibleux et al., 1996; Hansen, 1996, 1997; Serafini, 1994; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998... |

59 |
Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms
- Bentley, Wakefield
- 1997
(Show Context)
Citation Context ...ve optimization, test functions, multiobjective performance assessment. 1 Introduction Multiobjective optimization using evolutionary algorithms has been investigated by many authors in recent years (=-=Bentley and Wakefield, 1997-=-; Fonseca and Fleming, 1995; Horn et al., 1994; Horn and Nafpliotis, 1994; Parks and Miller, 1998; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the perfor... |

58 | On a Multi-Objective Evolutionary Algorithm and Its Convergence to the Pareto Set
- Rudolph
- 1998
(Show Context)
Citation Context ...kiewicz, 1998; Gandibleux et al., 1996; Hansen, 1996, 1997; Serafini, 1994; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (=-=Rudolph, 1998-=-, 1998a). However, it is currently quite unclear how c fl1999 by the Massachusetts Institute of Technology Evolutionary Computation 7(3):1-26 JOSHUA KNOWLES AND DAVID CORNE well local-search based mul... |

40 | Evolutionary search for minimal elements in partially ordered finite sets
- Rudolph
- 1998
(Show Context)
Citation Context ...kiewicz, 1998; Gandibleux et al., 1996; Hansen, 1996, 1997; Serafini, 1994; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (=-=Rudolph, 1998-=-, 1998a). However, it is currently quite unclear how c fl1999 by the Massachusetts Institute of Technology Evolutionary Computation 7(3):1-26 JOSHUA KNOWLES AND DAVID CORNE well local-search based mul... |

32 |
Selective Breeding in a Multiobjective Genetic Algorithm
- Parks, Miller
- 1998
(Show Context)
Citation Context ...optimization using evolutionary algorithms has been investigated by many authors in recent years (Bentley and Wakefield, 1997; Fonseca and Fleming, 1995; Horn et al., 1994; Horn and Nafpliotis, 1994; =-=Parks and Miller, 1998-=-; Schaffer, 1985; Srinivas and Deb, 1994). However, in some real-world optimization problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealin... |

31 |
A tabu search procedure to solve multiobjective combinatorial optimization problem
- Gandibleux, Mezdaoui, et al.
- 1997
(Show Context)
Citation Context ...zers which employ local search strategies would be promising to investigate and compare with population-based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; =-=Gandibleux et al., 1996-=-; Hansen, 1996, 1997; Serafini, 1994; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998, 1998a). However, it is ... |

21 | Evolutionary Algorithms in Theory and Practice - ck - 1996 |

19 |
Simulated annealing for multiple objective optimization problems
- Serafini
- 1994
(Show Context)
Citation Context ...ld be promising to investigate and compare with population-based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al., 1996; Hansen, 1996, 1997; =-=Serafini, 1994-=-; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998, 1998a). However, it is currently quite unclear how c fl1999... |

17 | Tabu search for multiobjective optimization: MOTS
- Hansen
- 1997
(Show Context)
Citation Context ...earch strategies would be promising to investigate and compare with population-based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al., 1996; =-=Hansen, 1997-=-, 1998; Serafini, 1994; Ulungu et al., 1995), and, recently, some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998a, 1998b). However, c fl2000 by the M... |

17 |
Multi-objective optimisation using nondominated sorting in genetic algorithms (Vol. 2). Journal of evolutionary computing
- Srinivas, Deb
- 1994
(Show Context)
Citation Context ...S performs consistently well on a range of multiobjective optimisation tasks. 1 Introduction Multiobjective optimisation using genetic algorithms has been investigated by many authors in recent years =-=[2, 6, 7, 10, 11, 17, 19, 20]-=-. However, in some real-world optimisation problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu search, either when a single o... |

16 |
Nafpliotis N. Multiobjective optimisation using the niched Pareto genetic algorithm
- Horn
- 1994
(Show Context)
Citation Context ...ent solution dominates it. Or, it could only accept the mutant if it dominates the current. We have tried both of these, however, and found the results to be very poor. Echoing Horn et al.'s findings =-=[11, 10]-=-, we find that the use of a nontrivially sized comparison set is crucial to reasonable results. We must note that the idea of maintaining a list of non-dominated solutions is not new. Parks et al. [17... |

