The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume

Hernández, Víctor Adrián Sosa; Schütze, Oliver; Rudolph, Günter; Trautmann, Heike

doi:10.1007/978-3-319-01128-8_13

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…1. To seek the corresponding searching direction, v, in the parameter space for d k i , the following equation is solved [6]:…”

Section: B Exploiting Searching Phasementioning

confidence: 99%

“…On the other hand, it is well-known that the vector or multiobjective EAs normally require a large amount of function evaluations, due to their slow convergence rate, to generate a suitable finite size approximation of the set of interests [6]. This deficiency often becomes the main obstacle in applying existing vector EAs to solve inverse problems, because highfidelity models such as finite-element analysis are generally involved in the solution procedures.…”

Section: Introductionmentioning

confidence: 98%

“…This deficiency often becomes the main obstacle in applying existing vector EAs to solve inverse problems, because highfidelity models such as finite-element analysis are generally involved in the solution procedures. To overcome the Manuscript [6]. It should be noted that although a single run of a polynomial deterministic optimization method is always faster than that of EA, it is often necessary for deterministic optimizers to perform multiple runs of such algorithms to obtain a reasonable estimation of the Pareto set.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integration of Directed Searches in Particle Swarm Optimization for Multi-Objective Optimization

Yang

et al. 2015

IEEE Trans. Magn.

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While a wealth of endeavors in optimization studies are devoted to the realization of the two ultimate goals, which are: 1) to minimize the distance between the found solutions from the true Pareto front and 2) to maximize the diversity among the found Pareto solutions in both objective and parameter spaces; only lukewarm efforts are given to the development and utilization of approximating techniques of non-dominated sets in continuous multi-objective optimization studies. In this regard, a directed search method embedded in a vector particle swarm optimization (PSO) algorithm, as an exploiting search phase to improve the efficiency of the algorithm, is proposed to steer the searches toward the desired direction. The proposed strategy excludes gradient computations of the Jacobian in determining the corresponding desired direction in the parameter space. The components of the PSO algorithm are also redesigned accordingly. The performances with the application of the proposed algorithm on two case studies are reported and compared with those of three well developed vector evolutionary algorithms.Index Terms-Direct search (DS), multi-objective optimization, Pareto optimal solution, particle swarm optimization (PSO).

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“…1. To seek the corresponding searching direction, v, in the parameter space for d k i , the following equation is solved [6]:…”

Section: B Exploiting Searching Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Integration of Directed Searches in Particle Swarm Optimization for Multi-Objective Optimization

Yang

et al. 2015

IEEE Trans. Magn.

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show abstract

“…To seek the corresponding searching direction, v, in the parameter space for k i d , the following equation is solved[8] …”

mentioning

confidence: 99%

A Vector Tabu Search Algorithm With Enhanced Searching Ability for Pareto Solutions and Its Application to Multiobjective Optimizations

Yang

2016

IEEE Trans. Magn.

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A vector tabu search algorithm encapsulating a new updating mechanism for current states and a directed search phase is proposed to enhance its searching ability for Pareto optimal solutions. The new updating mechanism considers quantitatively both the number of improved objectives and the amount of improvements in a specified objective, of multiobjective design problems. The directed search phase uses some desired directions, a priori knowledge about the objective space, as the moving direction to efficiently find improved solutions without any gradient computation procedure. The numerical results on both a high and a low frequency inverse problem are reported to demonstrate the pros and cons of the proposed algorithm. It is observed that the proposed vector tabu search method outperforms its ancestors in both the convergence performance and the solution quality.Index Terms-Design optimization, inverse problem, multiobjective, tabu search algorithm.

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A Memetic Variant of R-NSGA-II for Reference Point Problems

Mejía

Schütze

Deb

2014

Advances in Intelligent Systems and Computing

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The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume

Cited by 5 publications

References 14 publications

Integration of Directed Searches in Particle Swarm Optimization for Multi-Objective Optimization

Integration of Directed Searches in Particle Swarm Optimization for Multi-Objective Optimization

A Vector Tabu Search Algorithm With Enhanced Searching Ability for Pareto Solutions and Its Application to Multiobjective Optimizations

A Memetic Variant of R-NSGA-II for Reference Point Problems

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