## Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study (1998)

Citations: | 134 - 9 self |

### BibTeX

@INPROCEEDINGS{Zitzler98multiobjectiveoptimization,

author = {Eckart Zitzler and Lothar Thiele},

title = {Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study},

booktitle = {},

year = {1998},

pages = {292--301},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Since 1985 various evolutionary approaches to multiobjective optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of different methods available to date are mostly qualitative and restricted to two approaches. In this paper an extensive, quantitative comparison is presented, applying four multiobjective evolutionary algorithms to an extended 0/1 knapsack problem. 1 Introduction Many real-world problems involve simultaneous optimization of several incommensurable and often competing objectives. Usually, there is no single optimal solution, but rather a set of alternative solutions. These solutions are optimal in the wider sense that no other solutions in the search space are superior to them when all objectives are considered. They are known as Pareto-optimal solutions. Mathematically, the concept of Pareto-optimality can be defined as follows: Let us consider, without loss of generality, a multio...

### Citations

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Citation Context ...nce. Pareto-based EAs compare solutions according to thesrelation in order to determine the reproduction probability of each individual; this kind of fitness assignment was first proposed by Goldberg =-=[3]-=-. Since preservation of diversity is crucial in the field of multimodal optimization, many multiobjective EAs incorporate niching techniques, the mostly implemented of which is fitness sharing [2]. Fi... |

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Citation Context ...e task is to find a subset of all items which maximizes the total of the profits in the subset, yet, all selected items fit into the knapsack, i.e. the total weight does not exceed the given capacity =-=[7]-=-. This single-objective problem can be extended straight forward for the multiobjective case by allowing an arbitrary number of knapsacks. Formally, the multiobjective 0/1 knapsack problem considered ... |

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Citation Context ...erg [3]. Since preservation of diversity is crucial in the field of multimodal optimization, many multiobjective EAs incorporate niching techniques, the mostly implemented of which is fitness sharing =-=[2]-=-. Fitness sharing bases on the idea that individuals in a particular niche have to share the resources available, similar to nature. Thus, the fitness value of a certain individual is the more degrade... |

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Citation Context ...the Vector Evaluated Genetic Algorithm (VEGA) [10], an EA incorporating weighted-sum aggregation [4], the Niched Pareto Genetic Algorithm [5][6], and the Nondominated Sorting Genetic Algorithm (NSGA) =-=[11]-=-; all but VEGA use fitness sharing to maintain a population distributed along the Pareto-optimal front. Pure aggregation methods are disregarded here because they are not designed for finding a family... |

361 | An Overview of Evolutionary Algorithms in Multi-Objective Optimization. Evolutionary Computation
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Citation Context ...y exploiting similarities of solutions by crossover. Some researcher suggest that multiobjective search and optimization might be a problem area where EAs do better than other blind search strategies =-=[1]-=-[12]. Since the mid-eighties various multiobjective EAs have been developed, capable of searching for multiple Pareto-optimal solutions concurrently in a single run. But up to now, no extensive, quant... |

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Citation Context ...ng can be performed both in genotypic space and phenotypic space. In this study we consider two population-based non-Pareto EAs and two Pareto-based EAs: the Vector Evaluated Genetic Algorithm (VEGA) =-=[10]-=-, an EA incorporating weighted-sum aggregation [4], the Niched Pareto Genetic Algorithm [5][6], and the Nondominated Sorting Genetic Algorithm (NSGA) [11]; all but VEGA use fitness sharing to maintain... |

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Citation Context ... population-based non-Pareto EAs and two Pareto-based EAs: the Vector Evaluated Genetic Algorithm (VEGA) [10], an EA incorporating weighted-sum aggregation [4], the Niched Pareto Genetic Algorithm [5]=-=[6]-=-, and the Nondominated Sorting Genetic Algorithm (NSGA) [11]; all but VEGA use fitness sharing to maintain a population distributed along the Pareto-optimal front. Pure aggregation methods are disrega... |

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(Show Context)
Citation Context ...two population-based non-Pareto EAs and two Pareto-based EAs: the Vector Evaluated Genetic Algorithm (VEGA) [10], an EA incorporating weighted-sum aggregation [4], the Niched Pareto Genetic Algorithm =-=[5]-=-[6], and the Nondominated Sorting Genetic Algorithm (NSGA) [11]; all but VEGA use fitness sharing to maintain a population distributed along the Pareto-optimal front. Pure aggregation methods are disr... |

82 |
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Citation Context ...notypic space. In this study we consider two population-based non-Pareto EAs and two Pareto-based EAs: the Vector Evaluated Genetic Algorithm (VEGA) [10], an EA incorporating weighted-sum aggregation =-=[4]-=-, the Niched Pareto Genetic Algorithm [5][6], and the Nondominated Sorting Genetic Algorithm (NSGA) [11]; all but VEGA use fitness sharing to maintain a population distributed along the Pareto-optimal... |

42 |
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Citation Context ..., binary tournament selection. 5 . Unfortunately, a conventional combination of fitness sharing and tournament selection may lead to chaotic behavior of the EA, as reported by Oei, Goldberg and Chang =-=[9]-=-. Therefore, NSGA as well as Hajela's and Lin's approach were implemented using a slightly modified version of sharing, called continuously updated sharing, which was proposed by the same researchers.... |

18 | A nongenerational genetic algorithm for multiobjective optimization - Valenzuela-RendÃ³n, Uresti-Charre - 1997 |