14 |
A Comparison of Heuristics for Telecommunications Traffic Routing
- Mann, Smith
- 1996
(Show Context)
Citation Context ...give a concluding discussion in Section 7. 2 The PAES Algorithm Motivations PAES was initially developed as a multiobjective local search method for finding solutions to the Off-line Routing problem (=-=Mann and Smith, 1996-=-; Knowles and Corne, 1999), which is an important problem in the area of telecommunications routing optimization. Previous work on this problem used single-objective (penalty-function) methods, and it... |

10 |
Tabu search for multiobjective optimization
- Hansen
- 1997
(Show Context)
Citation Context ...earch strategies would be promising to investigate and compare with population-based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al., 1996; =-=Hansen, 1996-=-, 1997; Serafini, 1994; Ulungu et al., 1995), and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998, 1998a). However, it is currently quit... |

9 |
Multiple objective optimisation with vector evaluated genetic algorithms
- Schaffer
- 1985
(Show Context)
Citation Context ...S performs consistently well on a range of multiobjective optimisation tasks. 1 Introduction Multiobjective optimisation using genetic algorithms has been investigated by many authors in recent years =-=[2, 6, 7, 10, 11, 17, 19, 20]-=-. However, in some real-world optimisation problems the performance of the genetic algorithm is overshadowed by local search methods such as simulated annealing and tabu search, either when a single o... |

6 |
Heuristics for multi-objective combinatorial optimization by simulated annealing. Multiple Criteria Decision Making: Theory and Applications
- Ulungu, Teghem, et al.
- 1995
(Show Context)
Citation Context ...to investigate and compare with population-based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al., 1996; Hansen, 1996, 1997; Serafini, 1994; =-=Ulungu et al., 1995-=-), and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998, 1998a). However, it is currently quite unclear how c fl1999 by the Massachusetts... |

5 |
Introduction to Probability and Statistics - 9th edition
- Mendenhall, Beaver
(Show Context)
Citation Context ...then be used to summarize the distributions or to compare the distributions produced by two competing optimizers. We compare pairs of optimizers using the Mann-Whitney rank sum test (for example, see =-=Mendenhall and Beaver, 1994-=-) as our statistical comparator. 1.1 Overview of the Paper The remainder of the paper is organized as follows. In Section 2, we introduce PAES and its components. Pseudocode describing both the basic ... |

4 | Generating a Diversity of Good Solutions to a Practical Combinatorial Problem using Vectorized Simulated Annealing. Submitted to Control and Cybernetics - Hansen - 1997 |

4 | QoS based GA Parameter Selection for Autonomously Managed Distributed Information Systems - Oates, Corne - 1998 |

3 |
Introduction to Probability and Statistics - 9th ed
- Mendenhall, Beaver
- 1994
(Show Context)
Citation Context ...then be used to summarize the distributions or to compare the distributions produced by two competing optimizers. We compare pairs of optimizers using the Mann-Whitney rank sum test (for example, see =-=Mendenhall and Beaver, 1994-=-) as our statistical comparator. Overview of the Paper The remainder of the paper is organized as follows. In Section 2 we introduce PAES and its components. Pseudocode describing both the basic (1 + ... |

3 |
Tabu search in multiobjective optimisation
- Hansen
- 1997
(Show Context)
Citation Context ... been combined by the use of a weighted sum, e.g. see [14]. Unfortunately, little research has examined how stochastic local search methods can be applied to truly multiobjective problems (though see =-=[8, 9]-=-) in order to find diverse solutions in the Pareto optimal set. In this paper we introduce a novel evolutionary algorithm, called the Pareto Archived Evolution Strategy (PAES) which, in its baseline f... |

2 | Evolutionary Computation Volume 8, Number 2 171 - Knowles, Horn, et al. - 1994 |

1 | Evolutionary Computation Volume 7, Number 1 23 - KNOWLES, Knowles, et al. - 1999 |

1 |
Thomas Back, Evolutionary Algoirthms in Theory and Practice
- Back
- 1996
(Show Context)
Citation Context ...d by Rechenberg [18], following the seminal work of Peter Bienert, Ingo Rechenberg, and Hans-Paul Schwefel at the Technical University of Berlin in 1964. A modern and comprehensive introduction is in =-=[1]-=-. We find the ( + ) model of ESs to naturally fit the general structure of the PAES algorithm and the variants we use in this paper, but we should note that we use neither the adaptive stepsizes for m... |

1 | Performance Adaption Algorithm (draft 4x4c - Edwards - 1997 |

1 | Evolutionary approaches to off-line routing in backbone communications networks - Knowles, Corne, et al. - 1998 |