Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques

Schütze, Oliver; Mostaghim, Sanaz; Dellnitz, Michael; Teich, Jürgen

doi:10.1007/3-540-36970-8_9

Cited by 50 publications

(41 citation statements)

References 8 publications

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“…One possible solution for having a controllable exploration is to use Hybrid MOEA [13]. Indeed, this method is based on iterative division of the search space into subspaces (boxes) in the parameter space.…”

Section: A Covering By Hybrid Moeamentioning

confidence: 99%

“…To avoid gaps in the Pareto-optimal front, a strategy called Static Recovering is proposed in [13]. The idea is to run the Hybrid MOEA and obtain the possible optimal solutions.…”

Section: Subdivisionmentioning

confidence: 99%

“…Indeed, by covering we find a finite set of solutions which are very close to each other. Covering the Pareto-optimal front is studied by Hybrid MOEA [13]. In [13], the non-dominated solutions are found by MOEA and then a recovering method is applied to cover the Pareto-optimal front.…”

Section: Introductionmentioning

confidence: 99%

“…Covering the Pareto-optimal front is studied by Hybrid MOEA [13]. 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].…”

Section: Introductionmentioning

confidence: 99%

“…The particles in the population of the covering MOPSO are divided into subswarms after one generation by using the Sigma method in [10] and these subswarms take the responsibility to recover the Pareto-optimal front. This method is tested on different test functions and compared with the Hybrid MOEA covering technique in [13] for a real world application in antenna design. This paper has the following structure.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Covering By Hybrid Moeamentioning

confidence: 99%

“…To avoid gaps in the Pareto-optimal front, a strategy called Static Recovering is proposed in [13]. The idea is to run the Hybrid MOEA and obtain the possible optimal solutions.…”

Section: Subdivisionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping method

Qin

Xin

Sun

2019

Asian Journal of Control

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This paper presents a study of multi‐objective optimal design of nonlinear control systems and has validated the control design with a twin rotor model helicopter. The gains of the porportional integral differential (PID) control are designed in the framework of multi‐objective opitmization. Eight design paramaters are optimized to minimize six time‐domain objective objective functions. The study of multi‐objective optimal design of feedback control with such a number of design paramaters and objective functions is rare in the literature. The Pareto optimal solutions are obtained by the proposed parallel simple cell mapping method consisting of a robust Pareto set recovery algorithm and a rolling subdivision technique. The proposed parallel simple cell mapping algorithm has two features: the number of cells in the invariant set grows linearly with the rolling subdivisions, and the Pareto set is insensitive to the inital set of seed cells. The current control design is compared with the classical LQE control for linear systems, and is also experimentally validated. The current design provides improved control performance as compares with the LQR control, and is applicable to complex nonlinear systems.

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New analysis of the optimization of electromagnetic shielding properties using conducting polymers and a multi‐objective approach

Schütze

Jourdan

Legrand

et al. 2008

Polymers for Advanced Techs

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Recently, an approach was proposed to optimize multi-layer shields of polyaniline-polyurethane (PAni/PU) conducting composites in the microwave band. Though by this method shields for different applications can be obtained which are light-weight and offer a low percolation threshold, the full potential of the design process could not be tapped since the underlying optimization problem includes only one objective. In this work we go one step beyond and re-formulate the design problem as a multi-objective optimization problem (MOP). To be more precise, we involve simultaneously the shielding efficiency as well as the weight and the cost of the material-i.e. all the requirements for modern shielding materials-within the optimization process. After having stated the model we present two possible ways to approximate the solution set-the so-called Pareto setand address the related and important decision-making problem. All steps are demonstrated on a particular three-layered composite in order to show the applicability of the novel approach.

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Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques

Cited by 50 publications

References 8 publications

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

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

Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping method

New analysis of the optimization of electromagnetic shielding properties using conducting polymers and a multi‐objective approach

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