Dataset on a Benchmark for Equality Constrained Multi-objective Optimization

Cuate, Oliver; Uribe, Lourdes; Lara, Adriana; Schütze, Oliver

doi:10.1016/j.dib.2020.105130

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…Moreover, we test the standalone HVN method on large-scale, complicated MOPs. We choose the well-known DTLZ problems with one spherical constraint [57,58] with µ = 200 decision points, resulting in a relative large Hessian matrix (for an 11-dimensional decision space and one constraint, the DG(X, λ) object is of size 2400 × 2400). In this case, we use sparse matrix operations for the computation efficiency, exploiting the sparsity of the Hessian.…”

Section: Hvn As Standalone Algorithmmentioning

confidence: 99%

“…In the plot, we observe uniformly distributed final points (in green) in contrast to non-uniform initial ones (in red), showing the standalone HVN works properly as a local method for large-scale problems. In this section, we investigate the empirical performance of the HVN algorithm on more complicated, equality-constrained DTLZ (Eq-DTLZ) problems [57,58] and their inverted counterparts (Eq-IDTLZ). As Newton-like algorithms are local methods, running the standalone algorithm (Alg.…”

Section: Hvn As Standalone Algorithmmentioning

confidence: 99%

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The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Wang¹,

Emmerich²,

Deutz³

et al. 2022

Preprint

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Recently, the Hypervolume Newton method (HVN) has been proposed as fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions that are at least twice continuously differentiable. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton-Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily be applied to solve equality constraints with a high precision problems, and to some extend also inequalities. We finally use HVN as local search engine within a MOEA and show the benefit of this hybrid method on several benchmark problems.

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Section: Hvn As Standalone Algorithmmentioning

confidence: 99%

Section: Hvn As Standalone Algorithmmentioning

confidence: 99%

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Wang¹,

Emmerich²,

Deutz³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Lately, this platform has become a popular tool among scholars for handling MOPs. Many researchers have adopted PlatEMO for solving MOPs in different areas (e.g., [36], [37], [38], [39], [40], [41]).…”

Section: Deb Thiele Laumanns Zitzler Problem (Dtlz)mentioning

confidence: 99%

Shape Optimization of Rockfill Dam With Rubik Cube Reproduction Based Multi-Objective Particle Swarm Algorithm

Mahmoud

Yuan

2021

AEJ

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A rockfill dam's quality and its economic aspects are inextricably interwoven with each other. Approaching the optimal design of a rockfill dam paves the path to achieve the best quality with the fewest expenses. Choosing the Sardasht rockfill dam as a case study, two semi-empirical models are presented for seepage and safety factor. These two models, together with construction costs, were employed as three objective functions for the Sardasht rockfill dam's shape optimization. Optimization was handled using a robust multi-objective particle swarm optimization algorithm (RCR-MOPSO). A new reproducing method inspired by a Rubik's cube shape (RCR) and NSGA-III are building blocks of RCR-MOPSO. Three benchmark problems and two real-world problems were solved using RCR-MOPSO and compared with NSGA-III and MOPSO to ensure the performance of RCR-MOPSO. The solution quality and performance of RCR-MOPSO are significantly better than the original MOPSO and close to NSGA-III. Nevertheless, RCR-MOPSO recorded a 38% shorter runtime than NSGA-III. RCR-MOPSO presented a set of non-dominated solutions as final results for the Sardasht rockfill dam shape optimization. Due to the defined constraints, all solutions dominate the original design. Regarding the final results, compared with Sardasht dam's original design, the construction price was reduced by 31.12% on average, while seepage and safety factor improved by 15.84% and 27.78% on average, respectively.

show abstract

The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems

Wang

Emmerich

Deutz

et al. 2023

MCA

View full text Add to dashboard Cite

Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton–Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems, the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. Similar to the original variant, the first- and second-order derivatives of the involved functions have to be given either analytically or numerically. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily applied to solve equality constraints with high precision and to some extent also inequalities. We finally use HVN as a local search engine within an MOEA and show the benefit of this hybrid method on several benchmark problems.

show abstract

Dataset on a Benchmark for Equality Constrained Multi-objective Optimization

Cited by 3 publications

References 2 publications

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Shape Optimization of Rockfill Dam With Rubik Cube Reproduction Based Multi-Objective Particle Swarm Algorithm

The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems

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