A new perspective on multiobjective optimization by enhanced normalized normal constraint method

Sanchis, Javier; Martínez, M.; Blasco, X.; Salcedo, J. V.

doi:10.1007/s00158-007-0185-4

Cited by 68 publications

(46 citation statements)

References 14 publications

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“…The generalization and application of the weighted sum and normal boundary intersection methods to optimization problems with more than 2 objectives is straightforward (Marler and Arora 2004;Das and Dennis 1998). On the other hand, the normalized normal constraint method has to be modified in order to properly handle more than 2 objectives and the enhanced normalized normal constraint method of Sanchis et al (2008) can be used.…”

Section: Case Studymentioning

confidence: 99%

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Pecci

Abraham

Stoianov

2016

Struct Multidisc Optim

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In this paper, we study the multiobjective codesign problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.

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Section: Case Studymentioning

confidence: 99%

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Pecci

Abraham

Stoianov

2016

Struct Multidisc Optim

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“…Some of the classical strategies to approximate the Pareto set include: normal constraint method [32,33], normal boundary intersection (NBI) method [34], epsilon constraint techniques [28] and physical programming [35]. Multi-objective evolutionary algorithms (MOEA) have been used to approximate a Pareto set [36], due to their flexibility when evolving an entire population towards the Pareto front.…”

Section: Multi-objective Optimization Processmentioning

confidence: 99%

Multi-Objective Optimization for Wind Estimation and Aircraft Model Identification

Velasco-Carrau

García-Nieto

Salcedo

et al. 2016

Journal of Guidance, Control, and Dynamics

Self Cite

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In this paper, a novel method for aerodynamic model identification of a micro-air vehicle is proposed. The principal contribution is a technique of wind estimation that provides information about the existing wind during flight when no air-data sensors are available. The estimation technique employs multi-objective optimization algorithms that utilize identification errors to propose the wind-speed components that best fit the dynamic behavior observed. Once the wind speed is estimated, the flight experimentation data are corrected and utilized to perform an identification of the aircraft model parameters. A multi-objective optimization algorithm is also used, but with the objective of estimating the aerodynamic stability and control derivatives. Employing data from different flights offers the possibility of obtaining sets of models that form the Pareto fronts. Deciding which model best adjusts to the experiments performed (compromise model) will be the ultimate task of the control engineer.

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“…The tri-objective portfolio Problems (15) and (17) will be tackled by considering this extended version of the NC procedure, even if other more efficient solutions are possible (see, for instance, [47][48][49]), because these improvements necessitate much more modifications to the original optimization scheme.…”

Section: A New Variant Of the Normal Constraint Algorithmmentioning

confidence: 99%

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Kaucic¹,

Daris²

2015

Risks

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In the paper, we introduce a multi-objective scenario-based optimization approach for chance-constrained portfolio selection problems. More specifically, a modified version of the normal constraint method is implemented with a global solver in order to generate a dotted approximation of the Pareto frontier for bi-and tri-objective programming problems. Numerical experiments are carried out on a set of portfolios to be optimized for an EU-based non-life insurance company. Both performance indicators and risk measures are managed as objectives. Results show that this procedure is effective and readily applicable to achieve suitable risk-reward tradeoff analysis.

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A new perspective on multiobjective optimization by enhanced normalized normal constraint method

Cited by 68 publications

References 14 publications

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Multi-Objective Optimization for Wind Estimation and Aircraft Model Identification

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

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