Is NSGA-II Ready for Large-Scale Multi-Objective Optimization?

Nebro, Antonio J.; Galeano-Brajones, Jesús; Luna, Francisco; Coello, Carlos A. Coello

doi:10.3390/mca27060103

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…The multi-objective, binary nature of the problem determines the choice of the algorithm. The NSGA-II has shown to be the most popular metaheuristic for solving multi-objective optimization problems, even for a large number of variables [26].…”

Section: B Optimization Framework and Methodologymentioning

confidence: 99%

Ultralow-Loss Reconfigurable Phase-Shifting Metasurface in V Band: A Multiobjective Optimization Approach

Zapata Cano,

Vassos,

Zaharis

et al. 2024

IEEE Trans. Antennas Propagat.

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Future generations of satellite and mobile communications at mm-wave frequencies require the use of low-loss and wideband phase-shifting components. Pixelated metasurfaces provide large design versatility and constitute an attractive solution for wave manipulation, such as shifting the phase of an incident wave. However, their design often implies the simultaneous tuning of a large number of geometrical parameters. This article employs an enhanced multi-objective optimization algorithm to design a dynamically reconfigurable metasurface providing ultra-low losses and linear phase response. The presented methodology can be easily employed for different objective functions or technologies, constituting a versatile design strategy for electromechanically reconfigurable devices based on pixelated metasurfaces. A prototype is fabricated based on the optimization outcome, achieving a phase shifter capable of providing a continuous phase shift up to 180 • between 50 and 65 GHz. A piezo-electric actuator is used to dynamically adjust the phase shift with respect to the position of a metallic ground plane placed in front of the metasurface. A linear evolution of the phase w.r.t. the ground plane displacement is obtained while maintaining the losses around 1 dB for the whole frequency range.

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Section: B Optimization Framework and Methodologymentioning

confidence: 99%

Ultralow-Loss Reconfigurable Phase-Shifting Metasurface in V Band: A Multiobjective Optimization Approach

Zapata Cano,

Vassos,

Zaharis

et al. 2024

IEEE Trans. Antennas Propagat.

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“…The Non-dominated Sorting Genetic Algorithm (NSGA-II), introduced in [47], is an evolutionary algorithm to perform multiobjective optimization which has been proven to be suitable for largescale optimization problems [48,49]. The ultimate goal of NSGA-II is to find a set of optimal solutions for multiple cost functions.…”

Section: Non-dominated Sorting Genetic Algorithmmentioning

confidence: 99%

Multiobjective variational quantum optimization for constrained problems: an application to Cash Management

Díez-Valle¹,

Luis-Hita²,

Hernández-Santana³

et al. 2023

Preprint

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“…The NSGA-II, introduced in [51], is an evolutionary algorithm to perform multiobjective optimization which has been proven to be suitable for large-scale optimization problems [52,53]. The ultimate goal of NSGA-II is to find a set of optimal solutions for multiple cost functions.…”

Section: Non-dominated Sorting Genetic Algorithm (Nsga-ii)mentioning

confidence: 99%

Multiobjective variational quantum optimization for constrained problems: an application to cash handling

Díez-Valle

Luis-Hita

Hernández-Santana

et al. 2023

Quantum Sci. Technol.

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Combinatorial optimization problems are ubiquitous in industry. In addition to finding a solution with minimum cost, problems of high relevance involve a number of constraints that the solution must satisfy. Variational quantum algorithms have emerged as promising candidates for solving these problems in the noisy intermediate-scale quantum stage. However, the constraints are often complex enough to make their efficient mapping to quantum hardware difficult or even infeasible. An alternative standard approach is to transform the optimization problem to include these constraints as penalty terms, but this method involves additional hyperparameters and does not ensure that the constraints are satisfied due to the existence of local minima. In this paper, we introduce a new method for solving combinatorial optimization problems with challenging constraints using variational quantum algorithms. We propose the Multi-Objective Variational Constrained Optimizer (MOVCO) to classically update the variational parameters by a multiobjective optimization performed by a genetic algorithm. This optimization allows the algorithm to progressively sample only states within the in-constraints space, while optimizing the energy of these states. We test our proposal on a real-world problem with great relevance in finance: the Cash Handling problem. We introduce a novel mathematical formulation for this problem, and compare the performance of MOVCO versus a penalty based optimization. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima that do not satisfy any of the mandatory constraints.

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Is NSGA-II Ready for Large-Scale Multi-Objective Optimization?

Cited by 10 publications

References 26 publications

Ultralow-Loss Reconfigurable Phase-Shifting Metasurface in V Band: A Multiobjective Optimization Approach

Ultralow-Loss Reconfigurable Phase-Shifting Metasurface in V Band: A Multiobjective Optimization Approach

Multiobjective variational quantum optimization for constrained problems: an application to Cash Management

Multiobjective variational quantum optimization for constrained problems: an application to cash handling

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