A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization

Thiele, Lothar; Miettinen, Kaisa; Korhonen, Pekka; Molina, Julián

doi:10.1162/evco.2009.17.3.411

Cited by 332 publications

(204 citation statements)

References 23 publications

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“…We will not discuss further properties here and instead refer to [18], [20], [35] for detailed reviews of binary indicators. Preference information of a decision maker can be considered in the above binary epsilon indicator by extending the concepts described in [28] for pairs of solutions to sets. In order to prefer solutions that are close to a set of reference points r ∈ R in the objective space, we use the concept of an achievement function with respect to a reference point r s(x, r) = max where the specificity δ > 0 determines the minimal value of the normalized function and P denotes the current set of solutions.…”

Section: Proof: Consider a B ∈ ψ With (A B) ∧ (B A) If I(a B) ≤ I(mentioning

confidence: 99%

On Set-Based Multiobjective Optimization

Zitzler

Thiele

Bader

2010

IEEE Trans. Evol. Computat.

156

104

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Abstract-Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: (i) how to formalize what type of Pareto set approximation is sought, (ii) how to use this information within an algorithm to efficiently search for a good Pareto set approximation, and (iii) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general, preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.

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Section: Proof: Consider a B ∈ ψ With (A B) ∧ (B A) If I(a B) ≤ I(mentioning

confidence: 99%

On Set-Based Multiobjective Optimization

Zitzler

Thiele

Bader

2010

IEEE Trans. Evol. Computat.

156

104

View full text Add to dashboard Cite

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“…Hwang et al, 1979) have been developed in order to interactively explore the Pareto space without having to fully compute it in advance, thus mitigating the associate computational burden (e.g. Thiele et al, 2009). The complexity and high number of questions to be posed to the stakeholders remain an unsolved problem (Larichev, 1992).…”

Section: Current Statusmentioning

confidence: 99%

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

Maier

Kapelan

Kasprzyk

et al. 2014

Environmental Modelling & Software

530

317

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In all cases accepted manuscripts should:  link to the formal publication via its DOI  bear a CC-BY-NC-ND license -this is easy to do, click here to find out how  if aggregated with other manuscripts, for example in a repository or other site, be shared in alignment with our hosting policy  not be added to or enhanced in any way to appear more like, or to substitute for, the published journal article AbstractThe development and application of evolutionary algorithms (EAs) and other metaheuristics for the optimisation of water resources systems has been an active research field for over two decades. Research to date has emphasized algorithmic improvements and individual applications in specific areas (e.g., model calibration, water distribution systems, groundwater management, river-basin planning and management, etc.). However, there has been limited synthesis between shared problem traits, common EA challenges, and needed advances across major applications. This paper clarifies the current status and future research directions for better solving key water resources problems using EAs. Advances in understanding fitness landscape properties and their effects on algorithm performance are critical. Future EA-based applications to real-world problems require a fundamental shift of focus towards improving problem formulations, understanding general theoretic frameworks for problem decompositions, major advances in EA computational efficiency, and most importantly aiding real decision-making in complex, uncertain application contexts.

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“…The latter algorithm also integrated the DM to control the achievable accuracy of non-dominated solutions. A self-adaptive version of the ε logic is proposed in [62] To overcome the shortcomings of not having preference information in the selection process of the Indicator-Based Evolutionary Algorithm (IBEA) [77], the Preference-Based Evolutionary Algorithm (PBEA) was introduced in [65]. In [3] an approach that integrates the DM's preferences into an estimation of the dominated portion of the objective space (hypervolume) is presented.…”

Section: Progressive Preference Articulation: a Brief Reviewmentioning

confidence: 99%

Progressive preference articulation for decision making in multi-objective optimisation problems

Rostami

Neri

Epitropakis

2017

ICA

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Abstract.This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articulation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algorithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA).WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation.Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the proposed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest.

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A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization

Cited by 332 publications

References 23 publications

On Set-Based Multiobjective Optimization

On Set-Based Multiobjective Optimization

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

Progressive preference articulation for decision making in multi-objective optimisation problems

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