An exact algorithm for biobjective mixed integer linear programming problems

Soylu, Banu; Yıldız, Gazi Bilal

doi:10.1016/j.cor.2016.03.001

Cited by 40 publications

(27 citation statements)

References 21 publications

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“…Several other solution techniques for bi-objective mixedinteger optimization problems also exist; [44] presents one based on the -Tabu-constraint method and also provides a review of several others.…”

Section: Sampling the Pareto Frontiermentioning

confidence: 99%

Planning Low-Carbon Campus Energy Hubs

Olsen

Zhang

Chen

et al. 2019

IEEE Trans. Power Syst.

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Multi-energy systems can provide a constant level of service to end-use energy demands, while deriving delivered energy from a variety of primary/secondary energy sources. This fuel-switching capability can be used to reduce operating expenses, reduce environmental impacts, improve flexibility to accommodate renewable energy, and improve reliability.This paper presents four frameworks for incentivizing energy hub equipment investments for low-carbon operation targets. These frameworks vary in the measures taken to achieve lowcarbon operation (explicit constraint vs. carbon pricing) and in the relationship between the hub builder and operator (cooperative vs. uncoordinated). The underlying energy hub model upon which these frameworks are built is an enhanced greenfield model, introducing 'energy buses' to reduce dimensionality.A case study is conducted for a campus being designed in Beijing, and results from each framework are compared to illustrate their relative costs. When the operator cannot be trusted to cooperate in controlling emissions, the system must be 'overbuilt' with more expensive equipment to ensure emissions target are met. A taxation-based approach increases overall costs at moderate emissions targets, but this effect decreases at aggressive targets. This paper also compares the cost of less efficient institutional frameworks with the most efficient approach, i.e. cooperation between builder and operator with constraints on emissions.

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Section: Sampling the Pareto Frontiermentioning

confidence: 99%

Planning Low-Carbon Campus Energy Hubs

Olsen

Zhang

Chen

et al. 2019

IEEE Trans. Power Syst.

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“…al. [1] introduce the notion of a "slice" of a MOMIP, which is also used in an exact bi-objective algorithm [8]. Given a MOMIP where X = Z n ×R m , a "slice" of this problem is created by fixing the variables (x 1 , x 2 , .…”

Section: Optimisation Backgroundmentioning

confidence: 99%

“…The algorithm used for this phase is a modification of MOIP_AIRA [7] with Hamming constraint and slices [8]. Following MOIP_AIRA, as each solution point p is found, we use Benson's algorithm [4] to find all polytopes which are optimal in the given slice and contain p. Hamming constraints are then added to the problem to avoid the slice containing p (and thus avoid detecting the same polytope again).…”

Section: Phase 1: Collecting the Piecesmentioning

confidence: 99%

“…discuss this in Section 3.1 of their paper [9], and give an explicit algorithm to find all non-dominated solutions to bi-objective mixed-integer linear programs (BOMBLPs). Further work on the bi-objective algorithms include a local branchand-bound algorithm [1] and an exact bi-objective algorithm based on the ε-and Tabu-constraint methods [8].…”

Section: Introductionmentioning

confidence: 99%

“…Our new algorithm utilises existing multi-objective integer programming (MOIP) techniques, combined with slices [1] and Hamming constraints [8], to recursively build up a set which contains the complete non-dominated set of solutions. We then use techniques similar to those from [9], but generalised to arbitrary dimensionality, to reduce this set to the exact set of non-dominated solutions.…”

Section: Introductionmentioning

confidence: 99%

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Multi-objective mixed integer programming: An objective space algorithm

Pettersson¹,

Özlen²

2019

AIP Conference Proceedings

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This paper introduces the first objective space algorithm which can exactly find all supported and non-supported non-dominated solutions to a mixed-integer multi-objective linear program with an arbitrary number of objective functions. This algorithm is presented in three phases. First it builds up a super-set which contains the Pareto front. This super-set is then modified to not contain any intersecting polytopes. Once this is achieved, the algorithm efficiently calculates which portions of the super-set are not part of the Pareto front and removes them, leaving exactly the Pareto front.

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Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

Halffmann

Schäfer

Dächert

et al. 2022

Multi Criteria Decision Anal

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We provide a comprehensive overview of the literature of algorithmic approaches for multiobjective mixed-integer and integer linear optimization problems. More precisely, we categorize and display exact methods for multiobjective linear problems with integer variables for computing the entire set of nondominated images. Our review lists 108 articles and is intended to serve as a reference for all researchers who are familiar with basic concepts of multiobjective optimization and who have an interest in getting a thorough view on the state-of-the-art in multiobjective mixedinteger programming.

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An exact algorithm for biobjective mixed integer linear programming problems

Cited by 40 publications

References 21 publications

Planning Low-Carbon Campus Energy Hubs

Planning Low-Carbon Campus Energy Hubs

Multi-objective mixed integer programming: An objective space algorithm

Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

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