A Visualizable Test Problem Generator for Many-Objective Optimization

Fieldsend, Jonathan E.; Chugh, Tinkle; Allmendinger, Richard; Miettinen, Kaisa

doi:10.1109/tevc.2021.3084119

Cited by 14 publications

(5 citation statements)

References 49 publications

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“…In addition to DTLZ, we tested the proposed approach on a single instance of DBMOPP [10,11]. The results of hypervolume with five objectives and 10 decision variables are shown in Figure 10.…”

Section: Results On Dbmoppmentioning

confidence: 99%

Mono-surrogate vs multi-surrogate in multi-objective bayesian optimisation

Chugh

2022

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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Bayesian optimisation (BO) has been widely used to solve problems with expensive function evaluations. In multi-objective optimisation problems, BO aims to find a set of approximated Pareto optimal solutions. There are typically two ways to build surrogates in multiobjective BO: One surrogate by aggregating objective functions (by using a scalarising function, also called mono-surrogate approach) and multiple surrogates (for each objective function, also called multi-surrogate approach). In both approaches, an acquisition function (AF) is used to guide the search process. Mono-surrogate has the advantage that only one model is used, however, the approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of the AF can be used. In this work, we overcome these limitations by building a surrogate model for each objective function and show that the scalarising function distribution is not Gaussian. We approximate the distribution using Generalised extreme value distribution. The results and comparison with existing approaches on standard benchmark and real-world optimisation problems show the potential of the multi-surrogate approach.

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Section: Results On Dbmoppmentioning

confidence: 99%

Mono-surrogate vs multi-surrogate in multi-objective bayesian optimisation

Chugh

2022

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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“…These include visual distance minimization problems also known as P* problems [120,121], multiline distance minimization problems [122], and visualizable Euclidean distance-based test problems, i.e. DBMOPP [123]. Each of them provides a visualizable variable space and Pareto-optimal solutions, but the objective space is still high-dimensional.…”

Section: Approaches Representative Visualization Methodsmentioning

confidence: 99%

Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

Satō

Ishibuchi

2023

IEEJ Transactions Elec Engng

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Population‐based evolutionary algorithms are suitable for solving multi‐objective optimization problems involving multiple conflicting objectives. This is because a set of well‐distributed solutions can be obtained by a single run, which approximate the optimal tradeoff among the objectives. Over the past three decades, evolutionary multi‐objective optimization has been intensively studied and used in various real‐world applications. However, evolutionary multi‐objective optimization faces various difficulties as the number of objectives increases. The simultaneous optimization of more than three objectives, which is called many‐objective optimization, has attracted considerable research attention. This paper explains various difficulties in evolutionary many‐objective optimization, reviews representative approaches, and discusses their effects and limitations. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

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“…For visualization, the Pareto front or its approximations can be visualized by means of scatter plots for 2 or 3 objectives, or by means of dimensionality reduction for 3+ objectives [32]. Meanwhile, for representing the whole landscape, there exist some works on multi-objective continuous optimization, such as cost landscapes [10], gradient field heatmaps [14], local dominance landscapes [9], or the plot of landscapes with optimal trade-offs [27]. In the combinatorial case, the well-established local optima networks [23,24] have been extended to multi-objective optimization with the Pareto local optimal solutions networks (PLOS-net) [20] and the Pareto local optima networks (PLON) [8].…”

Section: Introductionmentioning

confidence: 99%

“…In the combinatorial case, the well-established local optima networks [23,24] have been extended to multi-objective optimization with the Pareto local optimal solutions networks (PLOS-net) [20] and the Pareto local optima networks (PLON) [8]. These multi-objective extensions have proven to be useful tools to better understand multi-objective landscapes [9,28].…”

Section: Introductionmentioning

confidence: 99%

Pareto Local Optimal Solutions Networks with Compression, Enhanced Visualization and Expressiveness

Liefooghe,

Ochoa,

Verel

et al. 2023

Proceedings of the Genetic and Evolutionary Computation Conference

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The structure of local optima in multi-objective combinatorial optimization and their impact on algorithm performance are not yet properly understood. In this paper, we are interested in the representation of multi-objective landscapes and their multi-modality. More specifically, we revise and extend the network of Pareto local optimal solutions (PLOS-net), inspired by the well-established local optima network from single-objective optimization. We first define a compressed PLOS-net which allows us to enhance its perception while preserving the important notion of connectedness between local optima. We then study an alternative visualization of the (compressed) PLOS-net that focuses on good-quality solutions, improves the distinction between connected components in the network, and generalizes well to landscapes with more than 2 objectives. We finally define a number of network metrics that characterize the PLOS-net, some of them being strongly correlated with search performance. We visualize and experiment with small-size multiobjective nk-landscapes, and we disclose the effect of PLOS-net metrics against well-established multi-objective local search and evolutionary algorithms. CCS CONCEPTS• Theory of computation → Optimization with randomized search heuristics; Design and analysis of algorithms; • Applied computing → Multi-criterion optimization and decision-making.

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A Visualizable Test Problem Generator for Many-Objective Optimization

Abstract: This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details.

Cited by 14 publications

References 49 publications

Mono-surrogate vs multi-surrogate in multi-objective bayesian optimisation

Mono-surrogate vs multi-surrogate in multi-objective bayesian optimisation

Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

Pareto Local Optimal Solutions Networks with Compression, Enhanced Visualization and Expressiveness

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