Covering Pareto Sets by Multilevel Subdivision Techniques

Dellnitz, Michael; Schütze, Oliver; Hestermeyer, Thorsten

doi:10.1007/s10957-004-6468-7

Cited by 154 publications

(139 citation statements)

References 17 publications

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“…There are Methods that approximate the whole pareto set, e.g. Dellnitz et al (2005), as well as methods which compute single pareto points by summarizing the whole objective vector into a single scalar objective function, e.g. Hillermeier (2001).…”

Section: Hierarchical Optimizationmentioning

confidence: 99%

Hybrid Planning for Self-Optimization in Railbound Mechatronic Systems

Adelt¹,

Esau²,

Hölscher³

et al. 2011

Intelligent Mechatronics

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Section: Hierarchical Optimizationmentioning

confidence: 99%

Hybrid Planning for Self-Optimization in Railbound Mechatronic Systems

Adelt¹,

Esau²,

Hölscher³

et al. 2011

Intelligent Mechatronics

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“…In general, there are a number of Pareto-optimal and locally Pareto-optimal solutions. It has been shown that local Pareto-optimal solutions locally form a (M − 1)-dimensional manifold [7,3], assuming N > M. This implies that they form curves in the variable space and in the objective space when M = 2. These curves are called local Pareto-optimal solution curves.…”

Section: Multi-objective Function Optimization (Moo)mentioning

confidence: 99%

“…The solutions to which no other feasible solutions are superior in all objective functions are called Pareto-optimal, and those to which no other solutions in the feasible ε-vicinity are superior are called locally Pareto-optimal. The dimension N of the variable space is generally bigger than the dimension M of the objective space, and it has been shown that local Pareto-optimal solutions locally form (M − 1)-dimensional manifold [7,3]. Considering the abundance of bi-objective problems, M = 2 is assumed in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Uniform sampling of local pareto-optimal solution curves by pareto path following and its applications in multi-objective GA

Harada

Sakuma

Kobayashi

et al. 2007

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation

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Although multi-objective GA (MOGA) is an efficient multiobjective optimization (MOO) method, it has some limitations that need to be tackled, which include unguaranteed uniformity of solutions and uncertain finding of periphery of Pareto-optimal solutions. It has been shown that, on bi-objective problems, which are the subject of this paper, local Pareto-optimal solutions form curves. In this case, some of the limitations of MOGA can be resolved by sampling the curves uniformly in the variable space and in the objective space. This paper proposes Pareto Path Following (PPF) which does the sampling by extending the framework of Numerical Path Following, verifies that PPF exhibits the desired behaviors, and addresses the extension of PPF for problems with more than two objective functions.Application of PPF is not limited to refinement of solutions obtained with MOGA. PPF makes it natural to have a local Pareto-optimal solution curve as the unit of search, which leads to curve-based MOGA. PPF also enables examination of which Pareto-optimal solution curves are found by MOO methods, and performance metrics based on it can be defined. This paper proposes these applications of PPF in MOGA and compares standard MOGA and curve-based MOGA using the metrics to reveal their characteristics.

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“…In [13], the non-dominated solutions are found by MOEA and then a recovering method is applied to cover the Pareto-optimal front. In this case, the recovering method is a combination of MOEA and a subdivision method [3]. Also, the -MOEA method is theoretically able to cover the approximated Pareto-optimal front in the case of using small values of [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Covering Pareto-optimal fronts by subswarms in multi-objective particle swarm optimization

Mostaghim

Teich

Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753)

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Abstract-Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimization methods. Because in general it is not possible to determine this set, a restricted amount of solutions are typically delivered in the output to decision makers. In this paper, we propose a new method using multi-objective particle swarm optimization to cover the Paretooptimal front. The method works in two phases. In phase 1 the goal is to obtain a good approximation of the Pareto-front. In a second run subswarms are generated to cover the Paretofront. The method is evaluated using different test functions and compared with an existing covering method using a real world example in antenna design.

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Covering Pareto Sets by Multilevel Subdivision Techniques

Cited by 154 publications

References 17 publications

Hybrid Planning for Self-Optimization in Railbound Mechatronic Systems

Hybrid Planning for Self-Optimization in Railbound Mechatronic Systems

Uniform sampling of local pareto-optimal solution curves by pareto path following and its applications in multi-objective GA

Covering Pareto-optimal fronts by subswarms in multi-objective particle swarm optimization

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