On the exactness of the ε-constraint method for biobjective nonlinear integer programming

Santis, Marianna De; Eichfelder, Gabriele; Patria, Daniele

doi:10.1016/j.orl.2022.04.007

Cited by 11 publications

(2 citation statements)

References 23 publications

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“…The ε − constraint method simplifies the problem by retaining only one primary objective function and transforming the remaining objective functions into constraints (Mavrotas, 2009;De Santis et al, 2022); moreover, this method has been widely used in the solution of multi-objective models (Biswas et al, 2018;Fathipour and Saidi-Mehrabad, 2018). Compared with the weighted method, the ε − constraint method has a smaller search range and better performance in efficiently finding the Pareto front solution.…”

Section: ε − Constraint Methodsmentioning

confidence: 99%

A multi-objective optimization model for the coordinated operation of hydropower and renewable energy

et al. 2023

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The rapid growth of wind and solar energy sources in recent years has brought challenges to power systems. One challenge is surging wind and solar electric generation, understanding how to consume such generation is important. Achieving the complementarity of hydropower and renewable energies such as wind and solar power by utilizing the flexible regulation performance of hydropower is helpful to provide firm power to help renewable energy consumption. However, the multi-energy complementary operation mode will change the traditional hydropower operation mode, causing challenges to the comprehensive utilization of hydropower. In this paper, a multi-objective optimal scheduling model is built by considering coordinated hydro-wind-solar system peak shaving and downstream navigation. First, the Gaussian mixture model is adopted to quantify the uncertainty of wind and solar power. Then, a hydro-wind-solar coordinated model was built to obtain the standard deviation of the residual load and the standard deviation of the downstream water level. Finally, the ε-constraint method is used to solve for the Pareto optimality. The results demonstrate the following: 1) The proposed model can effectively determine hydropower output schemes that can coordinate wind and solar power output to reconcile peak shaving and navigation; 2) The downstream hydropower stations’ reverse regulation of the upstream hydropower station is a positive factor in reconciling conflicts; and 3) Reasonable planning of wind power and solar power is helpful for hydro-wind solar power complement operation.

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Section: ε − Constraint Methodsmentioning

confidence: 99%

A multi-objective optimization model for the coordinated operation of hydropower and renewable energy

et al. 2023

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“…A possibility for the determination of a lower bound I of I is to use the finite cardinality of the set X I = [l I , u I ] ∩ Z m . Moreover, to ensure that I > 0 p and thus I ≤ I can be chosen such that I > 0 p we can use the following property introduced and examined in De Santis et al (2022.…”

Section: A Test Instance Generator For Multiobjective Mixed-integer O...mentioning

confidence: 99%

A test instance generator for multiobjective mixed-integer optimization

2023

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Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When developing and improving algorithms which hopefully allow to handle those difficulties in the future, good test instances are required. These can then be used to detect the strengths and weaknesses of different algorithmic approaches. In this paper we present a generator for test instances to evaluate solvers for multiobjective mixed-integer linear and nonlinear optimization problems. Based on test instances for purely continuous and purely integer problems with known efficient solutions and known nondominated points, suitable multiobjective mixed-integer test instances can be generated. The special structure allows to construct instances scalable in the number of variables and objective functions. Moreover, it allows to control the resulting efficient and nondominated sets as well as the number of efficient integer assignments.

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Optimising the Order Picking Process: The Case of a Retail Distribution Company in Italy

Di Puglia Pugliese,

Guerriero,

Macrina

et al. 2023

AIRO Springer Series

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On the exactness of the ε-constraint method for biobjective nonlinear integer programming

Cited by 11 publications

References 23 publications

A multi-objective optimization model for the coordinated operation of hydropower and renewable energy

A multi-objective optimization model for the coordinated operation of hydropower and renewable energy

A test instance generator for multiobjective mixed-integer optimization

Optimising the Order Picking Process: The Case of a Retail Distribution Company in Italy

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