On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem
In this paper, we study the influence of the number of objectives of a continuous multiobjective optimization problem on its hardness for evolution strategies which is of particular interest for many-objective optimization problems. To be more precise, we measure the hardness in terms of the evoluti...
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| Vydáno v: | IEEE transactions on evolutionary computation Ročník 15; číslo 4; s. 444 - 455 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
IEEE
01.08.2011
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-778X, 1941-0026 |
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| Abstract | In this paper, we study the influence of the number of objectives of a continuous multiobjective optimization problem on its hardness for evolution strategies which is of particular interest for many-objective optimization problems. To be more precise, we measure the hardness in terms of the evolution (or convergence) of the population toward the set of interest, the Pareto set. Previous related studies consider mainly the number of nondominated individuals within a population which greatly improved the understanding of the problem and has led to possible remedies. However, in certain cases this ansatz is not sophisticated enough to understand all phenomena, and can even be misleading. In this paper, we suggest alternatively to consider the probability to improve the situation of the population which can, to a certain extent, be measured by the sizes of the descent cones. As an example, we make some qualitative considerations on a general class of uni-modal test problems and conjecture that these problems get harder by adding an objective, but that this difference is practically not significant, and we support this by some empirical studies. Further, we address the scalability in the number of objectives observed in the literature. That is, we try to extract the challenges for the treatment of many-objective problems for evolution strategies based on our observations and use them to explain recent advances in this field. |
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| AbstractList | In this paper, we study the influence of the number of objectives of a continuous multiobjective optimization problem on its hardness for evolution strategies which is of particular interest for many-objective optimization problems. To be more precise, we measure the hardness in terms of the evolution (or convergence) of the population toward the set of interest, the Pareto set. Previous related studies consider mainly the number of nondominated individuals within a population which greatly improved the understanding of the problem and has led to possible remedies. However, in certain cases this ansatz is not sophisticated enough to understand all phenomena, and can even be misleading. In this paper, we suggest alternatively to consider the probability to improve the situation of the population which can, to a certain extent, be measured by the sizes of the descent cones. As an example, we make some qualitative considerations on a general class of uni-modal test problems and conjecture that these problems get harder by adding an objective, but that this difference is practically not significant, and we support this by some empirical studies. Further, we address the scalability in the number of objectives observed in the literature. That is, we try to extract the challenges for the treatment of many-objective problems for evolution strategies based on our observations and use them to explain recent advances in this field. |
| Author | Schutze, O. Lara, A. Coello, C. A. C. |
| Author_xml | – sequence: 1 givenname: O. surname: Schutze fullname: Schutze, O. email: schuetze@cs.cinvestav.mx organization: Dept. of Comput. Sci., CINVESTAV IPN, Mexico City, Mexico – sequence: 2 givenname: A. surname: Lara fullname: Lara, A. email: alara@computacion.cs.cinvestav.mx organization: Dept. of Comput. Sci., CINVESTAV IPN, Mexico City, Mexico – sequence: 3 givenname: C. A. C. surname: Coello fullname: Coello, C. A. C. email: ccoello@cs.cinvestav.mx organization: Dept. of Comput. Sci., CINVESTAV IPN, Mexico City, Mexico |
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| Keywords | Cone Modal analysis Probabilistic approach Scalability Pareto optimum Evolutionary algorithm Empirical method Multiobjective programming many-objective optimization Vibration test Hardness Convex programming Optimization Dynamic test multiobjective optimization evolutionary computation Non differentiable programming Descent method Problem solving Algorithm design Mathematical programming |
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| SubjectTerms | Algorithm design Algorithmics. Computability. Computer arithmetics Applied sciences Approximation methods Computational modeling Computer science; control theory; systems Computer systems and distributed systems. User interface Convergence Decision theory. Utility theory Descent Evolution Evolutionary computation Exact sciences and technology Hardness many-objective optimization Measurement multiobjective optimization Operational research and scientific management Operational research. Management science Optimization Pareto optimality Remedies Scalability Software Strategy Studies Theoretical computing |
| Title | On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem |
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