An Evolutionary Approach for Assessing the Degree of Robustness of Solutions to Multi-Objective Models

Barrico, Carlos; Antunes, Carlos Henggeler

doi:10.1007/978-3-540-49774-5_25

Cited by 9 publications

(10 citation statements)

References 15 publications

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“…For each solution, the fitness computation uses a "non-dominated sorting" technique as in "NSGA-II", [19], [26], and involves determining several solution fronts. For more details about this technique, see [9]- [11].…”

Section: The Evolutionary Algorithmmentioning

confidence: 99%

“…This mechanism is only applied when the number of solutions candidate for the secondary population (NCPS) is greater than the size of this population (NPS). For more details about this technique, see [9]- [11].…”

Section: The Evolutionary Algorithmmentioning

confidence: 99%

“…The degree of robustness depends on the size of a δ-neighborhood of scenario s and the percentage of the h neighboring points whose objective function values for x are better than f s (x) or belong to the η-neighborhood of f s (x). Those h neighboring points are randomly generated around scenario s (see also [5], [9]- [11]). The degree of robustness of solution x is a value k, such that (see Fig.…”

Section: Perturbations Of the Objective Function Coefficientsmentioning

confidence: 99%

“…In this way, the approach used herein is based on the solution behavior in the neighborhood of the reference scenario. This concept of degree of robustness conveys more information to a DM than a simple robust/not robust classification and enables him/her to wield control on the level of robustness of solutions obtained through the setting of some parameters (see also [9]- [11]). The size of the reference scenario neighborhood can be specified, both regarding the objective function and constraint coefficients as well as the objective function space.…”

Section: Introductionmentioning

confidence: 99%

“…Algorithms must strive for robust solutions, that is solutions that are relatively "immune" to perturbations, in the sense that their feasibility and objective function performances should not degrade significantly for small changes in the values estimated for the model data (coefficients of objective functions, coefficients of constraints, bounds of decision variables). Some studies have been devoted to compute robust solutions both in single-objective, [1]- [4], as well as in multi-objective evolutionary optimization, [5]- [11]. For more details about this topic see [12].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robustness Analysis in Evolutionary Multi-Objective Optimization Applied to VAR Planning in Electrical Distribution Networks

Barrico

Antunes

Pires

2009

Evolutionary Computation in Combinatorial Optimization

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Abstract.In this paper an approach to robustness analysis in evolutionary multi-objective optimization is applied to the problem of locating and sizing capacitors for reactive power compensation (VAR planning) in electric radial distribution networks. The main goal of this evolutionary algorithm is to find a non-dominated front containing the most robust non-dominated solutions also ensuring diversity along the front. A concept of degree of robustness is incorporated into the evolutionary algorithm, which intervenes in the computation of the fitness value assigned to solutions. Two objective functions of technical and economical nature are explicitly considered in the mathematical model: minimization of system losses and minimization of capacitor installation costs. Constraints refer to quality of service, power flow, and technical requirements. It is assumed that some input data are subject to perturbations, both concerning the objective functions and the constraints coefficients.

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Section: The Evolutionary Algorithmmentioning

confidence: 99%

Section: The Evolutionary Algorithmmentioning

confidence: 99%

Section: Perturbations Of the Objective Function Coefficientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robustness Analysis in Evolutionary Multi-Objective Optimization Applied to VAR Planning in Electrical Distribution Networks

Barrico

Antunes

Pires

2009

Evolutionary Computation in Combinatorial Optimization

Self Cite

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Editorial: Special issue on understanding complexity in multiobjective optimization

Greco

Klamroth

Knowles

et al. 2017

J. Multi-Crit. Decis. Anal.

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This special issue of JMCDA was inspired by the work of three Dagstuhl seminars aimed at strengthening the links between the scientific communities of multiple criteria decision making (MCDM) and evolutionary multiobjective optimization. These three Dagstuhl seminars were devoted to the following topics:• Hybrid and robust approaches to multiobjective optimization Mutzel investigate complexity for multiobjective combinatorial optimization problems, taking into consideration output-sensitive complexity of an algorithm for a general enumeration problem, that is, the property that its running time is bounded by a polynomial in the input and the output size. The paper shows that output-sensitive complexity is able to separate efficiently solvable from presumably not efficiently solvable problems, proving also that multiobjective s-t-path problems do not admit an output-sensitive algorithm under weak complexity theoretic assumptions as P ≠ NP. Rodrigo Lankaites Pinheiro, Dario Landa-Silva, and Jason Atkin present a technique that supports understanding the relationships between objectives in a multiobjective optimization problem through a visualization and analysis of the local and global relationships between objectives. The advantages of the proposed technique are shown in experiments on three different combinatorial optimization problems (multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows).view of navigation, that is, the interactive procedure of traversing through a set of points (the navigation set) in the objective space guided by a decision maker, with the ultimate goal of identifying the single most preferred Pareto optimal solution. The authors describe a general framework to capture a wide range of navigation methods taking also into account real-world problems to which these methods have been applied and highlighting directions of future research. consider complex systems composed of strongly interrelated subsystems or subproblems with single or multiple objectives that are usually not sequentially ordered or obviously decomposable. In the literature, these systems are also referred to as "interwoven systems" or "systems of systems." Due to the correlation between the components, the overall system performance does not equal the simple sum of their performances, and inclusion of complex synergy may imply possible inaccuracies in the model and prohibitively expensive computations. The authors review recent developments in this field and present a preliminary mathematical model of an interwoven system introducing some approaches to its multiobjective optimization. start from the consideration that despite the fact that in general multiobjective combinatorial optimization problems are known to be hard problems because very often they are NP-complete and intractable, there are also variants or cases of multiobjective combinatorial optimization problems that are easy. The article focuses on particular cases of...

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Guideline Identification for Optimization Under Uncertainty Through the Optimization of a Boomerang Trajectory

Marchi¹,

Rigoni²,

Russo³

et al. 2015

Lecture Notes in Computer Science

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An Evolutionary Approach for Assessing the Degree of Robustness of Solutions to Multi-Objective Models

Cited by 9 publications

References 15 publications

Robustness Analysis in Evolutionary Multi-Objective Optimization Applied to VAR Planning in Electrical Distribution Networks

Robustness Analysis in Evolutionary Multi-Objective Optimization Applied to VAR Planning in Electrical Distribution Networks

Editorial: Special issue on understanding complexity in multiobjective optimization

Guideline Identification for Optimization Under Uncertainty Through the Optimization of a Boomerang Trajectory

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