An augmented Lagrangian algorithm for multi-objective optimization

Cocchi, Guido; Lapucci, Matteo

doi:10.1007/s10589-020-00204-z

Cited by 23 publications

(16 citation statements)

References 49 publications

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“…In this paper, we employ the Augmented Lagrangian Method (ALM) for constraint handling, which was first discussed by Hestenes and Powell in 1969 [22]. Rockafellar modified the idea for inequality constraints [23]. ALM is similar to the penalty method.…”

Section: Prey Exploration Mechanismmentioning

confidence: 99%

ABWOA: Adaptive Boundary Whale Optimization Algorithm for Large-Scale Digital Twin Network Construction

Feng,

Cao,

Huang

et al. 2024

Preprint

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Digital twin network (DTN) as an emerging network paradigm, have garnered growing attention. For large-scale networks, a crucial problem is how to effectively map physical networks onto the infrastructure platform of DTN. To address this issue, we propose a heuristic method of the adaptive boundary whale optimization algorithm (ABWOA) to solve the digital twin network construction problem, improving the efficiency and reducing operational costs of DTN. Extensive comparison experiments are conducted between ABWOA and various algorithms such as genetic algorithm, particle swarm optimization, artificial bee colony, differential evolution algorithm, moth search algorithm and original whale optimization algorithm. The experimental results show that ABWOA is superior to other algorithms in terms of solution quality, convergence speed, and time cost. It can solve the digital twin network construction problem more effectively.

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Section: Prey Exploration Mechanismmentioning

confidence: 99%

ABWOA: Adaptive Boundary Whale Optimization Algorithm for Large-Scale Digital Twin Network Construction

Feng,

Cao,

Huang

et al. 2024

Preprint

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“…Once the penalty is calculated, it is added to all objective values for that evaluation. The addition of a strictly positive penalty term to all objectives is a natural extension of the augmented Lagrangian approach for nonlinear programming to the multiobjective case [25].…”

Section: Particle Accelerator Design Optimization With Vtmopmentioning

confidence: 99%

Algorithm 1028: VTMOP: Solver for Blackbox Multiobjective Optimization Problems

Chang

Watson

Larson

et al. 2022

ACM Trans. Math. Softw.

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VTMOP is a Fortran 2008 software package containing two Fortran modules for solving computationally expensive bound-constrained blackbox multiobjective optimization problems. VTMOP implements the algorithm of [32], which handles two or more objectives, does not require any derivatives, and produces well-distributed points over the Pareto front. The first module contains a general framework for solving multiobjective optimization problems by combining response surface methodology, trust region methodology, and an adaptive weighting scheme. The second module features a driver subroutine that implements this framework when the objective functions can be wrapped as a Fortran subroutine. Support is provided for both serial and parallel execution paradigms, and VTMOP is demonstrated on several test problems as well as one real-world problem in the area of particle accelerator optimization.

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“…Finally, we introduce a relaxation of Pareto stationarity, recalling the ε-Pareto-stationarity concept introduced in [8].…”

Section: Preliminariesmentioning

confidence: 99%

“…The other family of methods is that of MO descent methods (either first-order, second-order and derivative-free) [6,8,16,20,21,26,27]. These methods mimic classical iterative scalar optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

A Memetic Procedure for Global Multi-Objective Optimization

Lapucci¹,

Mansueto²,

Schoen³

2022

Preprint

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In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm (NSMA), besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions.

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An augmented Lagrangian algorithm for multi-objective optimization

Cited by 23 publications

References 49 publications

ABWOA: Adaptive Boundary Whale Optimization Algorithm for Large-Scale Digital Twin Network Construction

ABWOA: Adaptive Boundary Whale Optimization Algorithm for Large-Scale Digital Twin Network Construction

Algorithm 1028: VTMOP: Solver for Blackbox Multiobjective Optimization Problems

A Memetic Procedure for Global Multi-Objective Optimization

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